• 機器學習之LDA線性判別分析模型

# -*- coding: utf-8 -*-
"""
Created on Wed Nov 21 21:03:14 2018

@author: muli
"""

import matplotlib.pyplot as plt
import numpy as np
from sklearn import datasets, discriminant_analysis,cross_validation


def load_data():
    '''
    載入用於分類問題的資料集

    :return: 一個元組，用於分類問題。元組元素依次為：訓練樣本集、測試樣本集、訓練樣本集對應的標記、測試樣本集對應的標記
    '''
    # 使用 scikit-learn 自帶的 iris 資料集
    iris=datasets.load_iris() 
    X_train=iris.data
    y_train=iris.target
    # 分層取樣拆分成訓練集和測試集，測試集大小為原始資料集大小的 1/4
    return cross_validation.train_test_split(X_train, y_train,test_size=0.25,
		random_state=0,stratify=y_train)


def test_LinearDiscriminantAnalysis(*data):
    '''
    測試 LinearDiscriminantAnalysis 的用法

    param data: 可變引數。它是一個元組，這裡要求其元素依次為：訓練樣本集、測試樣本集、訓練樣本的標記、測試樣本的標記
    return:  None
    '''
    X_train,X_test,y_train,y_test=data
    # 載入LDA線性判別分析模型
    lda = discriminant_analysis.LinearDiscriminantAnalysis()
    # 訓練模型
    lda.fit(X_train, y_train)
    # 返回 W值 和 b值
    print('Coefficients:%s, intercept %s'%(lda.coef_,lda.intercept_))
    # 返回預測的準確率
    print('Score: %.2f' % lda.score(X_test, y_test))


def plot_LDA(converted_X,y):
    '''
    繪製經過 LDA 轉換後的資料

    :param converted_X: 經過 LDA轉換後的樣本集
    :param y: 樣本集的標記
    :return:  None
    '''
    from mpl_toolkits.mplot3d import Axes3D
    fig=plt.figure()
    ax=Axes3D(fig)
    colors='rgb'
    markers='o*s'
    for target,color,marker in zip([0,1,2],colors,markers):
        pos=(y==target).ravel()
        X=converted_X[pos,:]
        ax.scatter(X[:,0], X[:,1], X[:,2],color=color,marker=marker,
			label="Label %d"%target)
    ax.legend(loc="best")
    fig.suptitle("Iris After LDA")
    plt.show()


def run_plot_LDA():
    '''
    執行 plot_LDA 。
    其中資料集來自於 load_data() 函式

    :return: None
    '''
    X_train,X_test,y_train,y_test=load_data()
    X=np.vstack((X_train,X_test))
    Y=np.vstack((y_train.reshape(y_train.size,1),y_test.reshape(y_test.size,1)))
    lda = discriminant_analysis.LinearDiscriminantAnalysis()
    lda.fit(X, Y)
    converted_X=np.dot(X,np.transpose(lda.coef_))+lda.intercept_
    plot_LDA(converted_X,Y)


def test_LinearDiscriminantAnalysis_solver(*data):
    '''
    測試 LinearDiscriminantAnalysis 的預測效能隨 solver 引數的影響

    :param data: 可變引數。它是一個元組，這裡要求其元素依次為：訓練樣本集、測試樣本集、訓練樣本的標記、測試樣本的標記
    :return:  None
    '''
    X_train,X_test,y_train,y_test=data
    solvers=['svd','lsqr','eigen']
    for solver in solvers:
        if(solver=='svd'):
            lda = discriminant_analysis.LinearDiscriminantAnalysis(solver=solver)
        else:
            lda = discriminant_analysis.LinearDiscriminantAnalysis(solver=solver,
			shrinkage=None)
        lda.fit(X_train, y_train)
        print('Score at solver=%s: %.2f' %(solver, lda.score(X_test, y_test)))


def test_LinearDiscriminantAnalysis_shrinkage(*data):
    '''
    測試  LinearDiscriminantAnalysis 的預測效能隨 shrinkage 引數的影響

    :param data: 可變引數。它是一個元組，這裡要求其元素依次為：訓練樣本集、測試樣本集、訓練樣本的標記、測試樣本的標記
    :return:  None
    '''
    X_train,X_test,y_train,y_test=data
    shrinkages=np.linspace(0.0,1.0,num=20)
    scores=[]
    for shrinkage in shrinkages:
        lda = discriminant_analysis.LinearDiscriminantAnalysis(solver='lsqr',
			shrinkage=shrinkage)
        lda.fit(X_train, y_train)
        scores.append(lda.score(X_test, y_test))
    ## 繪圖
    fig=plt.figure()
    ax=fig.add_subplot(1,1,1)
    ax.plot(shrinkages,scores)
    ax.set_xlabel(r"shrinkage")
    ax.set_ylabel(r"score")
    ax.set_ylim(0,1.05)
    ax.set_title("LinearDiscriminantAnalysis")
    plt.show()


if __name__=='__main__':
    X_train,X_test,y_train,y_test=load_data() # 產生用於分類的資料集
    # 呼叫 test_LinearDiscriminantAnalysis
#    test_LinearDiscriminantAnalysis(X_train,X_test,y_train,y_test)
    # 呼叫 run_plot_LDA
#    run_plot_LDA() 
    # 呼叫 test_LinearDiscriminantAnalysis_solver
#    test_LinearDiscriminantAnalysis_solver(X_train,X_test,y_train,y_test) 
    # 呼叫 test_LinearDiscriminantAnalysis_shrinkage
    test_LinearDiscriminantAnalysis_shrinkage(X_train,X_test,y_train,y_test)