PCA降维实例

快来打我* 2023-07-03 15:29 15阅读 0赞

### 1.导入数据 ###

import numpy as np
    import pandas as pd
    df = pd.read_csv('iris.data')
    df.head()

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70]

### 2.修改列名 ###

df.columns=['sepal_len', 'sepal_wid', 'petal_len', 'petal_wid', 'class']
    df.head()

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70 1]

### 3.赋值 ###

# split data table into data X and class labels y
    
    X = df.iloc[:,0:4].values
    y = df.iloc[:,4].values

### 4.绘图 ###

plt.hist函数讲解

matplotlib.pyplot.hist(x, bins=None, range=None, normed=False, weights=None, cumulative=False, bottom=None, histtype=’bar’, align=’mid’, orientation=’vertical’, rwidth=None, log=False, color=None, label=None, stacked=False, hold=None, data=None, **kwargs)

x : 这个参数是指定每个bin(箱子)分布的数据,对应x轴；  
bins：这个参数指定bin(箱子)的个数,也就是总共有几条条状图；  
range : 设置显示的范围,范围之外的将被舍弃；  
normed : 这个参数指定密度,也就是每个条状图的占比例比,默认为1；  
histtype : 选择展示的类型,默认为bar；  
align : 对齐方式；  
orientation : 直方图方向；  
log : log刻度；  
color : 颜色设置；  
label : 刻度标签。

from matplotlib import pyplot as plt
    import math
    
    label_dict = { 1: 'Iris-Setosa',
                  2: 'Iris-Versicolor',
                  3: 'Iris-Virgnica'}
    
    feature_dict = { 0: 'sepal length [cm]',
                    1: 'sepal width [cm]',
                    2: 'petal length [cm]',
                    3: 'petal width [cm]'}
    
    
    plt.figure(figsize=(8, 6))
    for cnt in range(4):
        plt.subplot(2, 2, cnt+1)
        for lab in ('Iris-setosa', 'Iris-versicolor', 'Iris-virginica'):
            plt.hist(X[y==lab, cnt],
                         label=lab,
                         bins=10,
                         alpha=0.3,)
        plt.xlabel(feature_dict[cnt])
        plt.legend(loc='upper right', fancybox=True, fontsize=8)
    
    plt.tight_layout()
    plt.show()

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70 2]

from sklearn.preprocessing import StandardScaler
    X_std = StandardScaler().fit_transform(X)
    print (X_std)

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70 3]

### 5. 求协方差矩阵 ###

mean_vec = np.mean(X_std, axis=0)
    cov_mat = (X_std - mean_vec).T.dot((X_std - mean_vec)) / (X_std.shape[0]-1)
    print('Covariance matrix \n%s' %cov_mat)

![在这里插入图片描述][20200207210346428.png]

### 6.转置 ###

print('NumPy covariance matrix: \n%s' %np.cov(X_std.T))

![在这里插入图片描述][20200207211103387.png]

### 7.特征值和特征向量 ###

numpy.cov()  
Numpy中的 cov() 可以直接求得矩阵的协方差矩阵。  
numpy.linalg.eig(a)  
参数:

*  a：想要计算奇异值和右奇异值的方阵。

返回值：

*  w：特征值。每个特征值根据它的多重性重复。这个数组将是复杂类型，除非虚数部分为0。当传进的参数a是实数时，得到的特征值是实数。
 *  v：特征向量。

cov_mat = np.cov(X_std.T)
    
    eig_vals, eig_vecs = np.linalg.eig(cov_mat)
    
    print('Eigenvectors \n%s' %eig_vecs)
    print('\nEigenvalues \n%s' %eig_vals)

![在这里插入图片描述][20200207214400642.png]

### 8.将特征值做成特征对 ###

# Make a list of (eigenvalue, eigenvector) tuples
    eig_pairs = [(np.abs(eig_vals[i]), eig_vecs[:,i]) for i in range(len(eig_vals))]
    print (eig_pairs)
    print ('----------')
    # Sort the (eigenvalue, eigenvector) tuples from high to low
    eig_pairs.sort(key=lambda x: x[0], reverse=True)
    
    # Visually confirm that the list is correctly sorted by decreasing eigenvalues
    print('Eigenvalues in descending order:')
    for i in eig_pairs:
        print(i[0])

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70 4]

### 9.COMSUM ###

tot = sum(eig_vals)
    # 归一化成百分制
    var_exp = [(i / tot)*100 for i in sorted(eig_vals, reverse=True)]
    print (var_exp)
    cum_var_exp = np.cumsum(var_exp)
    cum_var_exp

![在这里插入图片描述][20200208142157408.png]COMSUM使用举例

a = np.array([1,2,3,4])
    print (a)
    print ('-----------')
    print (np.cumsum(a))

![在这里插入图片描述][20200210083231863.png]

### 10.绘图操作 ###

bar  
绘制柱形图  
step  
绘制动态越阶函数

plt.figure(figsize=(6, 4))
    
    plt.bar(range(4), var_exp, alpha=0.5, align='center',
                label='individual explained variance')
    plt.step(range(4), cum_var_exp, where='mid',
                 label='cumulative explained variance')
    plt.ylabel('Explained variance ratio')
    plt.xlabel('Principal components')
    plt.legend(loc='best')
    plt.tight_layout()
    plt.show()

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70 5]

### 11.水平组合 ###

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

![在这里插入图片描述][20200210090232550.png]

Y = X_std.dot(matrix_w)
    Y

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70 6]

### 12.原始绘图 ###

plt.figure(figsize=(6, 4))
    for lab, col in zip(('Iris-setosa', 'Iris-versicolor', 'Iris-virginica'),
                            ('blue', 'red', 'green')):
         plt.scatter(X[y==lab, 0],
                    X[y==lab, 1],
                    label=lab,
                    c=col)
    plt.xlabel('sepal_len')
    plt.ylabel('sepal_wid')
    plt.legend(loc='best')
    plt.tight_layout()
    plt.show()

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70 7]

### 13.PCA后绘图 ###

plt.figure(figsize=(6, 4))
    for lab, col in zip(('Iris-setosa', 'Iris-versicolor', 'Iris-virginica'),
                            ('blue', 'red', 'green')):
         plt.scatter(Y[y==lab, 0],
                    Y[y==lab, 1],
                    label=lab,
                    c=col)
    plt.xlabel('Principal Component 1')
    plt.ylabel('Principal Component 2')
    plt.legend(loc='lower center')
    plt.tight_layout()
    plt.show()

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70 8]

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