python 降维lda算法的使用_sklearn LDA降维算法

sklearn LDA降维算法

LDA(Linear Discriminant Analysis)线性判断别分析，可以用于降维和分类。其基本思想是类内散度尽可能小，类间散度尽可能大，是一种经典的监督式降维/分类技术。

sklearn代码实现

#coding=utf-8

import pandas as pd

import matplotlib.pyplot as plt

from sklearn.model_selection import train_test_split

from sklearn import datasets

from sklearn.discriminant_analysis import LinearDiscriminantAnalysis

import numpy as np

def main():

iris = datasets.load_iris() #典型分类数据模型

#这里我们数据统一用pandas处理

data = pd.DataFrame(iris.data, columns=iris.feature_names)

data['class'] = iris.target

#这里只取两类

# data = data[data['class']!=2]

#为了可视化方便，这里取两个属性为例

X = data[data.columns.drop('class')]

Y = data['class']

#划分数据集

X_train, X_test, Y_train, Y_test =train_test_split(X, Y)

lda = LinearDiscriminantAnalysis(n_components=2)

lda.fit(X_train, Y_train)

#显示训练结果

print lda.means_ #中心点

print lda.score(X_test, Y_test) #score是指分类的正确率

print lda.scalings_ #score是指分类的正确率

X_2d = lda.transform(X) #现在已经降到二维X_2d=np.dot(X-lda.xbar_,lda.scalings_)

#对于二维数据，我们做个可视化

#区域划分

lda.fit(X_2d,Y)

h = 0.02

x_min, x_max = X_2d[:, 0].min() - 1, X_2d[:, 0].max() + 1

y_min, y_max = X_2d[:, 1].min() - 1, X_2d[:, 1].max() + 1

xx, yy = np.meshgrid(np.arange(x_min, x_max, h),

np.arange(y_min, y_max, h))

Z = lda.predict(np.c_[xx.ravel(), yy.ravel()])

Z = Z.reshape(xx.shape)

plt.contourf(xx, yy, Z, cmap=plt.cm.Paired)

#做出原来的散点图

class1_x = X_2d[Y==0,0]

class1_y = X_2d[Y==0,1]

l1 = plt.scatter(class1_x,class1_y,color='b',label=iris.target_names[0])

class1_x = X_2d[Y==1,0]

class1_y = X_2d[Y==1,1]

l2 = plt.scatter(class1_x,class1_y,color='y',label=iris.target_names[1])

class1_x = X_2d[Y==2,0]

class1_y = X_2d[Y==2,1]

l3 = plt.scatter(class1_x,class1_y,color='r',label=iris.target_names[2])

plt.legend(handles = [l1, l2, l3], loc = 'best')

plt.grid(True)

plt.show()

if __name__ == '__main__':

main()

测试结果

Means: #各类的中心点

[[ 5.00810811 3.41891892 1.44594595 0.23513514]

[ 6.06410256 2.80769231 4.32564103 1.33589744]

[ 6.61666667 2.97222222 5.63055556 2.02777778]]

Score: #对于测试集的正确率

0.973684210526

Scalings:

[[ 1.19870893 0.76465114]

[ 1.20339741 -2.46937995]

[-2.55937543 0.42562073]

[-2.77824826 -2.4470865 ]]

Xbar:

[ 5.89285714 3.0625 3.79375 1.19464286]

#X'=np.dot(X-lda.xbar_,lda.scalings_)默认的线性变化方程