(1) 소스 코드 학 알고리즘: scikit - learn 라 이브 러 리 코드 예제 학 기계 학습 알고리즘 (총)
165611 단어 소스 코드 에서 알고리즘 까지
막 전업 하거나 새로 입문 한 기계 학습 학생 에 게 알고리즘 은 코드 의 골격 으로서 가장 핵심 적 이 고 튼튼한 부분 이 며 의심 할 여지없이 가장 관심 을 가지 고 가장 긴박 한 일이 다.일반적인 학습 알고리즘 의 사고방식 은 선생님 이 먼저 데이터 구 조 를 강의 한 다음 에 알고리즘 을 설명 한 다음 에 코드 예 시 를 통 해 설명 하 는 것 이다. 이렇게 하 는 장점 은 명백히 알 수 있 고 알고리즘 은 더욱 철저하게 배 울 수 있다.그러나 단기 적 으로 코드 능력 을 실현 하려 면 codingCapicity 는 시간 이 많이 걸 리 고 알고리즘 이 정교 하 며 코드 가 실현 되 기 어렵다. 본 고 는 scikit - learn 깊이 학습 라 이브 러 리 의 코드 예시 학습 을 통 해 조금 만 분석 하면 표리, 얕 은 것 에서 깊 은 것 으로 들 어가 코드 의 실질 - 알고리즘 을 깊이 이해 하고 속효 학습, 능력 에 한계 가 있다.잘못된 점 은 불가피 하 니 비판 과 시정 을 바 랍 니 다.
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Scikit - learn requires: Python (> = 2.7 or > = 3.3), NumPy (> = 1.8.2), Scipy (> = 0.13.3). pip install - U scikit - learn 또는 conda install scikit - learn 을 통 해 설치 빠 른 입문 scikit - learn 기계 학습 을 할 수 있 습 니 다.http://scikit-learn.org/stable/tutorial/basic/tutorial.html
1. 머 신 러 닝: 문제 설정 - CSDN 블 로그https://blog.csdn.net/hanyun9988/article/details/78992578
일반적으로 하나의 학습 문 제 는 이미 알 고 있 는 n 개의 견본 의 데이터 세트 가 알 수 없 는 데이터 의 성질 을 어떻게 예측 하 는 지 를 말한다.감독 학습 (Supervised learning) (분류 알고리즘, 회귀 알고리즘 등 포함), 무 감독 학습 (Unsupervised learning) (집합 알고리즘, 밀도 추정 알고리즘 등 포함) [그리고 반 감독 학습 및 강화 학습] 으로 나 뉜 다.다시 말 하면 기계 학습 은 이미 알 고 있 는 예측 을 통 해 알 수 없 는 알고리즘 을 찾 는 것 이다. 데이터 세트 에 대해 이미 알 고 있 는 샘플 집합 을 훈련 집합 이 라 고 하고 예측 하고 자 하 는 데이터 세트 를 테스트 집합 이 라 고 할 수 있다.
2. 샘플 데이터 세트 다운로드:
scikit - learn 에는 외부 에서 파일 을 다운로드 하지 않 고 작은 표준 인형 데이터 세트 가 많이 내장 되 어 있 습 니 다.이 다운로드 함수 들 은 loadboston([return_X_y]) Load and return the boston house-prices dataset (regression). load_iris([return_X_y]) Load and return the iris dataset (classification). load_diabetes([return_X_y]) Load and return the diabetes dataset (regression). load_digits([n_class, return_X_y]) Load and return the digits dataset (classification). load_linnerud([return_X_y]) Load and return the linnerud dataset (multivariate regression). load_wine([return_X_y]) Load and return the wine dataset (classification). load_breast_cancer ([return X y]) Load and return the breast cancer wisconsin dataset (classification). 이 데이터 세트 는 매우 유용 하 며, scikit 가 실현 하 는 여러 알고리즘 의 행동 방식 을 빠르게 알 수 있다.다음은 아이 리 스 플 라 워 데이터 세트 와 digits 손 으로 쓴 디지털 데이터 세트 를 예 로 들 어 분류 알고리즘 을 배 울 것 이다.python Python 3.6.6，scikit-learn v0.19.2，numpy1.15.1
>>> from sklearn import datasets
>>> iris = datasets.load_iris()
>>> digits = datasets.load_digits()데이터 세트 는 사전 모양 의 대상 으로 모든 데이터 와 데 이 터 를 포함 하 는 메타 데 이 터 를 가지 고 있다.이 인형 데이터 세트 의 다운로드 함 수 는 원 그룹 (X, y) 을 되 돌려 줍 니 다. X 는 데 이 터 를. data 구성원 에 저장 합 니 다. n 입 니 다.samples*n_features 의 배열, m 목표 치 y 는 길이 nsamples 의 배열 은 변 수 를 'target 멤버' 에 저장 합 니 다.GitHub 의 소스 코드 를 보면 iris 와 digits 데이터 세트 가 모두 CSV 파일 임 을 알 수 있다.https://github.com/scikit-learn/scikit-learn/tree/master/sklearn/datasets/data
`>>>print(digits.data)
[[ 0. 0. 5. ..., 0. 0. 0.]
[ 0. 0. 0. ..., 10. 0. 0.]
[ 0. 0. 0. ..., 16. 9. 0.]
...,
[ 0. 0. 1. ..., 6. 0. 0.]
[ 0. 0. 2. ..., 12. 0. 0.]
[ 0. 0. 10. ..., 12. 1. 0.]]``>>> digits.target
array([0, 1, 2, ..., 8, 9, 8])`아이 리 스 의 데 이 터 는 크기 가 n 이다.samples*n_features 의 배열.디지털 식별 사례 에서 모든 원시 견본 은 크기 가 8 * 8 인 그림 이다.
`>>> digits.images[0]
array([[ 0., 0., 5., 13., 9., 1., 0., 0.],
[ 0., 0., 13., 15., 10., 15., 5., 0.],
[ 0., 3., 15., 2., 0., 11., 8., 0.],
[ 0., 4., 12., 0., 0., 8., 8., 0.],
[ 0., 5., 8., 0., 0., 9., 8., 0.],
[ 0., 4., 11., 0., 1., 12., 7., 0.],
[ 0., 2., 14., 5., 10., 12., 0., 0.],
[ 0., 0., 6., 13., 10., 0., 0., 0.]])`3. 학습 과 예측
scikit - learn 에서 분 류 는 Python 대상 으로 fit (X, y) 와 predict (T) 를 통 해 이 루어 질 것 이 라 고 예측 했다.그 중 하 나 는 sklearn. svm. SVC 로 벡터 분 류 를 지원 합 니 다.이 예측 기의 알고리즘 메커니즘 은 벡터 기 를 지원 하 는데, 이 는 블랙박스 인터페이스 로 봉 인 됩 니 다
>>> from sklearn import svm
>>> clf = svm.SVC(gamma=0.001, C=100.)모델 매개 변수 선택
위 에 gamma 의 값 을 설정 할 수도 있 고, grid search 와 cross validation 도구 와 같은 도 구 를 통 해 자동 으로 좋 은 매개 변 수 를 찾 을 수도 있 습 니 다.예측 기의 인 스 턴 스 clf 도 분류 기 입 니 다. 모형 을 고정 시 키 고 배 워 야 합 니 다.fit 방법 으로 구현 가능 합 니 다.
>>> clf.fit(digits.data[:-1], digits.target[:-1])
SVC(C=100.0, cache_size=200, class_weight=None, coef0=0.0,
decision_function_shape='ovr', degree=3, gamma=0.001, kernel='rbf',
max_iter=-1, probability=False, random_state=None, shrinking=True,
tol=0.001, verbose=False)
， digits ， 。
>>> clf.predict(digits.data[-1:])
array([8])
###4.
Python pickle 。
>>> from sklearn import svm
>>> from sklearn import datasets
>>> clf = svm.SVC()
>>> iris = datasets.load_iris()
>>> X, y = iris.data, iris.target
>>> clf.fit(X, y)
SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0,
decision_function_shape='ovr', degree=3, gamma='auto', kernel='rbf',
max_iter=-1, probability=False, random_state=None, shrinking=True,
tol=0.001, verbose=False)
>>> import pickle
>>> s = pickle.dumps(clf)
>>> clf2 = pickle.loads(s)
>>> clf2.predict(X[0:1])
array([0])
>>> y[0]특수 한 상황 에서 우 리 는 피 클 대신 joblib. dump & joblib. load 를 사용 할 수 있 습 니 다. 전 자 는 빅 데이터 에 더 효과 적 이 고 후 자 는 문자열 작업 이 아 닌 하 드 디스크 에 만 저장 할 수 있 기 때 문 입 니 다.joblib. dump & joblib. load 도 파일 이름 대신 파일 대상 을 받 아들 입 니 다.
>>> from sklearn.externals import joblib
>>> joblib.dump(clf, 'filename.pkl') >>> clf = joblib.load('filename.pkl')5. 규칙
5.1 형식 변환
특별한 상황 이 없 을 때 float 64 형식 으로 입력 하 십시오:
>>> import numpy as np
>>> from sklearn import random_projection
>>> rng = np.random.RandomState(0)
>>> X = rng.rand(10, 2000)
>>> X = np.array(X, dtype='float32')
>>> X.dtype
dtype('float32')
>>> transformer = random_projection.GaussianRandomProjection()
>>> X_new = transformer.fit_transform(X)
>>> X_new.dtype
dtype('float64')상례 에서 X 는 float 32, fittransform (X) 을 float 64 로 변환 합 니 다.회귀 분석의 목표 데 이 터 는 float 64 로 전환 해 야 하 며 분류 목표 데 이 터 는 변 하지 않 을 수 있 습 니 다.
>>> from sklearn import datasets
>>> from sklearn.svm import SVC
>>> iris = datasets.load_iris()
>>> clf = SVC()
>>> clf.fit(iris.data, iris.target)
SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0,
decision_function_shape='ovr', degree=3, gamma='auto', kernel='rbf',
max_iter=-1, probability=False, random_state=None, shrinking=True,
tol=0.001, verbose=False)
>>> list(clf.predict(iris.data[:3]))
[0, 0, 0]
>>> clf.fit(iris.data, iris.target_names[iris.target])
SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0,
decision_function_shape='ovr', degree=3, gamma='auto', kernel='rbf',
max_iter=-1, probability=False, random_state=None, shrinking=True,
tol=0.001, verbose=False)
>>> list(clf.predict(iris.data[:3]))
['setosa', 'setosa', 'setosa']5.2 매개 변수 재 설정 및 업데이트
>>> import numpy as np
>>> from sklearn.svm import SVC
>>> rng = np.random.RandomState(0)
>>> X = rng.rand(100, 10)
>>> y = rng.binomial(1, 0.5, 100)
>>> X_test = rng.rand(5, 10)
>>> clf = SVC()
>>> clf.set_params(kernel='linear').fit(X, y)
SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0,
decision_function_shape='ovr', degree=3, gamma='auto', kernel='linear',
max_iter=-1, probability=False, random_state=None, shrinking=True,
tol=0.001, verbose=False)
>>> clf.predict(X_test)
array([1, 0, 1, 1, 0])
>>> clf.set_params(kernel='rbf').fit(X, y)
SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0,
decision_function_shape='ovr', degree=3, gamma='auto', kernel='rbf',
max_iter=-1, probability=False, random_state=None, shrinking=True,
tol=0.001, verbose=False)
>>> clf.predict(X_test)
array([0, 0, 0, 1, 0])5.3 여러 종류 와 다 중 태그
>>> from sklearn.svm import SVC
>>> from sklearn.multiclass import OneVsRestClassifier
>>> from sklearn.preprocessing import LabelBinarizer
>>> X = [[1, 2], [2, 4], [4, 5], [3, 2], [3, 1]]
>>> y = [0, 0, 1, 1, 2]
>>> classif = OneVsRestClassifier(estimator=SVC(random_state=0))
>>> classif.fit(X, y).predict(X)
array([0, 0, 1, 1, 2])
>>> y = LabelBinarizer().fit_transform(y)
>>> classif.fit(X, y).predict(X)
array([[1, 0, 0],
[1, 0, 0],
[0, 1, 0],
[0, 0, 0],
[0, 0, 0]])
>> from sklearn.preprocessing import MultiLabelBinarizer
>> y = [[0, 1], [0, 2], [1, 3], [0, 2, 3], [2, 4]]
>> y = MultiLabelBinarizer().fit_transform(y)
>> classif.fit(X, y).predict(X)
array([[1, 1, 0, 0, 0],
[1, 0, 1, 0, 0],
[0, 1, 0, 1, 0],
[1, 0, 1, 1, 0],
[0, 0, 1, 0, 1]])GitHub - sickit - learn: SVM 부분 소스 코드 감상 분석:
https://github.com/scikit-learn/scikit-learn scikit-learn/sklearn/svm/init.py “”” The :mod:
sklearn.svm module includes Support Vector Machine algorithms. “”“ # See http://scikit-learn.sourceforge.net/modules/svm.html for complete
# documentation.
# Author: Fabian Pedregosa with help from
# the scikit-learn community. LibSVM and LibLinear are copyright
# of their respective owners.
# License: BSD 3 clause (C) INRIA 2010from .classes import SVC, NuSVC, SVR, NuSVR, OneClassSVM, LinearSVC, \
LinearSVR
from .bounds import l1_min_c
from . import libsvm, liblinear, libsvm_sparse
__all__ = ['LinearSVC',
'LinearSVR',
'NuSVC',
'NuSVR',
'OneClassSVM',
'SVC',
'SVR',
'l1_min_c',
'liblinear',
'libsvm',
'libsvm_sparse']scikit-learn/sklearn/svm/setup.py
import os
from os.path import join
import numpy
from sklearn._build_utils import get_blas_info
def configuration(parent_package='', top_path=None):
from numpy.distutils.misc_util import Configuration
config = Configuration('svm', parent_package, top_path)
config.add_subpackage('tests')
# Section LibSVM
# we compile both libsvm and libsvm_sparse
config.add_library('libsvm-skl',
sources=[join('src', 'libsvm', 'libsvm_template.cpp')],
depends=[join('src', 'libsvm', 'svm.cpp'),
join('src', 'libsvm', 'svm.h')],
# Force C++ linking in case gcc is picked up instead
# of g++ under windows with some versions of MinGW
extra_link_args=['-lstdc++'],
)
libsvm_sources = ['libsvm.pyx']
libsvm_depends = [join('src', 'libsvm', 'libsvm_helper.c'),
join('src', 'libsvm', 'libsvm_template.cpp'),
join('src', 'libsvm', 'svm.cpp'),
join('src', 'libsvm', 'svm.h')]
config.add_extension('libsvm',
sources=libsvm_sources,
include_dirs=[numpy.get_include(),
join('src', 'libsvm')],
libraries=['libsvm-skl'],
depends=libsvm_depends,
)
# liblinear module
cblas_libs, blas_info = get_blas_info()
if os.name == 'posix':
cblas_libs.append('m')
liblinear_sources = ['liblinear.pyx',
join('src', 'liblinear', '*.cpp')]
liblinear_depends = [join('src', 'liblinear', '*.h'),
join('src', 'liblinear', 'liblinear_helper.c')]
config.add_extension('liblinear',
sources=liblinear_sources,
libraries=cblas_libs,
include_dirs=[join('..', 'src', 'cblas'),
numpy.get_include(),
blas_info.pop('include_dirs', [])],
extra_compile_args=blas_info.pop('extra_compile_args',
[]),
depends=liblinear_depends,
# extra_compile_args=['-O0 -fno-inline'],
** blas_info)
# end liblinear module
# this should go *after* libsvm-skl
libsvm_sparse_sources = ['libsvm_sparse.pyx']
config.add_extension('libsvm_sparse', libraries=['libsvm-skl'],
sources=libsvm_sparse_sources,
include_dirs=[numpy.get_include(),
join("src", "libsvm")],
depends=[join("src", "libsvm", "svm.h"),
join("src", "libsvm",
"libsvm_sparse_helper.c")])
return config
if __name__ == '__main__':
from numpy.distutils.core import setup
setup(**configuration(top_path='').todict())설정 함수 의 최상 위 경 로 를 사전 에 넣 고 setup () scikit - learn / sklearn / svm / base. py 에 여러 매개 변 수 를 전달 합 니 다.
from __future__ import print_function
import numpy as np
import scipy.sparse as sp
import warnings
from abc import ABCMeta, abstractmethod
from . import libsvm, liblinear
from . import libsvm_sparse
from ..base import BaseEstimator, ClassifierMixin
from ..preprocessing import LabelEncoder
from ..utils.multiclass import _ovr_decision_function
from ..utils import check_array, check_consistent_length, check_random_state
from ..utils import column_or_1d, check_X_y
from ..utils import compute_class_weight
from ..utils.extmath import safe_sparse_dot
from ..utils.validation import check_is_fitted, _check_large_sparse
from ..utils.multiclass import check_classification_targets
from ..externals import six
from ..exceptions import ConvergenceWarning
from ..exceptions import NotFittedError
LIBSVM_IMPL = ['c_svc', 'nu_svc', 'one_class', 'epsilon_svr', 'nu_svr']
def _one_vs_one_coef(dual_coef, n_support, support_vectors):
"""Generate primal coefficients from dual coefficients
for the one-vs-one multi class LibSVM in the case
of a linear kernel."""
# get 1vs1 weights for all n*(n-1) classifiers.
# this is somewhat messy.
# shape of dual_coef_ is nSV * (n_classes -1)
# see docs for details
n_class = dual_coef.shape[0] + 1
# XXX we could do preallocation of coef but
# would have to take care in the sparse case
coef = []
sv_locs = np.cumsum(np.hstack([[0], n_support]))
for class1 in range(n_class):
# SVs for class1:
sv1 = support_vectors[sv_locs[class1]:sv_locs[class1 + 1], :]
for class2 in range(class1 + 1, n_class):
# SVs for class1:
sv2 = support_vectors[sv_locs[class2]:sv_locs[class2 + 1], :]
# dual coef for class1 SVs:
alpha1 = dual_coef[class2 - 1, sv_locs[class1]:sv_locs[class1 + 1]]
# dual coef for class2 SVs:
alpha2 = dual_coef[class1, sv_locs[class2]:sv_locs[class2 + 1]]
# build weight for class1 vs class2
coef.append(safe_sparse_dot(alpha1, sv1)
+ safe_sparse_dot(alpha2, sv2))
return coef
class BaseLibSVM(six.with_metaclass(ABCMeta, BaseEstimator)):
"""Base class for estimators that use libsvm as backing library
This implements support vector machine classification and regression.
Parameter documentation is in the derived `SVC` class.
"""
# The order of these must match the integer values in LibSVM.
# XXX These are actually the same in the dense case. Need to factor
# this out.
_sparse_kernels = ["linear", "poly", "rbf", "sigmoid", "precomputed"]
@abstractmethod
def __init__(self, kernel, degree, gamma, coef0,
tol, C, nu, epsilon, shrinking, probability, cache_size,
class_weight, verbose, max_iter, random_state):
if self._impl not in LIBSVM_IMPL: # pragma: no cover
raise ValueError("impl should be one of %s, %s was given" % (
LIBSVM_IMPL, self._impl))
if gamma == 0:
msg = ("The gamma value of 0.0 is invalid. Use 'auto' to set"
" gamma to a value of 1 / n_features.")
raise ValueError(msg)
self.kernel = kernel
self.degree = degree
self.gamma = gamma
self.coef0 = coef0
self.tol = tol
self.C = C
self.nu = nu
self.epsilon = epsilon
self.shrinking = shrinking
self.probability = probability
self.cache_size = cache_size
self.class_weight = class_weight
self.verbose = verbose
self.max_iter = max_iter
self.random_state = random_state
@property
def _pairwise(self):
# Used by cross_val_score.
return self.kernel == "precomputed"
def fit(self, X, y, sample_weight=None):
"""Fit the SVM model according to the given training data.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Training vectors, where n_samples is the number of samples
and n_features is the number of features.
For kernel="precomputed", the expected shape of X is
(n_samples, n_samples).
y : array-like, shape (n_samples,)
Target values (class labels in classification, real numbers in
regression)
sample_weight : array-like, shape (n_samples,)
Per-sample weights. Rescale C per sample. Higher weights
force the classifier to put more emphasis on these points.
Returns
-------
self : object
Notes
------
If X and y are not C-ordered and contiguous arrays of np.float64 and
X is not a scipy.sparse.csr_matrix, X and/or y may be copied.
If X is a dense array, then the other methods will not support sparse
matrices as input.
"""
rnd = check_random_state(self.random_state)
sparse = sp.isspmatrix(X)
if sparse and self.kernel == "precomputed":
raise TypeError("Sparse precomputed kernels are not supported.")
self._sparse = sparse and not callable(self.kernel)
X, y = check_X_y(X, y, dtype=np.float64,
order='C', accept_sparse='csr',
accept_large_sparse=False)
y = self._validate_targets(y)
sample_weight = np.asarray([]
if sample_weight is None
else sample_weight, dtype=np.float64)
solver_type = LIBSVM_IMPL.index(self._impl)
# input validation
if solver_type != 2 and X.shape[0] != y.shape[0]:
raise ValueError("X and y have incompatible shapes.
" +
"X has %s samples, but y has %s." %
(X.shape[0], y.shape[0]))
if self.kernel == "precomputed" and X.shape[0] != X.shape[1]:
raise ValueError("X.shape[0] should be equal to X.shape[1]")
if sample_weight.shape[0] > 0 and sample_weight.shape[0] != X.shape[0]:
raise ValueError("sample_weight and X have incompatible shapes: "
"%r vs %r
"
"Note: Sparse matrices cannot be indexed w/"
"boolean masks (use `indices=True` in CV)."
% (sample_weight.shape, X.shape))
if self.gamma in ('scale', 'auto_deprecated'):
if sparse:
# std = sqrt(E[X^2] - E[X]^2)
X_std = np.sqrt((X.multiply(X)).mean() - (X.mean())**2)
else:
X_std = X.std()
if self.gamma == 'scale':
if X_std != 0:
self._gamma = 1.0 / (X.shape[1] * X_std)
else:
self._gamma = 1.0
else:
kernel_uses_gamma = (not callable(self.kernel) and self.kernel
not in ('linear', 'precomputed'))
if kernel_uses_gamma and not np.isclose(X_std, 1.0):
# NOTE: when deprecation ends we need to remove explicitly
# setting `gamma` in examples (also in tests). See
# https://github.com/scikit-learn/scikit-learn/pull/10331
# for the examples/tests that need to be reverted.
warnings.warn("The default value of gamma will change "
"from 'auto' to 'scale' in version 0.22 to "
"account better for unscaled features. Set "
"gamma explicitly to 'auto' or 'scale' to "
"avoid this warning.", FutureWarning)
self._gamma = 1.0 / X.shape[1]
elif self.gamma == 'auto':
self._gamma = 1.0 / X.shape[1]
else:
self._gamma = self.gamma
kernel = self.kernel
if callable(kernel):
kernel = 'precomputed'
fit = self._sparse_fit if self._sparse else self._dense_fit
if self.verbose: # pragma: no cover
print('[LibSVM]', end='')
seed = rnd.randint(np.iinfo('i').max)
fit(X, y, sample_weight, solver_type, kernel, random_seed=seed)
# see comment on the other call to np.iinfo in this file
self.shape_fit_ = X.shape
# In binary case, we need to flip the sign of coef, intercept and
# decision function. Use self._intercept_ and self._dual_coef_
# internally.
self._intercept_ = self.intercept_.copy()
self._dual_coef_ = self.dual_coef_
if self._impl in ['c_svc', 'nu_svc'] and len(self.classes_) == 2:
self.intercept_ *= -1
self.dual_coef_ = -self.dual_coef_
return self
def _validate_targets(self, y):
"""Validation of y and class_weight.
Default implementation for SVR and one-class; overridden in BaseSVC.
"""
# XXX this is ugly.
# Regression models should not have a class_weight_ attribute.
self.class_weight_ = np.empty(0)
return column_or_1d(y, warn=True).astype(np.float64)
def _warn_from_fit_status(self):
assert self.fit_status_ in (0, 1)
if self.fit_status_ == 1:
warnings.warn('Solver terminated early (max_iter=%i).'
' Consider pre-processing your data with'
' StandardScaler or MinMaxScaler.'
% self.max_iter, ConvergenceWarning)
def _dense_fit(self, X, y, sample_weight, solver_type, kernel,
random_seed):
if callable(self.kernel):
# you must store a reference to X to compute the kernel in predict
# TODO: add keyword copy to copy on demand
self.__Xfit = X
X = self._compute_kernel(X)
if X.shape[0] != X.shape[1]:
raise ValueError("X.shape[0] should be equal to X.shape[1]")
libsvm.set_verbosity_wrap(self.verbose)
# we don't pass **self.get_params() to allow subclasses to
# add other parameters to __init__
self.support_, self.support_vectors_, self.n_support_, \
self.dual_coef_, self.intercept_, self.probA_, \
self.probB_, self.fit_status_ = libsvm.fit(
X, y,
svm_type=solver_type, sample_weight=sample_weight,
class_weight=self.class_weight_, kernel=kernel, C=self.C,
nu=self.nu, probability=self.probability, degree=self.degree,
shrinking=self.shrinking, tol=self.tol,
cache_size=self.cache_size, coef0=self.coef0,
gamma=self._gamma, epsilon=self.epsilon,
max_iter=self.max_iter, random_seed=random_seed)
self._warn_from_fit_status()
def _sparse_fit(self, X, y, sample_weight, solver_type, kernel,
random_seed):
X.data = np.asarray(X.data, dtype=np.float64, order='C')
X.sort_indices()
kernel_type = self._sparse_kernels.index(kernel)
libsvm_sparse.set_verbosity_wrap(self.verbose)
self.support_, self.support_vectors_, dual_coef_data, \
self.intercept_, self.n_support_, \
self.probA_, self.probB_, self.fit_status_ = \
libsvm_sparse.libsvm_sparse_train(
X.shape[1], X.data, X.indices, X.indptr, y, solver_type,
kernel_type, self.degree, self._gamma, self.coef0, self.tol,
self.C, self.class_weight_,
sample_weight, self.nu, self.cache_size, self.epsilon,
int(self.shrinking), int(self.probability), self.max_iter,
random_seed)
self._warn_from_fit_status()
if hasattr(self, "classes_"):
n_class = len(self.classes_) - 1
else: # regression
n_class = 1
n_SV = self.support_vectors_.shape[0]
dual_coef_indices = np.tile(np.arange(n_SV), n_class)
dual_coef_indptr = np.arange(0, dual_coef_indices.size + 1,
dual_coef_indices.size / n_class)
self.dual_coef_ = sp.csr_matrix(
(dual_coef_data, dual_coef_indices, dual_coef_indptr),
(n_class, n_SV))
def predict(self, X):
"""Perform regression on samples in X.
For an one-class model, +1 (inlier) or -1 (outlier) is returned.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
For kernel="precomputed", the expected shape of X is
(n_samples_test, n_samples_train).
Returns
-------
y_pred : array, shape (n_samples,)
"""
X = self._validate_for_predict(X)
predict = self._sparse_predict if self._sparse else self._dense_predict
return predict(X)
def _dense_predict(self, X):
n_samples, n_features = X.shape
X = self._compute_kernel(X)
if X.ndim == 1:
X = check_array(X, order='C', accept_large_sparse=False)
kernel = self.kernel
if callable(self.kernel):
kernel = 'precomputed'
if X.shape[1] != self.shape_fit_[0]:
raise ValueError("X.shape[1] = %d should be equal to %d, "
"the number of samples at training time" %
(X.shape[1], self.shape_fit_[0]))
svm_type = LIBSVM_IMPL.index(self._impl)
return libsvm.predict(
X, self.support_, self.support_vectors_, self.n_support_,
self._dual_coef_, self._intercept_,
self.probA_, self.probB_, svm_type=svm_type, kernel=kernel,
degree=self.degree, coef0=self.coef0, gamma=self._gamma,
cache_size=self.cache_size)
def _sparse_predict(self, X):
# Precondition: X is a csr_matrix of dtype np.float64.
kernel = self.kernel
if callable(kernel):
kernel = 'precomputed'
kernel_type = self._sparse_kernels.index(kernel)
C = 0.0 # C is not useful here
return libsvm_sparse.libsvm_sparse_predict(
X.data, X.indices, X.indptr,
self.support_vectors_.data,
self.support_vectors_.indices,
self.support_vectors_.indptr,
self._dual_coef_.data, self._intercept_,
LIBSVM_IMPL.index(self._impl), kernel_type,
self.degree, self._gamma, self.coef0, self.tol,
C, self.class_weight_,
self.nu, self.epsilon, self.shrinking,
self.probability, self.n_support_,
self.probA_, self.probB_)
def _compute_kernel(self, X):
"""Return the data transformed by a callable kernel"""
if callable(self.kernel):
# in the case of precomputed kernel given as a function, we
# have to compute explicitly the kernel matrix
kernel = self.kernel(X, self.__Xfit)
if sp.issparse(kernel):
kernel = kernel.toarray()
X = np.asarray(kernel, dtype=np.float64, order='C')
return X
def _decision_function(self, X):
"""Distance of the samples X to the separating hyperplane.
Parameters
----------
X : array-like, shape (n_samples, n_features)
Returns
-------
X : array-like, shape (n_samples, n_class * (n_class-1) / 2)
Returns the decision function of the sample for each class
in the model.
"""
# NOTE: _validate_for_predict contains check for is_fitted
# hence must be placed before any other attributes are used.
X = self._validate_for_predict(X)
X = self._compute_kernel(X)
if self._sparse:
dec_func = self._sparse_decision_function(X)
else:
dec_func = self._dense_decision_function(X)
# In binary case, we need to flip the sign of coef, intercept and
# decision function.
if self._impl in ['c_svc', 'nu_svc'] and len(self.classes_) == 2:
return -dec_func.ravel()
return dec_func
def _dense_decision_function(self, X):
X = check_array(X, dtype=np.float64, order="C",
accept_large_sparse=False)
kernel = self.kernel
if callable(kernel):
kernel = 'precomputed'
return libsvm.decision_function(
X, self.support_, self.support_vectors_, self.n_support_,
self._dual_coef_, self._intercept_,
self.probA_, self.probB_,
svm_type=LIBSVM_IMPL.index(self._impl),
kernel=kernel, degree=self.degree, cache_size=self.cache_size,
coef0=self.coef0, gamma=self._gamma)
def _sparse_decision_function(self, X):
X.data = np.asarray(X.data, dtype=np.float64, order='C')
kernel = self.kernel
if hasattr(kernel, '__call__'):
kernel = 'precomputed'
kernel_type = self._sparse_kernels.index(kernel)
return libsvm_sparse.libsvm_sparse_decision_function(
X.data, X.indices, X.indptr,
self.support_vectors_.data,
self.support_vectors_.indices,
self.support_vectors_.indptr,
self._dual_coef_.data, self._intercept_,
LIBSVM_IMPL.index(self._impl), kernel_type,
self.degree, self._gamma, self.coef0, self.tol,
self.C, self.class_weight_,
self.nu, self.epsilon, self.shrinking,
self.probability, self.n_support_,
self.probA_, self.probB_)
def _validate_for_predict(self, X):
check_is_fitted(self, 'support_')
X = check_array(X, accept_sparse='csr', dtype=np.float64, order="C",
accept_large_sparse=False)
if self._sparse and not sp.isspmatrix(X):
X = sp.csr_matrix(X)
if self._sparse:
X.sort_indices()
if sp.issparse(X) and not self._sparse and not callable(self.kernel):
raise ValueError(
"cannot use sparse input in %r trained on dense data"
% type(self).__name__)
n_samples, n_features = X.shape
if self.kernel == "precomputed":
if X.shape[1] != self.shape_fit_[0]:
raise ValueError("X.shape[1] = %d should be equal to %d, "
"the number of samples at training time" %
(X.shape[1], self.shape_fit_[0]))
elif n_features != self.shape_fit_[1]:
raise ValueError("X.shape[1] = %d should be equal to %d, "
"the number of features at training time" %
(n_features, self.shape_fit_[1]))
return X
@property
def coef_(self):
if self.kernel != 'linear':
raise AttributeError('coef_ is only available when using a '
'linear kernel')
coef = self._get_coef()
# coef_ being a read-only property, it's better to mark the value as
# immutable to avoid hiding potential bugs for the unsuspecting user.
if sp.issparse(coef):
# sparse matrix do not have global flags
coef.data.flags.writeable = False
else:
# regular dense array
coef.flags.writeable = False
return coef
def _get_coef(self):
return safe_sparse_dot(self._dual_coef_, self.support_vectors_)
class BaseSVC(six.with_metaclass(ABCMeta, BaseLibSVM, ClassifierMixin)):
"""ABC for LibSVM-based classifiers."""
@abstractmethod
def __init__(self, kernel, degree, gamma, coef0, tol, C, nu,
shrinking, probability, cache_size, class_weight, verbose,
max_iter, decision_function_shape, random_state):
self.decision_function_shape = decision_function_shape
super(BaseSVC, self).__init__(
kernel=kernel, degree=degree, gamma=gamma,
coef0=coef0, tol=tol, C=C, nu=nu, epsilon=0., shrinking=shrinking,
probability=probability, cache_size=cache_size,
class_weight=class_weight, verbose=verbose, max_iter=max_iter,
random_state=random_state)
def _validate_targets(self, y):
y_ = column_or_1d(y, warn=True)
check_classification_targets(y)
cls, y = np.unique(y_, return_inverse=True)
self.class_weight_ = compute_class_weight(self.class_weight, cls, y_)
if len(cls) < 2:
raise ValueError(
"The number of classes has to be greater than one; got %d"
" class" % len(cls))
self.classes_ = cls
return np.asarray(y, dtype=np.float64, order='C')
def decision_function(self, X):
"""Distance of the samples X to the separating hyperplane.
Parameters
----------
X : array-like, shape (n_samples, n_features)
Returns
-------
X : array-like, shape (n_samples, n_classes * (n_classes-1) / 2)
Returns the decision function of the sample for each class
in the model.
If decision_function_shape='ovr', the shape is (n_samples,
n_classes)
"""
dec = self._decision_function(X)
if self.decision_function_shape == 'ovr' and len(self.classes_) > 2:
return _ovr_decision_function(dec < 0, -dec, len(self.classes_))
return dec
def predict(self, X):
"""Perform classification on samples in X.
For an one-class model, +1 or -1 is returned.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
For kernel="precomputed", the expected shape of X is
[n_samples_test, n_samples_train]
Returns
-------
y_pred : array, shape (n_samples,)
Class labels for samples in X.
"""
y = super(BaseSVC, self).predict(X)
return self.classes_.take(np.asarray(y, dtype=np.intp))
# Hacky way of getting predict_proba to raise an AttributeError when
# probability=False using properties. Do not use this in new code; when
# probabilities are not available depending on a setting, introduce two
# estimators.
def _check_proba(self):
if not self.probability:
raise AttributeError("predict_proba is not available when "
" probability=False")
if self._impl not in ('c_svc', 'nu_svc'):
raise AttributeError("predict_proba only implemented for SVC"
" and NuSVC")
@property
def predict_proba(self):
"""Compute probabilities of possible outcomes for samples in X.
The model need to have probability information computed at training
time: fit with attribute `probability` set to True.
Parameters
----------
X : array-like, shape (n_samples, n_features)
For kernel="precomputed", the expected shape of X is
[n_samples_test, n_samples_train]
Returns
-------
T : array-like, shape (n_samples, n_classes)
Returns the probability of the sample for each class in
the model. The columns correspond to the classes in sorted
order, as they appear in the attribute `classes_`.
Notes
-----
The probability model is created using cross validation, so
the results can be slightly different than those obtained by
predict. Also, it will produce meaningless results on very small
datasets.
"""
self._check_proba()
return self._predict_proba
def _predict_proba(self, X):
X = self._validate_for_predict(X)
if self.probA_.size == 0 or self.probB_.size == 0:
raise NotFittedError("predict_proba is not available when fitted "
"with probability=False")
pred_proba = (self._sparse_predict_proba
if self._sparse else self._dense_predict_proba)
return pred_proba(X)
@property
def predict_log_proba(self):
"""Compute log probabilities of possible outcomes for samples in X.
The model need to have probability information computed at training
time: fit with attribute `probability` set to True.
Parameters
----------
X : array-like, shape (n_samples, n_features)
For kernel="precomputed", the expected shape of X is
[n_samples_test, n_samples_train]
Returns
-------
T : array-like, shape (n_samples, n_classes)
Returns the log-probabilities of the sample for each class in
the model. The columns correspond to the classes in sorted
order, as they appear in the attribute `classes_`.
Notes
-----
The probability model is created using cross validation, so
the results can be slightly different than those obtained by
predict. Also, it will produce meaningless results on very small
datasets.
"""
self._check_proba()
return self._predict_log_proba
def _predict_log_proba(self, X):
return np.log(self.predict_proba(X))
def _dense_predict_proba(self, X):
X = self._compute_kernel(X)
kernel = self.kernel
if callable(kernel):
kernel = 'precomputed'
svm_type = LIBSVM_IMPL.index(self._impl)
pprob = libsvm.predict_proba(
X, self.support_, self.support_vectors_, self.n_support_,
self._dual_coef_, self._intercept_,
self.probA_, self.probB_,
svm_type=svm_type, kernel=kernel, degree=self.degree,
cache_size=self.cache_size, coef0=self.coef0, gamma=self._gamma)
return pprob
def _sparse_predict_proba(self, X):
X.data = np.asarray(X.data, dtype=np.float64, order='C')
kernel = self.kernel
if callable(kernel):
kernel = 'precomputed'
kernel_type = self._sparse_kernels.index(kernel)
return libsvm_sparse.libsvm_sparse_predict_proba(
X.data, X.indices, X.indptr,
self.support_vectors_.data,
self.support_vectors_.indices,
self.support_vectors_.indptr,
self._dual_coef_.data, self._intercept_,
LIBSVM_IMPL.index(self._impl), kernel_type,
self.degree, self._gamma, self.coef0, self.tol,
self.C, self.class_weight_,
self.nu, self.epsilon, self.shrinking,
self.probability, self.n_support_,
self.probA_, self.probB_)
def _get_coef(self):
if self.dual_coef_.shape[0] == 1:
# binary classifier
coef = safe_sparse_dot(self.dual_coef_, self.support_vectors_)
else:
# 1vs1 classifier
coef = _one_vs_one_coef(self.dual_coef_, self.n_support_,
self.support_vectors_)
if sp.issparse(coef[0]):
coef = sp.vstack(coef).tocsr()
else:
coef = np.vstack(coef)
return coef
def _get_liblinear_solver_type(multi_class, penalty, loss, dual):
"""Find the liblinear magic number for the solver.
This number depends on the values of the following attributes:
- multi_class
- penalty
- loss
- dual
The same number is also internally used by LibLinear to determine
which solver to use.
"""
# nested dicts containing level 1: available loss functions,
# level2: available penalties for the given loss function,
# level3: wether the dual solver is available for the specified
# combination of loss function and penalty
_solver_type_dict = {
'logistic_regression': {
'l1': {False: 6},
'l2': {False: 0, True: 7}},
'hinge': {
'l2': {True: 3}},
'squared_hinge': {
'l1': {False: 5},
'l2': {False: 2, True: 1}},
'epsilon_insensitive': {
'l2': {True: 13}},
'squared_epsilon_insensitive': {
'l2': {False: 11, True: 12}},
'crammer_singer': 4
}
if multi_class == 'crammer_singer':
return _solver_type_dict[multi_class]
elif multi_class != 'ovr':
raise ValueError("`multi_class` must be one of `ovr`, "
"`crammer_singer`, got %r" % multi_class)
_solver_pen = _solver_type_dict.get(loss, None)
if _solver_pen is None:
error_string = ("loss='%s' is not supported" % loss)
else:
_solver_dual = _solver_pen.get(penalty, None)
if _solver_dual is None:
error_string = ("The combination of penalty='%s' "
"and loss='%s' is not supported"
% (penalty, loss))
else:
solver_num = _solver_dual.get(dual, None)
if solver_num is None:
error_string = ("The combination of penalty='%s' and "
"loss='%s' are not supported when dual=%s"
% (penalty, loss, dual))
else:
return solver_num
raise ValueError('Unsupported set of arguments: %s, '
'Parameters: penalty=%r, loss=%r, dual=%r'
% (error_string, penalty, loss, dual))
def _fit_liblinear(X, y, C, fit_intercept, intercept_scaling, class_weight,
penalty, dual, verbose, max_iter, tol,
random_state=None, multi_class='ovr',
loss='logistic_regression', epsilon=0.1,
sample_weight=None):
"""Used by Logistic Regression (and CV) and LinearSVC/LinearSVR.
Preprocessing is done in this function before supplying it to liblinear.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Training vector, where n_samples in the number of samples and
n_features is the number of features.
y : array-like, shape (n_samples,)
Target vector relative to X
C : float
Inverse of cross-validation parameter. Lower the C, the more
the penalization.
fit_intercept : bool
Whether or not to fit the intercept, that is to add a intercept
term to the decision function.
intercept_scaling : float
LibLinear internally penalizes the intercept and this term is subject
to regularization just like the other terms of the feature vector.
In order to avoid this, one should increase the intercept_scaling.
such that the feature vector becomes [x, intercept_scaling].
class_weight : {dict, 'balanced'}, optional
Weights associated with classes in the form ``{class_label: weight}``.
If not given, all classes are supposed to have weight one. For
multi-output problems, a list of dicts can be provided in the same
order as the columns of y.
The "balanced" mode uses the values of y to automatically adjust
weights inversely proportional to class frequencies in the input data
as ``n_samples / (n_classes * np.bincount(y))``
penalty : str, {'l1', 'l2'}
The norm of the penalty used in regularization.
dual : bool
Dual or primal formulation,
verbose : int
Set verbose to any positive number for verbosity.
max_iter : int
Number of iterations.
tol : float
Stopping condition.
random_state : int, RandomState instance or None, optional (default=None)
The seed of the pseudo random number generator to use when shuffling
the data. If int, random_state is the seed used by the random number
generator; If RandomState instance, random_state is the random number
generator; If None, the random number generator is the RandomState
instance used by `np.random`.
multi_class : str, {'ovr', 'crammer_singer'}
`ovr` trains n_classes one-vs-rest classifiers, while `crammer_singer`
optimizes a joint objective over all classes.
While `crammer_singer` is interesting from an theoretical perspective
as it is consistent it is seldom used in practice and rarely leads to
better accuracy and is more expensive to compute.
If `crammer_singer` is chosen, the options loss, penalty and dual will
be ignored.
loss : str, {'logistic_regression', 'hinge', 'squared_hinge',
'epsilon_insensitive', 'squared_epsilon_insensitive}
The loss function used to fit the model.
epsilon : float, optional (default=0.1)
Epsilon parameter in the epsilon-insensitive loss function. Note
that the value of this parameter depends on the scale of the target
variable y. If unsure, set epsilon=0.
sample_weight : array-like, optional
Weights assigned to each sample.
Returns
-------
coef_ : ndarray, shape (n_features, n_features + 1)
The coefficient vector got by minimizing the objective function.
intercept_ : float
The intercept term added to the vector.
n_iter_ : int
Maximum number of iterations run across all classes.
"""
if loss not in ['epsilon_insensitive', 'squared_epsilon_insensitive']:
enc = LabelEncoder()
y_ind = enc.fit_transform(y)
classes_ = enc.classes_
if len(classes_) < 2:
raise ValueError("This solver needs samples of at least 2 classes"
" in the data, but the data contains only one"
" class: %r" % classes_[0])
class_weight_ = compute_class_weight(class_weight, classes_, y)
else:
class_weight_ = np.empty(0, dtype=np.float64)
y_ind = y
liblinear.set_verbosity_wrap(verbose)
rnd = check_random_state(random_state)
if verbose:
print('[LibLinear]', end='')
# LinearSVC breaks when intercept_scaling is <= 0
bias = -1.0
if fit_intercept:
if intercept_scaling <= 0:
raise ValueError("Intercept scaling is %r but needs to be greater than 0."
" To disable fitting an intercept,"
" set fit_intercept=False." % intercept_scaling)
else:
bias = intercept_scaling
libsvm.set_verbosity_wrap(verbose)
libsvm_sparse.set_verbosity_wrap(verbose)
liblinear.set_verbosity_wrap(verbose)
# Liblinear doesn't support 64bit sparse matrix indices yet
if sp.issparse(X):
_check_large_sparse(X)
# LibLinear wants targets as doubles, even for classification
y_ind = np.asarray(y_ind, dtype=np.float64).ravel()
y_ind = np.require(y_ind, requirements="W")
if sample_weight is None:
sample_weight = np.ones(X.shape[0])
else:
sample_weight = np.array(sample_weight, dtype=np.float64, order='C')
check_consistent_length(sample_weight, X)
solver_type = _get_liblinear_solver_type(multi_class, penalty, loss, dual)
raw_coef_, n_iter_ = liblinear.train_wrap(
X, y_ind, sp.isspmatrix(X), solver_type, tol, bias, C,
class_weight_, max_iter, rnd.randint(np.iinfo('i').max),
epsilon, sample_weight)
# Regarding rnd.randint(..) in the above signature:
# seed for srand in range [0..INT_MAX); due to limitations in Numpy
# on 32-bit platforms, we can't get to the UINT_MAX limit that
# srand supports
n_iter_ = max(n_iter_)
if n_iter_ >= max_iter:
warnings.warn("Liblinear failed to converge, increase "
"the number of iterations.", ConvergenceWarning)
if fit_intercept:
coef_ = raw_coef_[:, :-1]
intercept_ = intercept_scaling * raw_coef_[:, -1]
else:
coef_ = raw_coef_
intercept_ = 0.
return coef_, intercept_, n_iter_scikit-learn/sklearn/svm/bounds.py
"""Determination of parameter bounds"""
# Author: Paolo Losi
# License: BSD 3 clause
import numpy as np
from ..preprocessing import LabelBinarizer
from ..utils.validation import check_consistent_length, check_array
from ..utils.extmath import safe_sparse_dot
def l1_min_c(X, y, loss='squared_hinge', fit_intercept=True,
intercept_scaling=1.0):
"""
Return the lowest bound for C such that for C in (l1_min_C, infinity)
the model is guaranteed not to be empty. This applies to l1 penalized
classifiers, such as LinearSVC with penalty='l1' and
linear_model.LogisticRegression with penalty='l1'.
This value is valid if class_weight parameter in fit() is not set.
Parameters
----------
X : array-like or sparse matrix, shape = [n_samples, n_features]
Training vector, where n_samples in the number of samples and
n_features is the number of features.
y : array, shape = [n_samples]
Target vector relative to X
loss : {'squared_hinge', 'log'}, default 'squared_hinge'
Specifies the loss function.
With 'squared_hinge' it is the squared hinge loss (a.k.a. L2 loss).
With 'log' it is the loss of logistic regression models.
fit_intercept : bool, default: True
Specifies if the intercept should be fitted by the model.
It must match the fit() method parameter.
intercept_scaling : float, default: 1
when fit_intercept is True, instance vector x becomes
[x, intercept_scaling],
i.e. a "synthetic" feature with constant value equals to
intercept_scaling is appended to the instance vector.
It must match the fit() method parameter.
Returns
-------
l1_min_c : float
minimum value for C
"""
if loss not in ('squared_hinge', 'log'):
raise ValueError('loss type not in ("squared_hinge", "log")')
X = check_array(X, accept_sparse='csc')
check_consistent_length(X, y)
Y = LabelBinarizer(neg_label=-1).fit_transform(y).T
# maximum absolute value over classes and features
den = np.max(np.abs(safe_sparse_dot(Y, X)))
if fit_intercept:
bias = np.full((np.size(y), 1), intercept_scaling,
dtype=np.array(intercept_scaling).dtype)
den = max(den, abs(np.dot(Y, bias)).max())
if den == 0.0:
raise ValueError('Ill-posed l1_min_c calculation: l1 will always '
'select zero coefficients for this data')
if loss == 'squared_hinge':
return 0.5 / den
else: # loss == 'log':
return 2.0 / denscikit-learn/sklearn/svm/classes.py
import warnings
import numpy as np
from .base import _fit_liblinear, BaseSVC, BaseLibSVM
from ..base import BaseEstimator, RegressorMixin, OutlierMixin
from ..linear_model.base import LinearClassifierMixin, SparseCoefMixin, \
LinearModel
from ..utils import check_X_y
from ..utils.validation import _num_samples
from ..utils.multiclass import check_classification_targets
class LinearSVC(BaseEstimator, LinearClassifierMixin,
SparseCoefMixin):
"""Linear Support Vector Classification.
Similar to SVC with parameter kernel='linear', but implemented in terms of
liblinear rather than libsvm, so it has more flexibility in the choice of
penalties and loss functions and should scale better to large numbers of
samples.
This class supports both dense and sparse input and the multiclass support
is handled according to a one-vs-the-rest scheme.
Read more in the :ref:`User Guide `.
Parameters
----------
penalty : string, 'l1' or 'l2' (default='l2')
Specifies the norm used in the penalization. The 'l2'
penalty is the standard used in SVC. The 'l1' leads to ``coef_``
vectors that are sparse.
loss : string, 'hinge' or 'squared_hinge' (default='squared_hinge')
Specifies the loss function. 'hinge' is the standard SVM loss
(used e.g. by the SVC class) while 'squared_hinge' is the
square of the hinge loss.
dual : bool, (default=True)
Select the algorithm to either solve the dual or primal
optimization problem. Prefer dual=False when n_samples > n_features.
tol : float, optional (default=1e-4)
Tolerance for stopping criteria.
C : float, optional (default=1.0)
Penalty parameter C of the error term.
multi_class : string, 'ovr' or 'crammer_singer' (default='ovr')
Determines the multi-class strategy if `y` contains more than
two classes.
``"ovr"`` trains n_classes one-vs-rest classifiers, while
``"crammer_singer"`` optimizes a joint objective over all classes.
While `crammer_singer` is interesting from a theoretical perspective
as it is consistent, it is seldom used in practice as it rarely leads
to better accuracy and is more expensive to compute.
If ``"crammer_singer"`` is chosen, the options loss, penalty and dual
will be ignored.
fit_intercept : boolean, optional (default=True)
Whether to calculate the intercept for this model. If set
to false, no intercept will be used in calculations
(i.e. data is expected to be already centered).
intercept_scaling : float, optional (default=1)
When self.fit_intercept is True, instance vector x becomes
``[x, self.intercept_scaling]``,
i.e. a "synthetic" feature with constant value equals to
intercept_scaling is appended to the instance vector.
The intercept becomes intercept_scaling * synthetic feature weight
Note! the synthetic feature weight is subject to l1/l2 regularization
as all other features.
To lessen the effect of regularization on synthetic feature weight
(and therefore on the intercept) intercept_scaling has to be increased.
class_weight : {dict, 'balanced'}, optional
Set the parameter C of class i to ``class_weight[i]*C`` for
SVC. If not given, all classes are supposed to have
weight one.
The "balanced" mode uses the values of y to automatically adjust
weights inversely proportional to class frequencies in the input data
as ``n_samples / (n_classes * np.bincount(y))``
verbose : int, (default=0)
Enable verbose output. Note that this setting takes advantage of a
per-process runtime setting in liblinear that, if enabled, may not work
properly in a multithreaded context.
random_state : int, RandomState instance or None, optional (default=None)
The seed of the pseudo random number generator to use when shuffling
the data for the dual coordinate descent (if ``dual=True``). When
``dual=False`` the underlying implementation of :class:`LinearSVC`
is not random and ``random_state`` has no effect on the results. If
int, random_state is the seed used by the random number generator; If
RandomState instance, random_state is the random number generator; If
None, the random number generator is the RandomState instance used by
`np.random`.
max_iter : int, (default=1000)
The maximum number of iterations to be run.
Attributes
----------
coef_ : array, shape = [n_features] if n_classes == 2 else [n_classes, n_features]
Weights assigned to the features (coefficients in the primal
problem). This is only available in the case of a linear kernel.
``coef_`` is a readonly property derived from ``raw_coef_`` that
follows the internal memory layout of liblinear.
intercept_ : array, shape = [1] if n_classes == 2 else [n_classes]
Constants in decision function.
Examples
--------
>>> from sklearn.svm import LinearSVC
>>> from sklearn.datasets import make_classification
>>> X, y = make_classification(n_features=4, random_state=0)
>>> clf = LinearSVC(random_state=0, tol=1e-5)
>>> clf.fit(X, y)
LinearSVC(C=1.0, class_weight=None, dual=True, fit_intercept=True,
intercept_scaling=1, loss='squared_hinge', max_iter=1000,
multi_class='ovr', penalty='l2', random_state=0, tol=1e-05, verbose=0)
>>> print(clf.coef_)
[[0.085... 0.394... 0.498... 0.375...]]
>>> print(clf.intercept_)
[0.284...]
>>> print(clf.predict([[0, 0, 0, 0]]))
[1]
Notes
-----
The underlying C implementation uses a random number generator to
select features when fitting the model. It is thus not uncommon
to have slightly different results for the same input data. If
that happens, try with a smaller ``tol`` parameter.
The underlying implementation, liblinear, uses a sparse internal
representation for the data that will incur a memory copy.
Predict output may not match that of standalone liblinear in certain
cases. See :ref:`differences from liblinear `
in the narrative documentation.
References
----------
`LIBLINEAR: A Library for Large Linear Classification
`__
See also
--------
SVC
Implementation of Support Vector Machine classifier using libsvm:
the kernel can be non-linear but its SMO algorithm does not
scale to large number of samples as LinearSVC does.
Furthermore SVC multi-class mode is implemented using one
vs one scheme while LinearSVC uses one vs the rest. It is
possible to implement one vs the rest with SVC by using the
:class:`sklearn.multiclass.OneVsRestClassifier` wrapper.
Finally SVC can fit dense data without memory copy if the input
is C-contiguous. Sparse data will still incur memory copy though.
sklearn.linear_model.SGDClassifier
SGDClassifier can optimize the same cost function as LinearSVC
by adjusting the penalty and loss parameters. In addition it requires
less memory, allows incremental (online) learning, and implements
various loss functions and regularization regimes.
"""
def __init__(self, penalty='l2', loss='squared_hinge', dual=True, tol=1e-4,
C=1.0, multi_class='ovr', fit_intercept=True,
intercept_scaling=1, class_weight=None, verbose=0,
random_state=None, max_iter=1000):
self.dual = dual
self.tol = tol
self.C = C
self.multi_class = multi_class
self.fit_intercept = fit_intercept
self.intercept_scaling = intercept_scaling
self.class_weight = class_weight
self.verbose = verbose
self.random_state = random_state
self.max_iter = max_iter
self.penalty = penalty
self.loss = loss
def fit(self, X, y, sample_weight=None):
"""Fit the model according to the given training data.
Parameters
----------
X : {array-like, sparse matrix}, shape = [n_samples, n_features]
Training vector, where n_samples in the number of samples and
n_features is the number of features.
y : array-like, shape = [n_samples]
Target vector relative to X
sample_weight : array-like, shape = [n_samples], optional
Array of weights that are assigned to individual
samples. If not provided,
then each sample is given unit weight.
Returns
-------
self : object
"""
# FIXME Remove l1/l2 support in 1.0 -----------------------------------
msg = ("loss='%s' has been deprecated in favor of "
"loss='%s' as of 0.16. Backward compatibility"
" for the loss='%s' will be removed in %s")
if self.loss in ('l1', 'l2'):
old_loss = self.loss
self.loss = {'l1': 'hinge', 'l2': 'squared_hinge'}.get(self.loss)
warnings.warn(msg % (old_loss, self.loss, old_loss, '1.0'),
DeprecationWarning)
# ---------------------------------------------------------------------
if self.C < 0:
raise ValueError("Penalty term must be positive; got (C=%r)"
% self.C)
X, y = check_X_y(X, y, accept_sparse='csr',
dtype=np.float64, order="C",
accept_large_sparse=False)
check_classification_targets(y)
self.classes_ = np.unique(y)
self.coef_, self.intercept_, self.n_iter_ = _fit_liblinear(
X, y, self.C, self.fit_intercept, self.intercept_scaling,
self.class_weight, self.penalty, self.dual, self.verbose,
self.max_iter, self.tol, self.random_state, self.multi_class,
self.loss, sample_weight=sample_weight)
if self.multi_class == "crammer_singer" and len(self.classes_) == 2:
self.coef_ = (self.coef_[1] - self.coef_[0]).reshape(1, -1)
if self.fit_intercept:
intercept = self.intercept_[1] - self.intercept_[0]
self.intercept_ = np.array([intercept])
return self
class LinearSVR(LinearModel, RegressorMixin):
"""Linear Support Vector Regression.
Similar to SVR with parameter kernel='linear', but implemented in terms of
liblinear rather than libsvm, so it has more flexibility in the choice of
penalties and loss functions and should scale better to large numbers of
samples.
This class supports both dense and sparse input.
Read more in the :ref:`User Guide `.
Parameters
----------
epsilon : float, optional (default=0.1)
Epsilon parameter in the epsilon-insensitive loss function. Note
that the value of this parameter depends on the scale of the target
variable y. If unsure, set ``epsilon=0``.
tol : float, optional (default=1e-4)
Tolerance for stopping criteria.
C : float, optional (default=1.0)
Penalty parameter C of the error term. The penalty is a squared
l2 penalty. The bigger this parameter, the less regularization is used.
loss : string, optional (default='epsilon_insensitive')
Specifies the loss function. The epsilon-insensitive loss
(standard SVR) is the L1 loss, while the squared epsilon-insensitive
loss ('squared_epsilon_insensitive') is the L2 loss.
fit_intercept : boolean, optional (default=True)
Whether to calculate the intercept for this model. If set
to false, no intercept will be used in calculations
(i.e. data is expected to be already centered).
intercept_scaling : float, optional (default=1)
When self.fit_intercept is True, instance vector x becomes
[x, self.intercept_scaling],
i.e. a "synthetic" feature with constant value equals to
intercept_scaling is appended to the instance vector.
The intercept becomes intercept_scaling * synthetic feature weight
Note! the synthetic feature weight is subject to l1/l2 regularization
as all other features.
To lessen the effect of regularization on synthetic feature weight
(and therefore on the intercept) intercept_scaling has to be increased.
dual : bool, (default=True)
Select the algorithm to either solve the dual or primal
optimization problem. Prefer dual=False when n_samples > n_features.
verbose : int, (default=0)
Enable verbose output. Note that this setting takes advantage of a
per-process runtime setting in liblinear that, if enabled, may not work
properly in a multithreaded context.
random_state : int, RandomState instance or None, optional (default=None)
The seed of the pseudo random number generator to use when shuffling
the data. If int, random_state is the seed used by the random number
generator; If RandomState instance, random_state is the random number
generator; If None, the random number generator is the RandomState
instance used by `np.random`.
max_iter : int, (default=1000)
The maximum number of iterations to be run.
Attributes
----------
coef_ : array, shape = [n_features] if n_classes == 2 else [n_classes, n_features]
Weights assigned to the features (coefficients in the primal
problem). This is only available in the case of a linear kernel.
`coef_` is a readonly property derived from `raw_coef_` that
follows the internal memory layout of liblinear.
intercept_ : array, shape = [1] if n_classes == 2 else [n_classes]
Constants in decision function.
Examples
--------
>>> from sklearn.svm import LinearSVR
>>> from sklearn.datasets import make_regression
>>> X, y = make_regression(n_features=4, random_state=0)
>>> regr = LinearSVR(random_state=0, tol=1e-5)
>>> regr.fit(X, y)
LinearSVR(C=1.0, dual=True, epsilon=0.0, fit_intercept=True,
intercept_scaling=1.0, loss='epsilon_insensitive', max_iter=1000,
random_state=0, tol=1e-05, verbose=0)
>>> print(regr.coef_)
[16.35... 26.91... 42.30... 60.47...]
>>> print(regr.intercept_)
[-4.29...]
>>> print(regr.predict([[0, 0, 0, 0]]))
[-4.29...]
See also
--------
LinearSVC
Implementation of Support Vector Machine classifier using the
same library as this class (liblinear).
SVR
Implementation of Support Vector Machine regression using libsvm:
the kernel can be non-linear but its SMO algorithm does not
scale to large number of samples as LinearSVC does.
sklearn.linear_model.SGDRegressor
SGDRegressor can optimize the same cost function as LinearSVR
by adjusting the penalty and loss parameters. In addition it requires
less memory, allows incremental (online) learning, and implements
various loss functions and regularization regimes.
"""
def __init__(self, epsilon=0.0, tol=1e-4, C=1.0,
loss='epsilon_insensitive', fit_intercept=True,
intercept_scaling=1., dual=True, verbose=0,
random_state=None, max_iter=1000):
self.tol = tol
self.C = C
self.epsilon = epsilon
self.fit_intercept = fit_intercept
self.intercept_scaling = intercept_scaling
self.verbose = verbose
self.random_state = random_state
self.max_iter = max_iter
self.dual = dual
self.loss = loss
def fit(self, X, y, sample_weight=None):
"""Fit the model according to the given training data.
Parameters
----------
X : {array-like, sparse matrix}, shape = [n_samples, n_features]
Training vector, where n_samples in the number of samples and
n_features is the number of features.
y : array-like, shape = [n_samples]
Target vector relative to X
sample_weight : array-like, shape = [n_samples], optional
Array of weights that are assigned to individual
samples. If not provided,
then each sample is given unit weight.
Returns
-------
self : object
"""
# FIXME Remove l1/l2 support in 1.0 -----------------------------------
msg = ("loss='%s' has been deprecated in favor of "
"loss='%s' as of 0.16. Backward compatibility"
" for the loss='%s' will be removed in %s")
if self.loss in ('l1', 'l2'):
old_loss = self.loss
self.loss = {'l1': 'epsilon_insensitive',
'l2': 'squared_epsilon_insensitive'
}.get(self.loss)
warnings.warn(msg % (old_loss, self.loss, old_loss, '1.0'),
DeprecationWarning)
# ---------------------------------------------------------------------
if self.C < 0:
raise ValueError("Penalty term must be positive; got (C=%r)"
% self.C)
X, y = check_X_y(X, y, accept_sparse='csr',
dtype=np.float64, order="C",
accept_large_sparse=False)
penalty = 'l2' # SVR only accepts l2 penalty
self.coef_, self.intercept_, self.n_iter_ = _fit_liblinear(
X, y, self.C, self.fit_intercept, self.intercept_scaling,
None, penalty, self.dual, self.verbose,
self.max_iter, self.tol, self.random_state, loss=self.loss,
epsilon=self.epsilon, sample_weight=sample_weight)
self.coef_ = self.coef_.ravel()
return self
class SVC(BaseSVC):
"""C-Support Vector Classification.
The implementation is based on libsvm. The fit time complexity
is more than quadratic with the number of samples which makes it hard
to scale to dataset with more than a couple of 10000 samples.
The multiclass support is handled according to a one-vs-one scheme.
For details on the precise mathematical formulation of the provided
kernel functions and how `gamma`, `coef0` and `degree` affect each
other, see the corresponding section in the narrative documentation:
:ref:`svm_kernels`.
Read more in the :ref:`User Guide `.
Parameters
----------
C : float, optional (default=1.0)
Penalty parameter C of the error term.
kernel : string, optional (default='rbf')
Specifies the kernel type to be used in the algorithm.
It must be one of 'linear', 'poly', 'rbf', 'sigmoid', 'precomputed' or
a callable.
If none is given, 'rbf' will be used. If a callable is given it is
used to pre-compute the kernel matrix from data matrices; that matrix
should be an array of shape ``(n_samples, n_samples)``.
degree : int, optional (default=3)
Degree of the polynomial kernel function ('poly').
Ignored by all other kernels.
gamma : float, optional (default='auto')
Kernel coefficient for 'rbf', 'poly' and 'sigmoid'.
Current default is 'auto' which uses 1 / n_features,
if ``gamma='scale'`` is passed then it uses 1 / (n_features * X.std())
as value of gamma. The current default of gamma, 'auto', will change
to 'scale' in version 0.22. 'auto_deprecated', a deprecated version of
'auto' is used as a default indicating that no explicit value of gamma
was passed.
coef0 : float, optional (default=0.0)
Independent term in kernel function.
It is only significant in 'poly' and 'sigmoid'.
shrinking : boolean, optional (default=True)
Whether to use the shrinking heuristic.
probability : boolean, optional (default=False)
Whether to enable probability estimates. This must be enabled prior
to calling `fit`, and will slow down that method.
tol : float, optional (default=1e-3)
Tolerance for stopping criterion.
cache_size : float, optional
Specify the size of the kernel cache (in MB).
class_weight : {dict, 'balanced'}, optional
Set the parameter C of class i to class_weight[i]*C for
SVC. If not given, all classes are supposed to have
weight one.
The "balanced" mode uses the values of y to automatically adjust
weights inversely proportional to class frequencies in the input data
as ``n_samples / (n_classes * np.bincount(y))``
verbose : bool, default: False
Enable verbose output. Note that this setting takes advantage of a
per-process runtime setting in libsvm that, if enabled, may not work
properly in a multithreaded context.
max_iter : int, optional (default=-1)
Hard limit on iterations within solver, or -1 for no limit.
decision_function_shape : 'ovo', 'ovr', default='ovr'
Whether to return a one-vs-rest ('ovr') decision function of shape
(n_samples, n_classes) as all other classifiers, or the original
one-vs-one ('ovo') decision function of libsvm which has shape
(n_samples, n_classes * (n_classes - 1) / 2). However, one-vs-one
('ovo') is always used as multi-class strategy.
.. versionchanged:: 0.19
decision_function_shape is 'ovr' by default.
.. versionadded:: 0.17
*decision_function_shape='ovr'* is recommended.
.. versionchanged:: 0.17
Deprecated *decision_function_shape='ovo' and None*.
random_state : int, RandomState instance or None, optional (default=None)
The seed of the pseudo random number generator used when shuffling
the data for probability estimates. If int, random_state is the
seed used by the random number generator; If RandomState instance,
random_state is the random number generator; If None, the random
number generator is the RandomState instance used by `np.random`.
Attributes
----------
support_ : array-like, shape = [n_SV]
Indices of support vectors.
support_vectors_ : array-like, shape = [n_SV, n_features]
Support vectors.
n_support_ : array-like, dtype=int32, shape = [n_class]
Number of support vectors for each class.
dual_coef_ : array, shape = [n_class-1, n_SV]
Coefficients of the support vector in the decision function.
For multiclass, coefficient for all 1-vs-1 classifiers.
The layout of the coefficients in the multiclass case is somewhat
non-trivial. See the section about multi-class classification in the
SVM section of the User Guide for details.
coef_ : array, shape = [n_class * (n_class-1) / 2, n_features]
Weights assigned to the features (coefficients in the primal
problem). This is only available in the case of a linear kernel.
`coef_` is a readonly property derived from `dual_coef_` and
`support_vectors_`.
intercept_ : array, shape = [n_class * (n_class-1) / 2]
Constants in decision function.
Examples
--------
>>> import numpy as np
>>> X = np.array([[-1, -1], [-2, -1], [1, 1], [2, 1]])
>>> y = np.array([1, 1, 2, 2])
>>> from sklearn.svm import SVC
>>> clf = SVC(gamma='auto')
>>> clf.fit(X, y) #doctest: +NORMALIZE_WHITESPACE
SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0,
decision_function_shape='ovr', degree=3, gamma='auto', kernel='rbf',
max_iter=-1, probability=False, random_state=None, shrinking=True,
tol=0.001, verbose=False)
>>> print(clf.predict([[-0.8, -1]]))
[1]
See also
--------
SVR
Support Vector Machine for Regression implemented using libsvm.
LinearSVC
Scalable Linear Support Vector Machine for classification
implemented using liblinear. Check the See also section of
LinearSVC for more comparison element.
"""
_impl = 'c_svc'
def __init__(self, C=1.0, kernel='rbf', degree=3, gamma='auto_deprecated',
coef0=0.0, shrinking=True, probability=False,
tol=1e-3, cache_size=200, class_weight=None,
verbose=False, max_iter=-1, decision_function_shape='ovr',
random_state=None):
super(SVC, self).__init__(
kernel=kernel, degree=degree, gamma=gamma,
coef0=coef0, tol=tol, C=C, nu=0., shrinking=shrinking,
probability=probability, cache_size=cache_size,
class_weight=class_weight, verbose=verbose, max_iter=max_iter,
decision_function_shape=decision_function_shape,
random_state=random_state)
class NuSVC(BaseSVC):
"""Nu-Support Vector Classification.
Similar to SVC but uses a parameter to control the number of support
vectors.
The implementation is based on libsvm.
Read more in the :ref:`User Guide `.
Parameters
----------
nu : float, optional (default=0.5)
An upper bound on the fraction of training errors and a lower
bound of the fraction of support vectors. Should be in the
interval (0, 1].
kernel : string, optional (default='rbf')
Specifies the kernel type to be used in the algorithm.
It must be one of 'linear', 'poly', 'rbf', 'sigmoid', 'precomputed' or
a callable.
If none is given, 'rbf' will be used. If a callable is given it is
used to precompute the kernel matrix.
degree : int, optional (default=3)
Degree of the polynomial kernel function ('poly').
Ignored by all other kernels.
gamma : float, optional (default='auto')
Kernel coefficient for 'rbf', 'poly' and 'sigmoid'.
Current default is 'auto' which uses 1 / n_features,
if ``gamma='scale'`` is passed then it uses 1 / (n_features * X.std())
as value of gamma. The current default of gamma, 'auto', will change
to 'scale' in version 0.22. 'auto_deprecated', a deprecated version of
'auto' is used as a default indicating that no explicit value of gamma
was passed.
coef0 : float, optional (default=0.0)
Independent term in kernel function.
It is only significant in 'poly' and 'sigmoid'.
shrinking : boolean, optional (default=True)
Whether to use the shrinking heuristic.
probability : boolean, optional (default=False)
Whether to enable probability estimates. This must be enabled prior
to calling `fit`, and will slow down that method.
tol : float, optional (default=1e-3)
Tolerance for stopping criterion.
cache_size : float, optional
Specify the size of the kernel cache (in MB).
class_weight : {dict, 'balanced'}, optional
Set the parameter C of class i to class_weight[i]*C for
SVC. If not given, all classes are supposed to have
weight one. The "balanced" mode uses the values of y to automatically
adjust weights inversely proportional to class frequencies as
``n_samples / (n_classes * np.bincount(y))``
verbose : bool, default: False
Enable verbose output. Note that this setting takes advantage of a
per-process runtime setting in libsvm that, if enabled, may not work
properly in a multithreaded context.
max_iter : int, optional (default=-1)
Hard limit on iterations within solver, or -1 for no limit.
decision_function_shape : 'ovo', 'ovr', default='ovr'
Whether to return a one-vs-rest ('ovr') decision function of shape
(n_samples, n_classes) as all other classifiers, or the original
one-vs-one ('ovo') decision function of libsvm which has shape
(n_samples, n_classes * (n_classes - 1) / 2).
.. versionchanged:: 0.19
decision_function_shape is 'ovr' by default.
.. versionadded:: 0.17
*decision_function_shape='ovr'* is recommended.
.. versionchanged:: 0.17
Deprecated *decision_function_shape='ovo' and None*.
random_state : int, RandomState instance or None, optional (default=None)
The seed of the pseudo random number generator used when shuffling
the data for probability estimates. If int, random_state is the seed
used by the random number generator; If RandomState instance,
random_state is the random number generator; If None, the random
number generator is the RandomState instance used by `np.random`.
Attributes
----------
support_ : array-like, shape = [n_SV]
Indices of support vectors.
support_vectors_ : array-like, shape = [n_SV, n_features]
Support vectors.
n_support_ : array-like, dtype=int32, shape = [n_class]
Number of support vectors for each class.
dual_coef_ : array, shape = [n_class-1, n_SV]
Coefficients of the support vector in the decision function.
For multiclass, coefficient for all 1-vs-1 classifiers.
The layout of the coefficients in the multiclass case is somewhat
non-trivial. See the section about multi-class classification in
the SVM section of the User Guide for details.
coef_ : array, shape = [n_class * (n_class-1) / 2, n_features]
Weights assigned to the features (coefficients in the primal
problem). This is only available in the case of a linear kernel.
`coef_` is readonly property derived from `dual_coef_` and
`support_vectors_`.
intercept_ : array, shape = [n_class * (n_class-1) / 2]
Constants in decision function.
Examples
--------
>>> import numpy as np
>>> X = np.array([[-1, -1], [-2, -1], [1, 1], [2, 1]])
>>> y = np.array([1, 1, 2, 2])
>>> from sklearn.svm import NuSVC
>>> clf = NuSVC(gamma='scale')
>>> clf.fit(X, y) #doctest: +NORMALIZE_WHITESPACE
NuSVC(cache_size=200, class_weight=None, coef0=0.0,
decision_function_shape='ovr', degree=3, gamma='scale', kernel='rbf',
max_iter=-1, nu=0.5, probability=False, random_state=None,
shrinking=True, tol=0.001, verbose=False)
>>> print(clf.predict([[-0.8, -1]]))
[1]
See also
--------
SVC
Support Vector Machine for classification using libsvm.
LinearSVC
Scalable linear Support Vector Machine for classification using
liblinear.
"""
_impl = 'nu_svc'
def __init__(self, nu=0.5, kernel='rbf', degree=3, gamma='auto_deprecated',
coef0=0.0, shrinking=True, probability=False, tol=1e-3,
cache_size=200, class_weight=None, verbose=False, max_iter=-1,
decision_function_shape='ovr', random_state=None):
super(NuSVC, self).__init__(
kernel=kernel, degree=degree, gamma=gamma,
coef0=coef0, tol=tol, C=0., nu=nu, shrinking=shrinking,
probability=probability, cache_size=cache_size,
class_weight=class_weight, verbose=verbose, max_iter=max_iter,
decision_function_shape=decision_function_shape,
random_state=random_state)
class SVR(BaseLibSVM, RegressorMixin):
"""Epsilon-Support Vector Regression.
The free parameters in the model are C and epsilon.
The implementation is based on libsvm.
Read more in the :ref:`User Guide `.
Parameters
----------
kernel : string, optional (default='rbf')
Specifies the kernel type to be used in the algorithm.
It must be one of 'linear', 'poly', 'rbf', 'sigmoid', 'precomputed' or
a callable.
If none is given, 'rbf' will be used. If a callable is given it is
used to precompute the kernel matrix.
degree : int, optional (default=3)
Degree of the polynomial kernel function ('poly').
Ignored by all other kernels.
gamma : float, optional (default='auto')
Kernel coefficient for 'rbf', 'poly' and 'sigmoid'.
Current default is 'auto' which uses 1 / n_features,
if ``gamma='scale'`` is passed then it uses 1 / (n_features * X.std())
as value of gamma. The current default of gamma, 'auto', will change
to 'scale' in version 0.22. 'auto_deprecated', a deprecated version of
'auto' is used as a default indicating that no explicit value of gamma
was passed.
coef0 : float, optional (default=0.0)
Independent term in kernel function.
It is only significant in 'poly' and 'sigmoid'.
tol : float, optional (default=1e-3)
Tolerance for stopping criterion.
C : float, optional (default=1.0)
Penalty parameter C of the error term.
epsilon : float, optional (default=0.1)
Epsilon in the epsilon-SVR model. It specifies the epsilon-tube
within which no penalty is associated in the training loss function
with points predicted within a distance epsilon from the actual
value.
shrinking : boolean, optional (default=True)
Whether to use the shrinking heuristic.
cache_size : float, optional
Specify the size of the kernel cache (in MB).
verbose : bool, default: False
Enable verbose output. Note that this setting takes advantage of a
per-process runtime setting in libsvm that, if enabled, may not work
properly in a multithreaded context.
max_iter : int, optional (default=-1)
Hard limit on iterations within solver, or -1 for no limit.
Attributes
----------
support_ : array-like, shape = [n_SV]
Indices of support vectors.
support_vectors_ : array-like, shape = [nSV, n_features]
Support vectors.
dual_coef_ : array, shape = [1, n_SV]
Coefficients of the support vector in the decision function.
coef_ : array, shape = [1, n_features]
Weights assigned to the features (coefficients in the primal
problem). This is only available in the case of a linear kernel.
`coef_` is readonly property derived from `dual_coef_` and
`support_vectors_`.
intercept_ : array, shape = [1]
Constants in decision function.
sample_weight : array-like, shape = [n_samples]
Individual weights for each sample
Examples
--------
>>> from sklearn.svm import SVR
>>> import numpy as np
>>> n_samples, n_features = 10, 5
>>> np.random.seed(0)
>>> y = np.random.randn(n_samples)
>>> X = np.random.randn(n_samples, n_features)
>>> clf = SVR(gamma='scale', C=1.0, epsilon=0.2)
>>> clf.fit(X, y) #doctest: +NORMALIZE_WHITESPACE
SVR(C=1.0, cache_size=200, coef0=0.0, degree=3, epsilon=0.2, gamma='scale',
kernel='rbf', max_iter=-1, shrinking=True, tol=0.001, verbose=False)
See also
--------
NuSVR
Support Vector Machine for regression implemented using libsvm
using a parameter to control the number of support vectors.
LinearSVR
Scalable Linear Support Vector Machine for regression
implemented using liblinear.
"""
_impl = 'epsilon_svr'
def __init__(self, kernel='rbf', degree=3, gamma='auto_deprecated',
coef0=0.0, tol=1e-3, C=1.0, epsilon=0.1, shrinking=True,
cache_size=200, verbose=False, max_iter=-1):
super(SVR, self).__init__(
kernel=kernel, degree=degree, gamma=gamma,
coef0=coef0, tol=tol, C=C, nu=0., epsilon=epsilon, verbose=verbose,
shrinking=shrinking, probability=False, cache_size=cache_size,
class_weight=None, max_iter=max_iter, random_state=None)
class NuSVR(BaseLibSVM, RegressorMixin):
"""Nu Support Vector Regression.
Similar to NuSVC, for regression, uses a parameter nu to control
the number of support vectors. However, unlike NuSVC, where nu
replaces C, here nu replaces the parameter epsilon of epsilon-SVR.
The implementation is based on libsvm.
Read more in the :ref:`User Guide `.
Parameters
----------
nu : float, optional
An upper bound on the fraction of training errors and a lower bound of
the fraction of support vectors. Should be in the interval (0, 1]. By
default 0.5 will be taken.
C : float, optional (default=1.0)
Penalty parameter C of the error term.
kernel : string, optional (default='rbf')
Specifies the kernel type to be used in the algorithm.
It must be one of 'linear', 'poly', 'rbf', 'sigmoid', 'precomputed' or
a callable.
If none is given, 'rbf' will be used. If a callable is given it is
used to precompute the kernel matrix.
degree : int, optional (default=3)
Degree of the polynomial kernel function ('poly').
Ignored by all other kernels.
gamma : float, optional (default='auto')
Kernel coefficient for 'rbf', 'poly' and 'sigmoid'.
Current default is 'auto' which uses 1 / n_features,
if ``gamma='scale'`` is passed then it uses 1 / (n_features * X.std())
as value of gamma. The current default of gamma, 'auto', will change
to 'scale' in version 0.22. 'auto_deprecated', a deprecated version of
'auto' is used as a default indicating that no explicit value of gamma
was passed.
coef0 : float, optional (default=0.0)
Independent term in kernel function.
It is only significant in 'poly' and 'sigmoid'.
shrinking : boolean, optional (default=True)
Whether to use the shrinking heuristic.
tol : float, optional (default=1e-3)
Tolerance for stopping criterion.
cache_size : float, optional
Specify the size of the kernel cache (in MB).
verbose : bool, default: False
Enable verbose output. Note that this setting takes advantage of a
per-process runtime setting in libsvm that, if enabled, may not work
properly in a multithreaded context.
max_iter : int, optional (default=-1)
Hard limit on iterations within solver, or -1 for no limit.
Attributes
----------
support_ : array-like, shape = [n_SV]
Indices of support vectors.
support_vectors_ : array-like, shape = [nSV, n_features]
Support vectors.
dual_coef_ : array, shape = [1, n_SV]
Coefficients of the support vector in the decision function.
coef_ : array, shape = [1, n_features]
Weights assigned to the features (coefficients in the primal
problem). This is only available in the case of a linear kernel.
`coef_` is readonly property derived from `dual_coef_` and
`support_vectors_`.
intercept_ : array, shape = [1]
Constants in decision function.
Examples
--------
>>> from sklearn.svm import NuSVR
>>> import numpy as np
>>> n_samples, n_features = 10, 5
>>> np.random.seed(0)
>>> y = np.random.randn(n_samples)
>>> X = np.random.randn(n_samples, n_features)
>>> clf = NuSVR(gamma='scale', C=1.0, nu=0.1)
>>> clf.fit(X, y) #doctest: +NORMALIZE_WHITESPACE
NuSVR(C=1.0, cache_size=200, coef0=0.0, degree=3, gamma='scale',
kernel='rbf', max_iter=-1, nu=0.1, shrinking=True, tol=0.001,
verbose=False)
See also
--------
NuSVC
Support Vector Machine for classification implemented with libsvm
with a parameter to control the number of support vectors.
SVR
epsilon Support Vector Machine for regression implemented with libsvm.
"""
_impl = 'nu_svr'
def __init__(self, nu=0.5, C=1.0, kernel='rbf', degree=3,
gamma='auto_deprecated', coef0=0.0, shrinking=True,
tol=1e-3, cache_size=200, verbose=False, max_iter=-1):
super(NuSVR, self).__init__(
kernel=kernel, degree=degree, gamma=gamma, coef0=coef0,
tol=tol, C=C, nu=nu, epsilon=0., shrinking=shrinking,
probability=False, cache_size=cache_size, class_weight=None,
verbose=verbose, max_iter=max_iter, random_state=None)
class OneClassSVM(BaseLibSVM, OutlierMixin):
"""Unsupervised Outlier Detection.
Estimate the support of a high-dimensional distribution.
The implementation is based on libsvm.
Read more in the :ref:`User Guide `.
Parameters
----------
kernel : string, optional (default='rbf')
Specifies the kernel type to be used in the algorithm.
It must be one of 'linear', 'poly', 'rbf', 'sigmoid', 'precomputed' or
a callable.
If none is given, 'rbf' will be used. If a callable is given it is
used to precompute the kernel matrix.
degree : int, optional (default=3)
Degree of the polynomial kernel function ('poly').
Ignored by all other kernels.
gamma : float, optional (default='auto')
Kernel coefficient for 'rbf', 'poly' and 'sigmoid'.
Current default is 'auto' which uses 1 / n_features,
if ``gamma='scale'`` is passed then it uses 1 / (n_features * X.std())
as value of gamma. The current default of gamma, 'auto', will change
to 'scale' in version 0.22. 'auto_deprecated', a deprecated version of
'auto' is used as a default indicating that no explicit value of gamma
was passed.
coef0 : float, optional (default=0.0)
Independent term in kernel function.
It is only significant in 'poly' and 'sigmoid'.
tol : float, optional
Tolerance for stopping criterion.
nu : float, optional
An upper bound on the fraction of training
errors and a lower bound of the fraction of support
vectors. Should be in the interval (0, 1]. By default 0.5
will be taken.
shrinking : boolean, optional
Whether to use the shrinking heuristic.
cache_size : float, optional
Specify the size of the kernel cache (in MB).
verbose : bool, default: False
Enable verbose output. Note that this setting takes advantage of a
per-process runtime setting in libsvm that, if enabled, may not work
properly in a multithreaded context.
max_iter : int, optional (default=-1)
Hard limit on iterations within solver, or -1 for no limit.
random_state : int, RandomState instance or None, optional (default=None)
Ignored.
.. deprecated:: 0.20
``random_state`` has been deprecated in 0.20 and will be removed in
0.22.
Attributes
----------
support_ : array-like, shape = [n_SV]
Indices of support vectors.
support_vectors_ : array-like, shape = [nSV, n_features]
Support vectors.
dual_coef_ : array, shape = [1, n_SV]
Coefficients of the support vectors in the decision function.
coef_ : array, shape = [1, n_features]
Weights assigned to the features (coefficients in the primal
problem). This is only available in the case of a linear kernel.
`coef_` is readonly property derived from `dual_coef_` and
`support_vectors_`
intercept_ : array, shape = [1,]
Constant in the decision function.
offset_ : float
Offset used to define the decision function from the raw scores.
We have the relation: decision_function = score_samples - `offset_`.
The offset is the opposite of `intercept_` and is provided for
consistency with other outlier detection algorithms.
"""
_impl = 'one_class'
def __init__(self, kernel='rbf', degree=3, gamma='auto_deprecated',
coef0=0.0, tol=1e-3, nu=0.5, shrinking=True, cache_size=200,
verbose=False, max_iter=-1, random_state=None):
super(OneClassSVM, self).__init__(
kernel, degree, gamma, coef0, tol, 0., nu, 0.,
shrinking, False, cache_size, None, verbose, max_iter,
random_state)
def fit(self, X, y=None, sample_weight=None, **params):
"""
Detects the soft boundary of the set of samples X.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Set of samples, where n_samples is the number of samples and
n_features is the number of features.
sample_weight : array-like, shape (n_samples,)
Per-sample weights. Rescale C per sample. Higher weights
force the classifier to put more emphasis on these points.
y : Ignored
not used, present for API consistency by convention.
Returns
-------
self : object
Notes
-----
If X is not a C-ordered contiguous array it is copied.
"""
if self.random_state is not None:
warnings.warn("The random_state parameter is deprecated and will"
" be removed in version 0.22.", DeprecationWarning)
super(OneClassSVM, self).fit(X, np.ones(_num_samples(X)),
sample_weight=sample_weight, **params)
self.offset_ = -self._intercept_
return self
def decision_function(self, X):
"""Signed distance to the separating hyperplane.
Signed distance is positive for an inlier and negative for an outlier.
Parameters
----------
X : array-like, shape (n_samples, n_features)
Returns
-------
dec : array-like, shape (n_samples,)
Returns the decision function of the samples.
"""
dec = self._decision_function(X).ravel()
return dec
def score_samples(self, X):
"""Raw scoring function of the samples.
Parameters
----------
X : array-like, shape (n_samples, n_features)
Returns
-------
score_samples : array-like, shape (n_samples,)
Returns the (unshifted) scoring function of the samples.
"""
return self.decision_function(X) + self.offset_
def predict(self, X):
"""
Perform classification on samples in X.
For an one-class model, +1 or -1 is returned.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
For kernel="precomputed", the expected shape of X is
[n_samples_test, n_samples_train]
Returns
-------
y_pred : array, shape (n_samples,)
Class labels for samples in X.
"""
y = super(OneClassSVM, self).predict(X)
return np.asarray(y, dtype=np.intp) 요약: scikit - learn 은 python 언어 를 통 해 numpy 라 이브 러 리, scipy 라 이브 러 리 와 scikit - learn 자체 라 이브 러 리 를 이용 하여 이 루어 진 기계 학습 라 이브 러 리 로 대량의 기계 학습 알고리즘 을 밀봉 하여 코드 를 통 해 기계 학습 과정 을 쉽게 실현 할 수 있 습 니 다. 이러한 복잡 한 알고리즘 의 소스 코드 는 층 이 겹 쳐 있어 정확 한 절 차 를 찾 을 수 없 으 며 소스 코드 를 읽 으 면 알고리즘 의 일 부 를 알 수 있 습 니 다.허 단서 및 체험 알고리즘 의 응용 묘 는 여전히 도움 이 됩 니 다. 기계 학습 과정 은 문 제 를 확정 하고 데 이 터 를 축적 하 며 모델 을 만 들 고 인삼, 훈련, 인삼 조절, 예측, 고정 저장 모델 등 절차 로 요약 할 수 있 습 니 다. 모델 구축 절차 에서 코드 는 간단 하지만 그 뒤의 알고리즘 은 비교적 복잡 합 니 다. 이 예 에서 scikit - learn 은 기계 학습 에서 매우 중요 합 니 다.필요 한 SVM 알고리즘 은 원본 코드 만 으로 는 원본 을 찾기 어렵 지만 공식 문서 와 제 공 된 문헌 을 조합 하면 알고리즘 이 해 를 강화 할 수 있 습 니 다.
SVM 공식 문서http://scikit-learn.org/stable/modules/svm.html
LIBSVM: A Library for Support Vector Machines
[1]http://scikit-learn.org/stable/index.html“>:http://scikit-learn.org/stable/index.html [2]http://scikit-learn.org/stable/auto_examples/index.html“>:http://scikit-learn.org/stable/auto_examples/index.html 、
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