第10章 Principal Component Analysis 人臉識別（PCA+SVM）

阿新 • • 發佈：2018-12-23

sklearn.decomposition.PCA

Linear dimensionality reduction using Singular Value Decomposition of the data to project it to a lower dimensional space.

PCA 用於對一組連續正交分量中的多變數資料集進行方差最大方向的分解。在 scikit-learn 中， PCA 被實現為一個變換物件，通過 fit 方法可以降維成 n 個成分，並且可以將新的資料投影（project, 亦可理解為分解）到這些成分中。

人臉資料集來自英國劍橋AT&T實驗室，包含40位人員照片，每個人10張。sklearn.datasets自帶此資料集。下載連結：

The Database of Faces_AT&T

import matplotlib.pyplot as plt
import numpy as np

import time
import logging
from sklearn.datasets import fetch_olivetti_faces

logging.basicConfig(level=logging.INFO, format='%(asctime)s %(message)s')

data_home=r'C:\Users\Qiuyi\Desktop\scikit-learn code\code\datasets\olivetti_py3' 

logging.info('Start to load dataset')
faces = fetch_olivetti_faces(data_home=data_home)
logging.info('Done with load dataset')

2018-12-19 23:04:40,449 Start to load dataset
2018-12-19 23:04:40,484 Done with load dataset

logging模組使用教程
預設情況下，logging模組將日誌列印到螢幕上(stdout)，日誌級別為WARNING(即只有日誌級別高於WARNING的日誌資訊才會輸出)。

日誌級別	何時使用
DEBUG	詳細資訊，典型地除錯問題時會感興趣。
INFO	證明事情按預期工作。
WARNING	表明發生了一些意外，或者不久的將來會發生問題（如‘磁碟滿了’）。軟體還是在正常工作。
ERROR	由於更嚴重的問題，軟體已不能執行一些功能了。
CRITICAL	嚴重錯誤，表明軟體已不能繼續運行了。

basicConfig關鍵字引數
format handler使用指明的格式化字串。
%(asctime)s 列印日誌的時間
%(message)s 列印日誌資訊

sklearn.datasets.fetch_olivetti_faces()
如果電腦裡沒有資料集也沒關係，fetch_olivetti_faces()會幫你自動從網上下載並儲存在get_data_home()獲得的地址中。

return

data : numpy array of shape (400, 4096)
Each row corresponds to a ravelled face image of original size 64 x 64 pixels.
images : numpy array of shape (400, 64, 64)
Each row is a face image corresponding to one of the 40 subjects of the dataset.
target : numpy array of shape (400, )
Labels associated to each face image. Those labels are ranging from 0-39 and correspond to the Subject IDs.
DESCR : string
Description of the modified Olivetti Faces Dataset.

2018-12-19 23:34:27,591 Start to load dataset
downloading Olivetti faces from https://ndownloader.figshare.com/files/5976027 to C:\Users\Qiuyi\scikit_learn_data
2018-12-19 23:35:11,625 Done with load dataset

顯示資料的概要資訊：

X = faces.data
y = faces.target
targets = np.unique(faces.target)
target_names = np.array(["c%d" % t for t in targets])
n_targets = target_names.shape[0]
n_samples, h, w = faces.images.shape
print('Sample count: {}\nTarget count: {}'.format(n_samples, n_targets))
print('Image size: {}x{}\nDataset shape: {}\n'.format(w, h, X.shape))

Sample count: 400
Target count: 40
Image size: 64x64
Dataset shape: (400, 4096)

觀察人臉圖片，隨機選擇n_row * n_col個人，並自動調節視窗尺寸：

def plot_gallery(images, titles, h, w, n_row=2, n_col=5):
    """顯示圖片陣列"""
    plt.figure(figsize=(2 * n_col, 2.2 * n_row), dpi=144)
    plt.subplots_adjust(bottom=0, left=.01, right=.99, top=.90, hspace=.01)
    for i in range(n_row * n_col):
        plt.subplot(n_row, n_col, i + 1)
        plt.imshow(images[i].reshape((h, w)), cmap=plt.cm.gray)
        plt.title(titles[i])
        plt.axis('off')
        
n_row = 2
n_col = 6
sample_images = None
sample_titles = []
for i in range(n_targets):
    people_images = X[y==i]
    people_sample_index = np.random.randint(0, people_images.shape[0], 1)
    people_sample_image = people_images[people_sample_index, :]
    if sample_images is not None:
        sample_images = np.concatenate((sample_images, people_sample_image), axis=0)
    else:
        sample_images = people_sample_image
    sample_titles.append(target_names[i])

plot_gallery(sample_images, sample_titles, h, w, n_row, n_col)

在這裡插入圖片描述

劃分訓練集和測試集，並用SVC訓練，預測：

from sklearn.model_selection import train_test_split

X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.2, random_state=4)
from sklearn.svm import SVC

start = time.clock()
print('Fitting train datasets ...')
clf = SVC(class_weight='balanced')
clf.fit(X_train, y_train)
print('Done in {0:.2f}s'.format(time.clock()-start))

Fitting train datasets …
Done in 1.21s

start = time.clock()
print("Predicting test dataset ...")
y_pred = clf.predict(X_test)
print('Done in {0:.2f}s'.format(time.clock()-start))

Predicting test dataset …
Done in 0.17s

from sklearn.metrics import confusion_matrix

cm = confusion_matrix(y_test, y_pred, labels=range(n_targets))
print("confusion matrix:\n")

np.set_printoptions(threshold=np.nan)
#為了確保完整的輸出cm陣列的內容，40x40
print(cm)

confusion matrix:

[[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2]]

混淆矩陣理想的輸出，是對角線上有數字，其他地方都沒有數字。

再看看classification_report的結果：

from sklearn.metrics import classification_report

print(classification_report(y_test, y_pred, target_names=target_names))

	             precision    recall  f1-score   support
	
	         c0       0.00      0.00      0.00         1
	         c1       0.00      0.00      0.00         3
	         c2       0.00      0.00      0.00         2
	         c3       0.00      0.00      0.00         1
	         c4       0.00      0.00      0.00         1
	         c5       0.00      0.00      0.00         1
	         c6       0.00      0.00      0.00         4
	         c7       0.00      0.00      0.00         2
	         c8       0.00      0.00      0.00         4
	         c9       0.00      0.00      0.00         2
	        c10       0.00      0.00      0.00         1
	        c11       0.00      0.00      0.00         0
	        c12       0.00      0.00      0.00         4
	        c13       0.00      0.00      0.00         4
	        c14       0.00      0.00      0.00         1
	        c15       0.00      0.00      0.00         1
	        c16       0.00      0.00      0.00         3
	        c17       0.00      0.00      0.00         2
	        c18       0.00      0.00      0.00         2
	        c19       0.00      0.00      0.00         2
	        c20       0.00      0.00      0.00         1
	        c21       0.00      0.00      0.00         2
	        c22       0.00      0.00      0.00         3
	        c23       0.00      0.00      0.00         2
	        c24       0.00      0.00      0.00         3
	        c25       0.00      0.00      0.00         3
	        c26       0.00      0.00      0.00         2
	        c27       0.00      0.00      0.00         2
	        c28       0.00      0.00      0.00         0
	        c29       0.00      0.00      0.00         2
	        c30       0.00      0.00      0.00         2
	        c31       0.00      0.00      0.00         3
	        c32       0.00      0.00      0.00         2
	        c33       0.00      0.00      0.00         2
	        c34       0.00      0.00      0.00         0
	        c35       0.00      0.00      0.00         2
	        c36       0.00      0.00      0.00         3
	        c37       0.00      0.00      0.00         1
	        c38       0.00      0.00      0.00         2
	        c39       0.00      0.00      0.00         2
	    avg / total   0.00      0.00      0.00        80

C:\Python36\lib\site-packages\sklearn\metrics\classification.py:1135: UndefinedMetricWarning: Precision and F-score are ill-defined and being set to 0.0 in labels with no predicted samples.
‘precision’, ‘predicted’, average, warn_for)
C:\Python36\lib\site-packages\sklearn\metrics\classification.py:1137: UndefinedMetricWarning: Recall and F-score are ill-defined and being set to 0.0 in labels with no true samples.
‘recall’, ‘true’, average, warn_for)

查準率、召回率、F1 Score全為0，可見直接預測效果非常差。

因為把每個畫素都作為輸入特徵來處理，使資料噪聲太嚴重。特徵有4096個，比400個數據集數量還多。而且還要分出20%作為測試資料集。

因此需要使用資料降維：

from sklearn.decomposition import PCA

print("Exploring explained variance ratio for dataset ...")
candidate_components = range(10, 300, 30) #(10,40,70,100,...,250,280)
explained_ratios = []
start = time.clock()
for c in candidate_components:
    pca = PCA(n_components=c)
    X_pca = pca.fit_transform(X)
    explained_ratios.append(np.sum(pca.explained_variance_ratio_))
print('Done in {0:.2f}s'.format(time.clock()-start))

Exploring explained variance ratio for dataset …
Done in 8.13s

PCA(n_components) : int, float, None or string
Number of components to keep. if n_components is not set all components are kept:
n_components == min(n_samples, n_features)

explained_variance_ratio_ : array, shape (n_components,)
經PCA處理後的資料還原率。
Percentage of variance explained by each of the selected components.

plt.figure(figsize=(10, 6), dpi=144)
plt.grid()
plt.plot(candidate_components, explained_ratios)
plt.xlabel('Number of PCA Components')
plt.ylabel('Explained Variance Ratio')
plt.title('Explained variance ratio for PCA')
plt.yticks(np.arange(0.5, 1.05, .05))
plt.xticks(np.arange(0, 300, 20));

在這裡插入圖片描述

取出之前挑選的人臉圖片中的前五個，利用 pca.inverse_transform() 視覺化不同 n_components 下圖片的還原率：

def title_prefix(prefix, title):
    return "{}: {}".format(prefix, title)

n_row = 1
n_col = 5

sample_images = sample_images[0:5]
sample_titles = sample_titles[0:5]

plotting_images = sample_images
plotting_titles = [title_prefix('orig', t) for t in sample_titles] #原始圖片title
candidate_components = [140, 75, 37, 19, 8]
for c in candidate_components:
    print("Fitting and projecting on PCA(n_components={}) ...".format(c))
    start = time.clock()
    pca = PCA(n_components=c)
    pca.fit(X)
    
    X_sample_pca = pca.transform(sample_images) #原始圖片
    X_sample_inv = pca.inverse_transform(X_sample_pca) #還原後的圖片
    plotting_images = np.concatenate((plotting_images, X_sample_inv), axis=0)
    
    sample_title_pca = [title_prefix('{}'.format(c), t) for t in sample_titles]
    plotting_titles = np.concatenate((plotting_titles, sample_title_pca), axis=0)
	#測試圖片title
    print("Done in {0:.2f}s".format(time.clock() - start))

print("Plotting sample image with different number of PCA conpoments ...")
plot_gallery(plotting_images, plotting_titles, h, w,
    n_row * (len(candidate_components) + 1), n_col)

Fitting and projecting on PCA(n_components=140) …
Done in 0.82s
Fitting and projecting on PCA(n_components=75) …
Done in 0.40s
Fitting and projecting on PCA(n_components=37) …
Done in 0.15s
Fitting and projecting on PCA(n_components=19) …
Done in 0.12s
Fitting and projecting on PCA(n_components=8) …
Done in 0.09s
Plotting sample image with different number of PCA conpoments …
在這裡插入圖片描述
可見即使在 n_components=8時，圖片依然能比較清楚地反映出人物的臉部特徵輪廓。

選擇還原率在95%時的 n_components，即140。

n_components = 140

print("Fitting PCA by using training data ...")
start = time.clock()
pca = PCA(n_components=n_components, svd_solver='randomized', whiten=True).fit(X_train)
print("Done in {0:.2f}s".format(time.clock() - start))

print("Projecting input data for PCA ...")
start = time.clock()
X_train_pca = pca.transform(X_train)
X_test_pca = pca.transform(X_test)
print("Done in {0:.2f}s".format(time.clock() - start))

Fitting PCA by using training data …
Done in 0.87s
Projecting input data for PCA …
Done in 0.02s

GridSearchCV

用於系統地遍歷多種引數組合，通過交叉驗證確定最佳效果引數。

estimator —— 分類器
param_grid —— 字典或列表
scoring : 評分函式，例如 scoring=‘roc_auc’，預設None
n_jobs : 並行任務個數，int, default=1
cv : int, 交叉驗證，預設3
verbose：int：日誌冗長度，0：不輸出訓練過程，1：偶爾輸出，>1：對每個子模型都輸出。

return：

best_params_ : dict
Parameter setting that gave the best results on the hold out data.
best_estimator_ : estimator or dict
Estimator that was chosen by the search

sklearn.model_selection.GridSearchCV
Exhaustive search over specified parameter values for an estimator.

from sklearn.model_selection import GridSearchCV

print("Searching the best parameters for SVC ...")
param_grid = {'C': [1, 5, 10, 50, 100],
              'gamma': [0.0001, 0.0005, 0.001, 0.005, 0.01]}
clf = GridSearchCV(SVC(kernel='rbf', class_weight='balanced'), 
						param_grid, verbose=2, n_jobs=4)
clf = clf.fit(X_train_pca, y_train)
print("Best parameters found by grid search:")
print(clf.best_params_)

Searching the best parameters for SVC …
Fitting 3 folds for each of 25 candidates, totalling 75 fits

[Parallel(n_jobs=4)]: Done 36 tasks | elapsed: 2.2s

Best parameters found by grid search:
{‘C’: 10, ‘gamma’: 0.001}

[Parallel(n_jobs=4)]: Done 75 out of 75 | elapsed: 2.8s finished

直接用 GridSearchCV 返回的 best_estimator_ 進行預測：

start = time.clock()
print("Predict test dataset ...")
y_pred = clf.best_estimator_.predict(X_test_pca)
cm = confusion_matrix(y_test, y_pred, labels=range(n_targets))
print("Done in {0:.2f}.\n".format(time.clock()-start))
print("confusion matrix:")
np.set_printoptions(threshold=np.nan)
print(cm)

Predict test dataset …
Done in 0.01.

confusion matrix:
[[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2]]

print(classification_report(y_test, y_pred))

             precision    recall  f1-score   support

          0       0.50      1.00      0.67         1
          1       1.00      0.67      0.80         3
          2       1.00      0.50      0.67         2
          3       1.00      1.00      1.00         1
          4       1.00      1.00      1.00         1
          5       1.00      1.00      1.00         1
          6       1.00      0.75      0.86         4
          7       1.00      1.00      1.00         2
          8       1.00      1.00      1.00         4
          9       1.00      1.00      1.00         2
         10       1.00      1.00      1.00         1
         12       1.00      1.00      1.00         4
         13       1.00      1.00      1.00         4
         14       1.00      1.00      1.00         1
         15       1.00      1.00      1.00         1
         16       0.75      1.00      0.86         3
         17       1.00      1.00      1.00         2
         18       1.00      1.00      1.00         2
         19       1.00      1.00      1.00         2
         20       1.00      1.00      1.00         1
         21       1.00      1.00      1.00         2
         22       0.75      1.00      0.86         3
         23       1.00      1.00      1.00         2
         24       1.00      1.00      1.00         3
         25       0.67      0.67      0.67         3
         26       1.00      1.00      1.00         2
         27       1.00      1.00      1.00         2
         29       1.00      1.00      1.00         2
         30       1.00      1.00      1.00         2
         31       1.00      1.00      1.00         3
         32       1.00      1.00      1.00         2
         33       1.00      1.00      1.00         2
         35       1.00      1.00      1.00         2
         36       1.00      1.00      1.00         3
         37       1.00      1.00      1.00         1
         38       1.00      1.00      1.00         2
         39       1.00      1.00      1.00         2
avg / total       0.96      0.95      0.95        80

參考網址：

張洋
PCA的數學原理

孟巖
理解矩陣（一）
理解矩陣（二）
理解矩陣（三）

第10章 Principal Component Analysis 人臉識別（PCA+SVM）

sklearn.decomposition.PCA

參考網址：

第10章 Principal Component Analysis 人臉識別（PCA+SVM）

第十八天呼叫攝像頭人臉識別（有誤判）

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人臉識別（初學篇）-VS2015+opencv3.2的配置

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【練習題】第六章--有返回值的函式（Think Python）

《機器學習》周志華學習筆記第七章貝葉斯分類器（課後習題）python 實現

【RTX作業系統教程】第5章 RTX作業系統庫方式移植（超級簡單）

【2018.12.24】python3.7+OpenCV 人臉識別（圖片+攝像頭）

演算法競賽入門經典(第二版)-劉汝佳-第三章陣列與字串例題+習題（17/18）

【SpringCloud Greenwich版本】第八章：配置中心客戶端（config client）

【SpringCloud Greenwich版本】第七章：配置中心服務端（config server）

利用python、tensorflow、opencv實現人臉識別（包會）！

GZIP壓縮原理分析（04）——第三章 gzip檔案格式詳解（三02） gzip檔案頭

MOOC清華《VC++面向物件與視覺化程式設計》第1章：空白視窗的建立（空專案）

CNN人臉識別（python實現）

Matlab實現手寫數字識別（PCA+KNN）

Coursera-吳恩達-機器學習-第八週-測驗-Principal Component Analysis

第10章 Principal Component Analysis 人臉識別（PCA+SVM）

參考網址：

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