sklearn实战-乳腺癌细胞数据挖掘（博主亲自录制视频）

因子得分（factor score）

因子得分是各变量的线性组合。

经过程序运算，x_i不是原始变量，而是标准化变量

f1=[-0.105,0.18,0.3,0.372,-0.104,0.281]

1985481.5535567512

运算结果和答案不符合，说明 x_i不是原始变量，而是标准化变量

A scree plot displays the eigenvalues associated with a component or factor in descending order versus the number of the component or factor. You can use scree plots in principal components analysis and factor analysis to visually assess which components or factors explain most of the variability in the data. 碎石图用于主成分分析或因子分析

横轴是因子，纵轴是特征值 
观察第五个因素后，斜率慢慢变缓，前五个因素解释了大部分原因。

A factor analysis was conducted on 12 different characteristics of job applicants. This scree plot shows that 5 of those factors explain most of the variability because the line starts to straighten after factor 5. The remaining factors explain a very small proportion of the variability and are likely unimportant.

The ideal pattern in a scree plot is a steep curve, followed by a bend and then a flat or horizontal line. Retain those components or factors in the steep curve before the first point that starts the flat line trend. You might have difficulty interpreting a scree plot. Use your knowledge of the data and the results from the other approaches of selecting components or factors to help decide the number of important components or factors.

碎石图中，前三个因子特征根值大于1，可以被筛选

• fit(X,y=None)

fit()可以说是scikit-learn中通用的方法，每个需要训练的算法都会有fit()方法，它其实就是算法中的“训练”这一步骤。因为PCA是无监督学习算法，此处y自然等于None。

• fit_transform(X)

用X来训练PCA模型，同时返回降维后的数据。

• inverse_transform()

将降维后的数据转换成原始数据，X=pca.inverse_transform(newX)

• transform(X)

将数据X转换成降维后的数据。当模型训练好后，对于新输入的数据，都可以用transform方法来降维。

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
%matplotlib inline
from sklearn.datasets.samples_generator import make_blobs
# X为样本特征，Y为样本簇类别， 共1000个样本，每个样本3个特征，共4个簇
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')

from sklearn.decomposition import PCA
pca = PCA(n_components=3)
pca.fit(X)
print pca.explained_variance_ratio_
print pca.explained_variance_

pca = PCA(n_components=2)
pca.fit(X)
print pca.explained_variance_ratio_
print pca.explained_variance_

X_new = pca.transform(X)
plt.scatter(X_new[:, 0], X_new[:, 1],marker='o')
plt.show()

pca = PCA(n_components=0.95)
pca.fit(X)
print pca.explained_variance_ratio_
print pca.explained_variance_
print pca.n_components_

[ 0.98318212]
[ 3.78483785]
1

pca = PCA(n_components=0.99)
pca.fit(X)
print pca.explained_variance_ratio_
print pca.explained_variance_
print pca.n_components_

pca = PCA(n_components='mle')
pca.fit(X)
print pca.explained_variance_ratio_
print pca.explained_variance_
print pca.n_components_

# -*- coding: utf-8 -*-
"""
Created on Thu Apr 5 22:44:32 2018

@author: Administrator
"""
from sklearn.datasets import load_breast_cancer
from sklearn.decomposition import PCA
import numpy as np

X = np.array([[-1, -1], [-2, -1], [-3, -2], [1, 1], [2, 1], [3, 2]])
pca = PCA(n_components=2)
pca.fit(X)
#保留两个因子
PCA(copy=True, n_components=2, whiten=False)

#可以看到第一个特征的单个变量方差贡献率已经到达0.99,意味着几乎保留了所有的信息。所以只保留一个特征即可
print("two component explained_variance_ratio_:")
print(pca.explained_variance_ratio_)
'''
[ 0.99244289 0.00755711]
'''

#自动保留因子，现在我们将n_components设置成"mle",发现自动保留了一个特征。
pca_auto=PCA(n_components='mle')
pca_auto.fit(X)
print("mle explained_variance_ratio_:")
print(pca_auto.explained_variance_ratio_)
'''
[ 0.99244289]
'''

pca1=PCA(n_components=1)
#返回降维后的数据newData
newData=pca1.fit_transform(X)
#将降维后的数据转换成原始数据，X=pca.inverse_transform(newX)
#测试结果不对
original_data=pca1.inverse_transform(newData)

'''
cancer=load_breast_cancer()
data=cancer.data
pca_cancer=PCA(n_components='mle')
pca_cancer.fit(data)
print("cancer data explained_variance_ratio_:")
print(pca_cancer.explained_variance_ratio_)
'''

# -*- coding: utf-8 -*-
"""
Created on Thu Apr  5 23:32:12 2018@author: Administrator
"""import numpy as np
import matplotlib.pyplot as pltfrom sklearn import linear_model, decomposition, datasets
from sklearn.pipeline import Pipeline
from sklearn.model_selection import GridSearchCV
from sklearn.datasets import load_breast_cancercancer=load_breast_cancer()logistic = linear_model.LogisticRegression()pca = decomposition.PCA()
pipe = Pipeline(steps=[('pca', pca), ('logistic', logistic)])digits = load_breast_cancer()
X_digits = cancer.data
y_digits = digits.target# Plot the PCA spectrum
pca.fit(X_digits)plt.figure(1, figsize=(4, 3))
plt.clf()
plt.axes([.2, .2, .7, .7])
plt.plot(pca.explained_variance_, linewidth=2)
plt.axis('tight')
plt.xlabel('n_components')
plt.ylabel('explained_variance_')# Prediction
n_components = [10, 20, 30]
Cs = np.logspace(-4, 4, 3)# Parameters of pipelines can be set using ‘__’ separated parameter names:
estimator = GridSearchCV(pipe,dict(pca__n_components=n_components,logistic__C=Cs))
estimator.fit(X_digits, y_digits)plt.axvline(estimator.best_estimator_.named_steps['pca'].n_components,linestyle=':', label='n_components chosen')
plt.legend(prop=dict(size=12))
plt.show()

# -*- coding: utf-8 -*-
"""
Created on Thu Apr 5 23:32:12 2018
@author: Administrator

pca =PCA(n_components='mle')报错
elif n_components >= 1 and n_components < .8 * min(X.shape):

TypeError: '>=' not supported between instances of 'str' and 'int'
"""

import numpy as np
import matplotlib.pyplot as plt
from sklearn import linear_model, decomposition, datasets
from sklearn.pipeline import Pipeline
from sklearn.model_selection import GridSearchCV
from sklearn.datasets import load_breast_cancer
from sklearn.decomposition import PCA

cancer=load_breast_cancer()
pca =PCA(n_components=0.98)
#pca= PCA(n_components='mle')

digits = load_breast_cancer()
X_digits = cancer.data
y_digits = digits.target

# Plot the PCA spectrum
pca.fit(X_digits)
print (pca.explained_variance_ratio_)
print (pca.explained_variance_)
print (pca.n_components_)

#计算协方差
pca.get_covariance()
#Estimated precision of data.计算数据估计的准确性
pca.get_precision()

'''
返回模型参数
{'copy': True,
'iterated_power': 'auto',
'n_components': 0.98,
'random_state': None,
'svd_solver': 'auto',
'tol': 0.0,
'whiten': False}
'''
pca.get_params(deep=True)
#返回降维后的数据
new_data=pca.fit_transform(X_digits)
#返回原始数据,测试结果和原始数据不一致
origin_data=pca.inverse_transform(new_data)

# -*- coding: utf-8 -*-
"""
Created on Sun Apr  8 23:39:10 2018@author: Administratorscikit中的make_blobs方法常被用来生成聚类算法的测试数据，直观地说，make_blobs会根据
用户指定的特征数量、中心点数量、范围等来生成几类数据，这些数据可用于测试聚类算法的效果
"""import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from sklearn.datasets.samples_generator import make_blobsfrom sklearn.decomposition import PCA# X为样本特征，Y为样本簇类别， 共1000个样本，每个样本3个特征，共4个簇
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')'''
我们先不降维，只对数据进行投影，看看投影后的三个维度的方差分布.
可以看出投影后三个特征维度的方差比例大约为98.3%：0.8%：0.8%。投影后第一个特征占了绝大多数的主成分比例。
'''
pca = PCA(n_components=3)
pca.fit(X)
print (pca.explained_variance_ratio_)
print (pca.explained_variance_)'''
现在我们来进行降维，从三维降到2维
'''
pca1 = PCA(n_components=2)
pca1.fit(X)
print (pca1.explained_variance_ratio_)
print (pca1.explained_variance_)'''
可见降维后的数据依然可以很清楚的看到我们之前三维图中的4个簇
'''
X_new = pca1.transform(X)
plt.scatter(X_new[:, 0], X_new[:, 1],marker='o')
plt.show()'''
现在我们看看不直接指定降维的维度，而指定降维后的主成分方差和比例
我们指定了主成分至少占95%，输出如下：[ 0.98318212]
[ 3.78483785]
1可见只有第一个投影特征被保留。这也很好理解，我们的第一个主成分占投影特征的方差比例高达98%。
只选择这一个特征维度便可以满足95%的阈值。
'''
pca2 = PCA(n_components=0.95)
pca2.fit(X)
print (pca2.explained_variance_ratio_)
print (pca2.explained_variance_)
print (pca2.n_components_)'''
我们现在选择阈值99%看看此时的输出如下：[ 0.98318212  0.00850037]
[ 3.78483785  0.03272285]
2这个结果也很好理解，因为我们第一个主成分占了98.3%的方差比例，第二个主成分占了0.8%的方差比例，两者一起可以满足我们的阈值。
'''
pca3 = PCA(n_components=0.99)
pca3.fit(X)
print (pca3.explained_variance_ratio_)
print (pca3.explained_variance_)
print (pca3.n_components_)'''
最后我们看看让MLE算法自己选择降维维度的效果输出结果如下：[ 0.98318212]
[ 3.78483785]
1可见由于我们的数据的第一个投影特征的方差占比高达98.3%，MLE算法只保留了我们的第一个特征。
'''
pca4 = PCA(n_components='mle')
#pca4 = PCA()
pca4.fit(X)
print (pca4.explained_variance_ratio_)
print (pca4.explained_variance_)
print (pca4.n_components_)

# -*- coding: utf-8 -*-
"""
Created on Thu Apr  5 22:44:32 2018@author: Administrator
"""
from __future__ import print_functionfrom time import time
import logging
import matplotlib.pyplot as pltfrom sklearn.model_selection import train_test_split
from sklearn.model_selection import GridSearchCV
from sklearn.datasets import fetch_lfw_people
from sklearn.metrics import classification_report
from sklearn.metrics import confusion_matrix
from sklearn.decomposition import PCA
from sklearn.svm import SVCprint(__doc__)# Display progress logs on stdout
logging.basicConfig(level=logging.INFO, format='%(asctime)s %(message)s')# #############################################################################
# Download the data, if not already on disk and load it as numpy arrayslfw_people = fetch_lfw_people(min_faces_per_person=70, resize=0.4)# introspect the images arrays to find the shapes (for plotting)
n_samples, h, w = lfw_people.images.shape# for machine learning we use the 2 data directly (as relative pixel
# positions info is ignored by this model)
X = lfw_people.data
n_features = X.shape[1]# the label to predict is the id of the person
y = lfw_people.target
target_names = lfw_people.target_names
n_classes = target_names.shape[0]print("Total dataset size:")
print("n_samples: %d" % n_samples)
print("n_features: %d" % n_features)
print("n_classes: %d" % n_classes)# #############################################################################
# Split into a training set and a test set using a stratified k fold# split into a training and testing set
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.25, random_state=42)# #############################################################################
# Compute a PCA (eigenfaces) on the face dataset (treated as unlabeled
# dataset): unsupervised feature extraction / dimensionality reduction
n_components = 150print("Extracting the top %d eigenfaces from %d faces"% (n_components, X_train.shape[0]))
t0 = time()
pca = PCA(n_components=n_components, svd_solver='randomized',whiten=True).fit(X_train)
print("done in %0.3fs" % (time() - t0))eigenfaces = pca.components_.reshape((n_components, h, w))print("Projecting the input data on the eigenfaces orthonormal basis")
t0 = time()
X_train_pca = pca.transform(X_train)
X_test_pca = pca.transform(X_test)
print("done in %0.3fs" % (time() - t0))# #############################################################################
# Train a SVM classification modelprint("Fitting the classifier to the training set")
t0 = time()
param_grid = {'C': [1e3, 5e3, 1e4, 5e4, 1e5],'gamma': [0.0001, 0.0005, 0.001, 0.005, 0.01, 0.1], }
clf = GridSearchCV(SVC(kernel='rbf', class_weight='balanced'), param_grid)
clf = clf.fit(X_train_pca, y_train)
print("done in %0.3fs" % (time() - t0))
print("Best estimator found by grid search:")
print(clf.best_estimator_)# #############################################################################
# Quantitative evaluation of the model quality on the test setprint("Predicting people's names on the test set")
t0 = time()
y_pred = clf.predict(X_test_pca)
print("done in %0.3fs" % (time() - t0))print(classification_report(y_test, y_pred, target_names=target_names))
print(confusion_matrix(y_test, y_pred, labels=range(n_classes)))# #############################################################################
# Qualitative evaluation of the predictions using matplotlibdef plot_gallery(images, titles, h, w, n_row=3, n_col=4):"""Helper function to plot a gallery of portraits"""plt.figure(figsize=(1.8 * n_col, 2.4 * n_row))plt.subplots_adjust(bottom=0, left=.01, right=.99, top=.90, hspace=.35)for i in range(n_row * n_col):plt.subplot(n_row, n_col, i + 1)plt.imshow(images[i].reshape((h, w)), cmap=plt.cm.gray)plt.title(titles[i], size=12)plt.xticks(())plt.yticks(())# plot the result of the prediction on a portion of the test setdef title(y_pred, y_test, target_names, i):pred_name = target_names[y_pred[i]].rsplit(' ', 1)[-1]true_name = target_names[y_test[i]].rsplit(' ', 1)[-1]return 'predicted: %s\ntrue:      %s' % (pred_name, true_name)prediction_titles = [title(y_pred, y_test, target_names, i)for i in range(y_pred.shape[0])]plot_gallery(X_test, prediction_titles, h, w)# plot the gallery of the most significative eigenfaceseigenface_titles = ["eigenface %d" % i for i in range(eigenfaces.shape[0])]
plot_gallery(eigenfaces, eigenface_titles, h, w)plt.show()

因子分析是一种数据简化的技术，通过研究众多变量之间的内部依赖关系，探求观测数据中的基本结构，并用少数几个假想变量来表示其基本的数据结构。

工具/原料

1.因子分析

2.主成分分析

python风控评分卡建模和风控常识

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