sklearn矩阵分解类库学习

sklearn.decomposition模块提供矩阵分解算法、其他PCA、NMF 或ICA，其中大部分算法都被视为降维技术。

①主成分分析：sklearn.decomposition.PCA(n_components=None, copy=True, whiten=False, svd_solver=’auto’, tol=0.0, iterated_power=’auto’, random_state=None)

主要参数说明：

n_components：参数主要用于指定保留的特征个数，其数据类型为整数、浮点数、None或字符型。若n_components为None时，表示保留所有特征；若n_components为整数时，表示保留的特征个数；若n_components为浮点数时，表示保留后特征的方差之和占所有特征方差的最小阈值；若n_components = ‘mle’ and svd_solver = ‘full’时，该算法会用MLE算法去选择保留的特征。

whiten：表示对保留后的特征数据是否进行标准化(转化成特征方差都为1)标识

svd_solver : SVD分解方式，可选项‘auto’, ‘full’, ‘arpack’, ‘randomized’

构建简单例子

In [1]: import numpy as np   ...: import matplotlib.pyplot as plt   ...: from mpl_toolkits.mplot3d import Axes3D   ...: from sklearn.datasets.samples_generator import make_blobs   ...: X, y = make_blobs(n_samples=10000, n_features=3, centers=[[3,3, 3], [0,   ...: 0,0], [1,1,1], [2,2,2]], cluster_std=[0.2, 0.1, 0.2, 0.2],   ...:                   random_state =9)   ...: fig = plt.figure()   ...: ax = Axes3D(fig, rect=[0, 0, 1, 1], elev=30, azim=20)   ...: plt.scatter(X[:, 0], X[:, 1], X[:, 2],marker='o')   ...: plt.show()   ...:

利用PCA训练数据情况：

a、n_components=None,保留所有特征

In [2]: from sklearn.decomposition import PCA   ...: pca = PCA()   ...: pca.fit(X)   ...: print(pca.n_components_)   ...:3

训练后，观察三个特征的方差及方差比

In [3]: pca.explained_variance_Out[3]: array([ 3.78483785,  0.03272285,  0.03201892])In [4]: pca.explained_variance_ratio_Out[4]: array([ 0.98318212,  0.00850037,  0.00831751])

b、n_components为整数M，若M小于X的特征总数，则挑选前M个方差大的特征

In [5]: from sklearn.decomposition import PCA   ...: pca = PCA(n_components=2)#保留2个特征值   ...: pca.fit(X)   ...: print(pca.explained_variance_)   ...: print(pca.explained_variance_ratio_)   ...:[ 3.78483785  0.03272285][ 0.98318212  0.00850037]

c、n_components为浮点数，选择特征方差占比大于阈值n_components的最大特征方差且特征个数最小

In [6]: pca = PCA(n_components=0.006)   ...: pca.fit(X)   ...: print(pca.explained_variance_)   ...: print(pca.explained_variance_ratio_)   ...: print(pca.n_components_)   ...:[ 3.78483785][ 0.98318212]1

d、n_components为mle时，svd_solver参数必须为full，否则报错

In [7]: pca = PCA(n_components='mle',svd_solver='full')   ...: pca.fit(X)   ...: print(pca.explained_variance_)   ...: print(pca.explained_variance_ratio_)   ...: print(pca.n_components_)   ...:[ 3.78483785][ 0.98318212]1In [8]: pca = PCA(n_components='mle',svd_solver='arpack')   ...: pca.fit(X)   ...:---------------------------------------------------------------------------ValueError                                Traceback (most recent call last)<ipython-input-8-b62bafac46ff> in <module>()      1 pca = PCA(n_components='mle',svd_solver='arpack')----> 2 pca.fit(X)d:\softwore\python\lib\site-packages\sklearn\decomposition\pca.py in fit(self, X, y)    305             Returns the instance itself.    306         """--> 307         self._fit(X)    308         return self    309d:\softwore\python\lib\site-packages\sklearn\decomposition\pca.py in _fit(self,X)    368             return self._fit_full(X, n_components)    369         elif svd_solver in ['arpack', 'randomized']:--> 370             return self._fit_truncated(X, n_components, svd_solver)    371    372     def _fit_full(self, X, n_components):d:\softwore\python\lib\site-packages\sklearn\decomposition\pca.py in _fit_truncated(self, X, n_components, svd_solver)    433             raise ValueError("n_components=%r cannot be a string "    434                              "with svd_solver='%s'"--> 435                              % (n_components, svd_solver))    436         elif not 1 <= n_components <= n_features:    437             raise ValueError("n_components=%r must be between 1 and "ValueError: n_components='mle' cannot be a string with svd_solver='arpack'In [9]: pca = PCA(n_components='mle',svd_solver='randomized')   ...: pca.fit(X)   ...:---------------------------------------------------------------------------ValueError                                Traceback (most recent call last)<ipython-input-9-1f9c5b9ac3af> in <module>()      1 pca = PCA(n_components='mle',svd_solver='randomized')----> 2 pca.fit(X)d:\softwore\python\lib\site-packages\sklearn\decomposition\pca.py in fit(self, X, y)    305             Returns the instance itself.    306         """--> 307         self._fit(X)    308         return self    309d:\softwore\python\lib\site-packages\sklearn\decomposition\pca.py in _fit(self,X)    368             return self._fit_full(X, n_components)    369         elif svd_solver in ['arpack', 'randomized']:--> 370             return self._fit_truncated(X, n_components, svd_solver)    371    372     def _fit_full(self, X, n_components):d:\softwore\python\lib\site-packages\sklearn\decomposition\pca.py in _fit_truncated(self, X, n_components, svd_solver)    433             raise ValueError("n_components=%r cannot be a string "    434                              "with svd_solver='%s'"--> 435                              % (n_components, svd_solver))    436         elif not 1 <= n_components <= n_features:    437             raise ValueError("n_components=%r must be between 1 and "ValueError: n_components='mle' cannot be a string with svd_solver='randomized'In [10]: pca = PCA(n_components='mle')    ...: pca.fit(X)    ...:---------------------------------------------------------------------------TypeError                                 Traceback (most recent call last)<ipython-input-10-92060cf30409> in <module>()      1 pca = PCA(n_components='mle')----> 2 pca.fit(X)d:\softwore\python\lib\site-packages\sklearn\decomposition\pca.py in _fit(self,X)    358             if max(X.shape) <= 500:    359                 svd_solver = 'full'--> 360             elif n_components >= 1 and n_components < .8 * min(X.shape):    361                 svd_solver = 'randomized'    362             # This is also the case of n_components in (0,1)TypeError: unorderable types: str() >= int()