[人工智能]降维：LDA(线性判别分析)

#1.读取数据（可以下载，也可以直接读取）
   #下载
from os import read, sep
import pandas as pd
# df = pd.io.parsers.read_csv(filepath='https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data',
#                 header=None,sep=",",)
    #读取
df = pd.read_csv("iris.data")
 #指定列名
feature_dict = {i:label for i,label in zip(range(4),
            ('sepal length in cm',
            'sepal width in cm',
            'petal length in cm',
            'petal width in cm', ))}

df.columns = [l for i,l in sorted(feature_dict.items())] + ['class label']
print(df.head())

#2.需要将四维降到二维，特征已经是数值数据，不许处理但需转换标签
from sklearn.preprocessing import LabelEncoder
X = df[['sepal length in cm','sepal width in cm','petal length in cm','petal width in cm']].values
y = df['class label'].values

enc =LabelEncoder()
label_encoder = enc.fit(y)
y = label_encoder.transform(y) + 1

import numpy as np
#设置小数点数
np.set_printoptions(precision=4)
# 创建列表保存均值
mean_vectors = []
for yi in range(1,4):    # y = 1，2，3
    #求当前类别的各个特征的均值
    mean_vectors.append(np.mean(X[y==yi], axis=0))   #     axis=0 按行求平均值
    print('均值的类别 %s: %s\n' %(yi, mean_vectors[yi-1]))    #两个%s分别对应元组中第一个和第二个元素

#3.计算散布矩阵
#原始数据中的四个特征  
S_W = np.zeros((4,4))
# 分别计算三个类别自己的
for cl,mv in zip(range(1,4), mean_vectors):
    class_sc_mat = np.zeros((4,4))                  # 每个类的散点矩阵 
    #选中属于当前列别的数据
    for row in X[y == cl]:  #cl取1，2，3
        #这里对各个特征进行分别进行计算
        row, mv = row.reshape(4,1), mv.reshape(4,1) # make column vectors
        class_sc_mat += (row-mv).dot((row-mv).T)
    S_W += class_sc_mat                             # sum class scatter matrices
print('类内的散布矩阵:\n', S_W)

#全局的均值
overall_mean = np.mean(X, axis=0)
#构建类间散布矩阵
S_B = np.zeros((4,4))
#对各个类别进行计算
for i,mean_vec in enumerate(mean_vectors):  
    #当前类别的样本数
    n = X[y==i+1,:].shape[0]
    mean_vec = mean_vec.reshape(4,1) # 做列向量
    overall_mean = overall_mean.reshape(4,1) # make column vector
    #安照公式计算
    S_B += n * (mean_vec - overall_mean).dot((mean_vec - overall_mean).T)

print('类间散布矩阵:\n', S_B)

#得到了两个散布矩阵后，组合在一起，然后求矩阵的特征向量
eig_vals, eig_vecs = np.linalg.eig(np.linalg.inv(S_W).dot(S_B))
#得到每一个特征值和对应的特征向量
for i in range(len(eig_vals)):
    eigvec_sc = eig_vecs[:,i].reshape(4,1)   
    print('\n特征向量 {}: \n{}'.format(i+1, eigvec_sc.real))
    print('特征值 {:}: {:.2e}'.format(i+1, eig_vals[i].real))

#Make a list of (eigenvalue, eigenvector) tuples
eig_pairs = [(np.abs(eig_vals[i]), eig_vecs[:,i]) for i in range(len(eig_vals))]
# Sort the (eigenvalue, eigenvector) tuples from high to low
eig_pairs = sorted(eig_pairs, key=lambda k: k[0], reverse=True)
# Visually confirm that the list is correctly sorted by decreasing eigenvalues
print('按降序排列的特征值特征值排序结果:\n')
for i in eig_pairs:
    print(i[0])

print('特征值占总体的百分率:\n')
eigv_sum = sum(eig_vals)
for i,j in enumerate(eig_pairs):
    print('特征值 {0:}: {1:.2%}'.format(i+1, (j[0]/eigv_sum).real))  #:.2%保留两位有效小数


#选取前两维的特征
W = np.hstack((eig_pairs[0][1].reshape(4,1), eig_pairs[1][1].reshape(4,1)))
print('Matrix W:\n', W.real)

#执行降维操作
X_lda = X.dot(W)
assert X_lda.shape == (149,2), "The matrix is not 150x2 dimensional."



#可视化展示
from matplotlib import pyplot as plt
label_dict = {1: 'Setosa', 2: 'Versicolor', 3:'Virginica'}

#在原始数据中随机选取两维进行展示

def plot_step_():
    ax = plt.subplot(111)
    for label,marker,color in zip(
        range(1,4),('^', 's', 'o'),('blue', 'red', 'green')):

        plt.scatter(x=X[:,0].real[y == label],
                y=X[:,1].real[y == label],
                marker=marker,
                color=color,
                alpha=0.5,
                label=label_dict[label]
                )

    plt.xlabel('LD1')
    plt.ylabel('LD2')

    leg = plt.legend(loc='upper right', fancybox=True)
    leg.get_frame().set_alpha(0.5)
    plt.title('降维前随机选取的2维数据')

    # hide axis ticks
    plt.tick_params(axis="both", which="both", bottom="off", top="off",  
            labelbottom="on", left="off", right="off", labelleft="on")

    # remove axis spines
    ax.spines["top"].set_visible(False)  
    ax.spines["right"].set_visible(False)
    ax.spines["bottom"].set_visible(False)
    ax.spines["left"].set_visible(False)    

    plt.grid()
    plt.tight_layout
    plt.show()

plot_step_()

def plot_step_lda():

    ax = plt.subplot(111)
    for label,marker,color in zip(
        range(1,4),('^', 's', 'o'),('blue', 'red', 'green')):

        plt.scatter(x=X_lda[:,0].real[y == label],
                y=X_lda[:,1].real[y == label],
                marker=marker,
                color=color,
                alpha=0.5,
                label=label_dict[label]
                )

    plt.xlabel('LD1')
    plt.ylabel('LD2')

    leg = plt.legend(loc='upper right', fancybox=True)
    leg.get_frame().set_alpha(0.5)
    plt.title('LDA: Iris projection onto the first 2 linear discriminants')

    # hide axis ticks
    plt.tick_params(axis="both", which="both", bottom="off", top="off",  
            labelbottom="on", left="off", right="off", labelleft="on")

    # remove axis spines
    ax.spines["top"].set_visible(False)  
    ax.spines["right"].set_visible(False)
    ax.spines["bottom"].set_visible(False)
    ax.spines["left"].set_visible(False)    

    plt.grid()
    plt.tight_layout
    plt.show()






def plot_scikit_lda(X, title):

    ax = plt.subplot(111)
    for label,marker,color in zip(
        range(1,4),('^', 's', 'o'),('blue', 'red', 'green')):

        plt.scatter(x=X[:,0][y == label],
                    y=X[:,1][y == label] * -1, # flip the figure
                    marker=marker,
                    color=color,
                    alpha=0.5,
                    label=label_dict[label])

    plt.xlabel('LD1')
    plt.ylabel('LD2')

    leg = plt.legend(loc='upper right', fancybox=True)
    leg.get_frame().set_alpha(0.5)
    plt.title(title)

    # hide axis ticks
    plt.tick_params(axis="both", which="both", bottom="off", top="off",  
            labelbottom="on", left="off", right="off", labelleft="on")

    # remove axis spines
    ax.spines["top"].set_visible(False)  
    ax.spines["right"].set_visible(False)
    ax.spines["bottom"].set_visible(False)
    ax.spines["left"].set_visible(False)    

    plt.grid()
    plt.tight_layout
    plt.show()



from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA

# LDA方法直接
sklearn_lda = LDA(n_components=2)
X_lda_sklearn = sklearn_lda.fit_transform(X, y)

plot_step_lda()
plot_scikit_lda(X_lda_sklearn, title='默认 LDA via scikit-learn')







# Python3 输入和输出
# str.format() 的基本使用如下:
print('{}网址： "{}!"'.format('菜鸟教程', 'www.runoob.com'))
# 菜鸟教程网址： "www.runoob.com!"

# 在括号中的数字用于指向传入对象在 format() 中的位置
print('{0} 和 {1}'.format('Google', 'Runoob'))
# Google 和 Runoob
print('{1} 和 {0}'.format('Google', 'Runoob'))
# Runoob 和 Google

format("关键字参数")
print('{name}网址： {site}'.format(name='菜鸟教程', site='www.runoob.com'))
# 菜鸟教程网址： www.runoob.com

# 位置及关键字参数可以任意的结合:
print('站点列表 {0}, {1}, 和 {other}。'.format('Google', 'Runoob', other='Taobao'))
# 站点列表 Google, Runoob, 和 Taobao。