python中的线性判别分析

Question

我在python中进行线性判别分析，但遇到了一些问题。使用给定here的教程能够使用python计算线性判别分析并获得如下图：

使用下面给出的代码：

import pandas as pd
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 = pd.io.parsers.read_csv(
filepath_or_buffer='https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data',
header=None,
sep=',',
)

df.columns = [l for i,l in sorted(feature_dict.items())] + ['class label']
df.dropna(how="all", inplace=True)


from sklearn.preprocessing import LabelEncoder
X = df[[0,1,2,3]].values
y = df['class label'].values
enc = LabelEncoder()
label_encoder = enc.fit(y)
y = label_encoder.transform(y) + 1
label_dict = {1: 'Setosa', 2: 'Versicolor', 3:'Virginica'}


from matplotlib import pyplot as plt
import numpy as np
import math


np.set_printoptions(precision=4)
mean_vectors = []
for cl in range(1,4):
    mean_vectors.append(np.mean(X[y==cl], axis=0))
    print('Mean Vector class %s: %s\n' %(cl, mean_vectors[cl-1]))

S_W = np.zeros((4,4))
for cl,mv in zip(range(1,4), mean_vectors):
    class_sc_mat = np.zeros((4,4))        # scatter matrix for every class
for row in X[y == cl]:
    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('within-class Scatter Matrix:\n', S_W)


overall_mean = np.mean(X, axis=0)
S_B = np.zeros((4,4))
for i,mean_vec in enumerate(mean_vectors):  
    n = X[y==i+1,:].shape[0]
    mean_vec = mean_vec.reshape(4,1) # make column vector
    overall_mean = overall_mean.reshape(4,1) # make column vector
    S_B += n * (mean_vec - overall_mean).dot((mean_vec - overall_mean).T)
print('between-class Scatter Matrix:\n', S_B)


eig_vals, eig_vecs = np.linalg.eig(np.linalg.inv(S_W).dot(S_B))
for i in range(len(eig_vals)):
    eigvec_sc = eig_vecs[:,i].reshape(4,1)   
    print('\nEigenvector {}: \n{}'.format(i+1, eigvec_sc.real))
    print('Eigenvalue {:}: {:.2e}'.format(i+1, eig_vals[i].real))


for i in range(len(eig_vals)):
    eigv = eig_vecs[:,i].reshape(4,1)
    np.testing.assert_array_almost_equal(
    np.linalg.inv(S_W).dot(S_B).dot(eigv),
    eig_vals[i] * eigv,
    decimal=6, err_msg='', verbose=True)

# 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 list is correctly sorted by decreasing eigenvalues

print('Eigenvalues in decreasing order:\n')
for i in eig_pairs:
    print(i[0])



print('Variance explained:\n')
eigv_sum = sum(eig_vals)
for i,j in enumerate(eig_pairs):
    print('eigenvalue {0:}: {1:.2%}'.format(i+1, (j[0]/eigv_sum).real))


W = np.hstack((eig_pairs[0][1].reshape(4,1),eig_pairs[1][1].reshape(4,1)))
print('Matrix W:\n', W.real)
X_lda = X.dot(W)

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()

plot_step_lda()

但我想要一个如下图所示的情节：

第二个图（即显示变量的图）可以在xlstat中创建，但我想用python创建它。有什么方法可以搞清楚吗？