引言
目标在本课程项目中，学生将单独构建人脸识别系统系统学生需要应用主成分分析（PCA）来执行数据降维和可视化，以了解底层数据分布。然后，要求学生训练并应用三种分类模型——线性判别分析（LDA）、支持向量机（SVM）和卷积神经网络（CNN）–对人脸图像进行分类。通过该项目，学生有望获得基本的以及当前流行的模式识别技术的重要知识。编程语言学生可以在项目中使用他们选择的任何语言，尽管至少从MATLAB或Python开始。建议使用MATLAB，因为它提供了一个简单、完整的环境，以及可视化结果。特别是，可以在项目并在网上找到。
【numpy手写系列】用PCA、LDA、SVM与CNN手写人脸识别代码
• PCA based data distribution visualization
• PCA plus nearest neighbor classifification results
• PCA based data distribution visualization
• PCA plus nearest neighbor classifification results
• LDA based data distribution visualization
• LDA plus nearest neighbor classifification results 编辑
工作区文件结构
请务必按照以下结构构建工作区域，取名请随意。
数据集
介绍
项目将在CMU PIE数据集上进行，使用70%的所提供的图像用于训练，剩余的30%用于测试。PIE是一个人脸识别数据集，内含68个人，每个人有170张图片，随机抽样一个人取出2张图片看看：
数据集获取方式：
提取码：3x2z
https://pan.baidu.com/s/172uo2gLluo47wBTbn3LfHA%C2%A0
用于特征提取、可视化和分类的PCA
任务
原始人脸图像的大小为32×32像素，因此每个图像的1024维矢量年龄从CMU PIE训练集中随机抽取500张图片和您自己的照片。应用PCA将矢量化图像的维数分别降低到2和3。可视化二维和三维绘图中的投影数据矢量。突出显示与照片还可视化用于降维的相应3个特征面。然后应用PCA将人脸图像的维数分别降低到40、80和200。使用最近邻规则对测试图像进行分类。报告分类准确性分别在CMU PIE测试图像和您自己的照片上。
实现代码
• PCA based data distribution visualization
-
import os
-
from numpy
import *
-
import numpy
as np
-
import cv2
-
import matplotlib.pyplot
as plt
-
from pylab
import mpl
-
-
def
img2vector(
im_path):
-
im = cv2.imread(im_path,
0)
-
rows, cols = im.shape
-
imgVector = np.zeros((
1, rows * cols))
-
imgVector = np.reshape(im, (
1, rows * cols))
-
return imgVector
-
-
def
load_dataset(
k):
-
faceData_path =
'../PIE'
-
faceData_length =
len(os.listdir(faceData_path))
-
train_face = np.zeros((faceData_length * k,
32 *
32))
-
train_label = np.zeros(faceData_length * k)
-
test_face = np.zeros((faceData_length * (
170 - k),
32 *
32))
-
test_label = np.zeros(faceData_length * (
170 - k))
-
-
sample = random.permutation(
170) +
1
-
-
for i
in
range(faceData_length):
-
people_idx = i +
1
-
if people_idx ==
26:
-
for j
in
range(
10):
-
face_im_path = os.path.join(faceData_path,
str(people_idx),
str(j+
1) +
'.jpg')
-
faceVector_im = img2vector(face_im_path)
-
if j <=
7:
-
train_face[i*k+j, :] = faceVector_im
-
train_label[i*k + j] = people_idx
-
else:
-
test_face[i*(
170-k) + (j-k), :] = faceVector_im
-
test_label[i*(
170-k) + (j-k)] = people_idx
-
-
for j
in
range(
170):
-
face_im_path = os.path.join(faceData_path,
str(people_idx),
str(sample[j]) +
'.jpg')
-
faceVector_im = img2vector(face_im_path)
-
if j < k:
-
train_face[i*k+j, :] = faceVector_im
-
train_label[i*k + j] = people_idx
-
else:
-
test_face[i*(
170-k) + (j-k), :] = faceVector_im
-
test_label[i*(
170-k) + (j-k)] = people_idx
-
-
return train_face, train_label, test_face, test_label
-
-
def
PCA_fit(
data, r):
-
data = np.float32(np.mat(data))
-
rows, cols = np.shape(data)
-
data_mean = np.mean(data,
0)
-
A = data - np.tile(data_mean, (rows,
1))
-
C = A * A.T
-
D, V = np.linalg.eig(C)
-
V_r = V[:,
0:r]
-
V_r = A.T * V_r
-
for i
in
range(r):
-
V_r[:, i] = V_r[:, i] / np.linalg.norm(V_r[:, i])
-
-
final_data = A * V_r
-
return final_data, data_mean, V_r
-
-
if __name__ ==
"__main__":
-
for r
in [
2,
3]:
-
print(
'dimensionality of face images to {}:'.
format(r))
-
x_value = []
-
y_value = []
-
k =
int(
170*
0.9)
-
train_face, train_label, test_face, test_label = load_dataset(k)
-
data_train_new, data_mean, V_r = PCA_fit(train_face[:-
501], r)
-
data_train_new = np.array(data_train_new).astype(
float)
-
if r ==
2:
-
x_plot, y_plot = [], []
-
for data
in data_train_new:
-
x_plot.append(data[
0])
-
y_plot.append(data[
1])
-
fig = plt.figure()
-
plt.scatter(x_plot, y_plot)
-
plt.show()
-
if r ==
3 :
-
x_plot, y_plot, z_plot = [], [], []
-
for data
in data_train_new:
-
x_plot.append(data[
0])
-
y_plot.append(data[
1])
-
z_plot.append(data[
2])
-
fig = plt.figure()
-
ax = fig.add_subplot(
111,projection=
'3d')
-
plt.set_cmap(plt.get_cmap(
"seismic",
100))
-
im = ax.scatter(x_plot, y_plot, z_plot)
-
ax.set_xlabel(
'x')
-
ax.set_ylabel(
'y')
-
ax.set_zlabel(
'z')
-
plt.show()
• PCA plus nearest neighbor classifification results
-
import os
-
from numpy
import *
-
import numpy
as np
-
import cv2
-
import matplotlib.pyplot
as plt
-
from pylab
import mpl
-
-
def
img2vector(
im_path):
-
im = cv2.imread(im_path,
0)
-
rows, cols = im.shape
-
imgVector = np.zeros((
1, rows * cols))
-
imgVector = np.reshape(im, (
1, rows * cols))
-
return imgVector
-
-
def
load_dataset(
k):
-
faceData_path =
'../PIE'
-
faceData_length =
len(os.listdir(faceData_path))
-
train_face = np.zeros((faceData_length * k,
32 *
32))
-
train_label = np.zeros(faceData_length * k)
-
test_face = np.zeros((faceData_length * (
170 - k),
32 *
32))
-
test_label = np.zeros(faceData_length * (
170 - k))
-
-
sample = random.permutation(
170) +
1
-
-
for i
in
range(faceData_length):
-
people_idx = i +
1
-
if people_idx ==
26:
-
for j
in
range(
10):
-
face_im_path = os.path.join(faceData_path,
str(people_idx),
str(j+
1) +
'.jpg')
-
faceVector_im = img2vector(face_im_path)
-
if j <=
7:
-
train_face[i*k+j, :] = faceVector_im
-
train_label[i*k + j] = people_idx
-
else:
-
test_face[i*(
170-k) + (j-k), :] = faceVector_im
-
test_label[i*(
170-k) + (j-k)] = people_idx
-
-
for j
in
range(
170):
-
face_im_path = os.path.join(faceData_path,
str(people_idx),
str(sample[j]) +
'.jpg')
-
faceVector_im = img2vector(face_im_path)
-
if j < k:
-
train_face[i*k+j, :] = faceVector_im
-
train_label[i*k + j] = people_idx
-
else:
-
test_face[i*(
170-k) + (j-k), :] = faceVector_im
-
test_label[i*(
170-k) + (j-k)] = people_idx
-
-
return train_face, train_label, test_face, test_label
-
-
def
PCA_fit(
data, r):
-
data = np.float32(np.mat(data))
-
rows, cols = np.shape(data)
-
data_mean = np.mean(data,
0)
-
A = data - np.tile(data_mean, (rows,
1))
-
C = A * A.T
-
D, V = np.linalg.eig(C)
-
V_r = V[:,
0:r]
-
V_r = A.T * V_r
-
for i
in
range(r):
-
V_r[:, i] = V_r[:, i] / np.linalg.norm(V_r[:, i])
-
-
final_data = A * V_r
-
return final_data, data_mean, V_r
-
-
if __name__ ==
"__main__":
-
for r
in [
40,
80,
200]:
-
print(
'dimensionality of face images to {}:'.
format(r))
-
x_value = []
-
y_value = []
-
k =
int(
170*
0.7)
-
train_face, train_label, test_face, test_label = load_dataset(k)
-
-
data_train_new, data_mean, V_r = PCA_fit(train_face, r)
-
-
num_train = data_train_new.shape[
0]
-
num_test = test_face.shape[
0]
-
-
temp_face = test_face - np.tile(data_mean, (num_test,
1))
-
-
data_test_new = temp_face * V_r
-
data_test_new = np.array(data_test_new)
-
-
data_train_new = np.array(data_train_new)
-
-
# -
-
is_true_count =
0
-
for i
in
range(num_test):
-
testFace = data_test_new[i, :]
-
diffMat = data_train_new - np.tile(testFace, (num_train,
1))
-
sqDiffMat = diffMat **
2
-
sqDistances = sqDiffMat.
sum(axis=
1)
-
sortedDistIndicies = sqDistances.argsort()
-
indexMin = sortedDistIndicies[
0]
-
if train_label[indexMin] == test_label[i]:
-
is_true_count +=
1
-
else:
-
pass
-
-
accuracy =
float(is_true_count) / num_test
-
x_value.append(k)
-
y_value.append(
round(accuracy,
2))
-
-
print(
'The classify accuracy is: {:.2f}'.
format(accuracy*
100))
结果
• PCA based data distribution visualization
• PCA plus nearest neighbor classifification results
用于特征提取和分类的LDA
任务
应用LDA将数据维度从2、3和9降低维度分别为2和3的采样数据（如PCA部分）（类似于PCA）。分别报告维度为2、3和9的数据的分类精度，基于最近邻分类器。报告CMU PIE测试的分类准确性图片和你自己的照片分开。
实现代码
这题不同于PCA那题，因为需要降低维度刚好是可视化需要的2，3，所以一个代码回答了两个问题。
-
import numpy
as np
-
import matplotlib.pyplot
as plt
-
import cv2
-
from numpy
import *
-
import os
-
def
img2vector(
im_path):
-
im = cv2.imread(im_path,
0)
-
rows, cols = im.shape
-
imgVector = np.zeros((
1, rows * cols))
-
imgVector = np.reshape(im, (
1, rows * cols))
-
return imgVector
-
-
def
load_dataset(
k):
-
faceData_path =
'../PIE'
-
faceData_length =
len(os.listdir(faceData_path))
-
train_face = np.zeros((faceData_length * k,
32 *
32))
-
train_label = np.zeros(faceData_length * k)
-
test_face = np.zeros((faceData_length * (
170 - k),
32 *
32))
-
test_label = np.zeros(faceData_length * (
170 - k))
-
-
sample = random.permutation(
170) +
1
-
-
for i
in
range(faceData_length):
-
people_idx = i +
1
-
if people_idx ==
26:
-
for j
in
range(
10):
-
face_im_path = os.path.join(faceData_path,
str(people_idx),
str(j+
1) +
'.jpg')
-
faceVector_im = img2vector(face_im_path)
-
if j <=
7:
-
train_face[i*k+j, :] = faceVector_im
-
train_label[i*k + j] = people_idx
-
else:
-
test_face[i*(
170-k) + (j-k), :] = faceVector_im
-
test_label[i*(
170-k) + (j-k)] = people_idx
-
-
for j
in
range(
170):
-
face_im_path = os.path.join(faceData_path,
str(people_idx),
str(sample[j]) +
'.jpg')
-
faceVector_im = img2vector(face_im_path)
-
if j < k:
-
train_face[i*k+j, :] = faceVector_im
-
train_label[i*k + j] = people_idx
-
else:
-
test_face[i*(
170-k) + (j-k), :] = faceVector_im
-
test_label[i*(
170-k) + (j-k)] = people_idx
-
-
return train_face, train_label, test_face, test_label
-
-
def
LDA(
face,label,k):
-
x, y = face.shape
-
classes = np.unique(label)
-
meanAll = face.mean(axis=
0)
-
Sb = np.zeros((y, y),dtype = np.float32)
-
Sw = np.zeros((y, y), dtype=np.float32)
-
for i
in classes:
-
face_i = face[np.where(label == i)[
0],:]
-
mean_i = face_i.mean(axis =
0)
-
n = face_i.shape[
0]
-
Sw = Sw + np.dot((face_i - mean_i).T,(face_i-mean_i))
-
Sb = Sb + n*np.dot((mean_i - meanAll).T,(mean_i - meanAll))
-
#print("Sw");print(Sw);print("end");print("Sb");print(Sb);print("end")
-
tmp = np.ones(Sw.shape)/
500
-
Sw = tmp + Sw
-
matrix = np.linalg.inv(Sw) @ Sb
-
eigenvalue,eigenvector = np.linalg.eigh(matrix)
-
#print("vec");print(eigenvector);print("end")
-
index = np.argsort(eigenvalue)
# 排序
-
index = index[:-(k +
1):-
1]
-
select = eigenvector[:, index]
-
return select
-
-
def
recognize_lda():
-
eachNum =
int(
170*
0.7)
# 每个人拿出eachNum张照片进行训练
-
train_face, train_label, test_face, test_label = load_dataset(eachNum)
-
for k
in [
2,
3,
9]:
-
print(
'when k={}:'.
format(k), end=
' ')
-
W = LDA(train_face, train_label, k)
-
train = np.dot(train_face, W)
-
test = np.dot(test_face, W)
-
if k ==
2:
-
x_plot, y_plot = [], []
-
for data
in train[:-
501]:
-
x_plot.append(data[
0])
-
y_plot.append(data[
1])
-
fig = plt.figure()
-
plt.scatter(x_plot, y_plot)
-
plt.show()
-
if k ==
3 :
-
x_plot, y_plot, z_plot = [], [], []
-
for data
in train[:-
501]:
-
x_plot.append(data[
0])
-
y_plot.append(data[
1])
-
z_plot.append(data[
2])
-
fig = plt.figure()
-
ax = fig.add_subplot(
111,projection=
'3d')
-
plt.set_cmap(plt.get_cmap(
"seismic",
100))
-
im = ax.scatter(x_plot, y_plot, z_plot)
-
ax.set_xlabel(
'x')
-
ax.set_ylabel(
'y')
-
ax.set_zlabel(
'z')
-
plt.show()
-
acc = KNN(train,train_label,test,test_label,eachNum)
-
print(
"the acc=", acc*
100);
-
-
def
KNN_classify(
face,train_face,train_label,k):
-
dis = np.
sum(np.power((train_face - face),
2),axis=
1)
-
index = np.argsort(dis)[:k]
-
weight = []
-
for i
in
range(k):
-
weight.append(dis[index[k-
1]] - dis[index[i]] / (dis[index[k-
1]] - dis[index[
0]]))
-
count = [
0
for i
in
range (train_face.shape[
0])]
-
tmp =
0
-
for i
in index:
-
count[
int(train_label[i])] +=
1 + weight[tmp]
-
tmp +=
1
-
label = np.argmax(count);
-
return label
-
-
def
KNN(
train_faces, train_labels,test_faces, test_labels, k):
-
sum = test_faces.shape[
0]
-
err =
0
-
for i
in
range(
sum):
-
count = KNN_classify(test_faces[i],train_faces,train_labels,k)
-
if count != test_labels[i]:
-
err +=
1
-
acc = (
sum - err) /
sum
-
return acc
-
-
if __name__ ==
"__main__":
-
recognize_lda()
结果
• LDA based data distribution visualization
• LDA plus nearest neighbor classifification results 
用于分类的SVM
任务
使用原始面部图像（矢量化）和PCA预处理后的面部向量（维度为80和200）作为线性SVM的输入。惩罚参数C的尝试值｛1×10英寸−2, 1 × 10−1, 1}. 报告不同参数和尺寸。讨论数据维度和参数C对最终分类的影响精确。
实现代码
-
import os
-
from numpy
import *
-
import numpy
as np
-
import cv2
-
import matplotlib.pyplot
as plt
-
from pylab
import mpl
-
-
def
img2vector(
im_path):
-
im = cv2.imread(im_path,
0)
-
rows, cols = im.shape
-
imgVector = np.zeros((
1, rows * cols))
-
imgVector = np.reshape(im, (
1, rows * cols))
-
return imgVector
-
-
def
load_dataset(
k):
-
faceData_path =
'../PIE'
-
faceData_length =
len(os.listdir(faceData_path))
-
train_face = np.zeros((faceData_length * k,
32 *
32))
-
train_label = np.zeros(faceData_length * k)
-
test_face = np.zeros((faceData_length * (
170 - k),
32 *
32))
-
test_label = np.zeros(faceData_length * (
170 - k))
-
-
sample = random.permutation(
170) +
1
-
-
for i
in
range(faceData_length):
-
people_idx = i +
1
-
if people_idx ==
26:
-
for j
in
range(
10):
-
face_im_path = os.path.join(faceData_path,
str(people_idx),
str(j+
1) +
'.jpg')
-
faceVector_im = img2vector(face_im_path)
-
if j <=
7:
-
train_face[i*k+j, :] = faceVector_im
-
train_label[i*k + j] = people_idx
-
else:
-
test_face[i*(
170-k) + (j-k), :] = faceVector_im
-
test_label[i*(
170-k) + (j-k)] = people_idx
-
-
for j
in
range(
170):
-
face_im_path = os.path.join(faceData_path,
str(people_idx),
str(sample[j]) +
'.jpg')
-
faceVector_im = img2vector(face_im_path)
-
if j < k:
-
train_face[i*k+j, :] = faceVector_im
-
train_label[i*k + j] = people_idx
-
else:
-
test_face[i*(
170-k) + (j-k), :] = faceVector_im
-
test_label[i*(
170-k) + (j-k)] = people_idx
-
-
return train_face, train_label, test_face, test_label
-
-
def
PCA_fit(
data, r):
-
data = np.float32(np.mat(data))
-
rows, cols = np.shape(data)
-
data_mean = np.mean(data,
0)
-
A = data - np.tile(data_mean, (rows,
1))
-
C = A * A.T
-
D, V = np.linalg.eig(C)
-
V_r = V[:,
0:r]
-
V_r = A.T * V_r
-
for i
in
range(r):
-
V_r[:, i] = V_r[:, i] / np.linalg.norm(V_r[:, i])
-
-
final_data = A * V_r
-
return final_data, data_mean, V_r
-
-
if __name__ ==
"__main__":
-
for r
in [
80,
200]:
-
for c
in [
0.01,
0.1,
1]:
-
print(
'dimensionality of face images to {}, the value of parameter C is: {}'.
format(r, c))
-
x_value = []
-
y_value = []
-
k =
int(
170*
0.7)
-
train_face, train_label, test_face, test_label = load_dataset(k)
-
data_train_new, data_mean, V_r = PCA_fit(train_face, r)
-
data_train_new = np.array(data_train_new).astype(
float)
-
from sklearn
import svm
-
lin = svm.SVC(kernel=
'linear', C=c)
-
lin.fit(data_train_new, train_label)
-
predict = lin.predict(data_train_new)
-
acc =
sum(train_label==predict) // data_train_new.shape[
0]
-
print(
'accuarcy:{}'.
format(acc*
100))
结果
用于分类的神经网络
任务
训练具有两个卷积层和一个完全连接层的CNN，其架构如下：number节点数：20-50-500-21。最后一层的节点数固定为21执行21个类别（20个CMU PIE人脸加1个自己）分类。卷积内核大小设置为5。每个卷积层后面是一个最大池层内核大小为2，步幅为2。完全连接层之后是ReLU。训练网络并报告最终分类性能。
实现代码
-
import tensorflow
as tf
-
import os
-
from numpy
import *
-
import numpy
as np
-
import cv2
-
-
def
load_dataset(
k):
-
faceData_path =
'../PIE'
-
faceData_length =
len(os.listdir(faceData_path))
-
-
train_face, train_label = [], []
-
test_face, test_label = [], []
-
sample = random.permutation(
170) +
1
-
# 48, 68
-
for i
in
range(faceData_length-
20, faceData_length):
-
people_idx = i +
1
-
for j
in
range(
170):
-
face_im_path = os.path.join(faceData_path,
str(people_idx),
str(sample[j]) +
'.jpg')
-
faceVector_im = cv2.imread(face_im_path)
-
if j < k:
-
train_face.append(faceVector_im)
-
train_label.append(people_idx-(faceData_length-
20))
-
else:
-
test_face.append(faceVector_im)
-
test_label.append(people_idx-(faceData_length-
20))
-
-
return np.array(train_face).astype(
float), np.array(train_label), np.array(test_face).astype(
float), np.array(test_label)
-
-
if __name__ ==
'__main__':
-
train_face, train_label, test_face, test_label = load_dataset(
int(
170*
0.7))
-
-
model = tf.keras.models.Sequential([
-
tf.keras.layers.Conv2D(filters=
20,kernel_size=(
5,
5),padding=
'same',input_shape=(
32,
32,
3),activation=
'relu'),
-
tf.keras.layers.MaxPool2D(pool_size=(
2,
2), strides=
2),
-
tf.keras.layers.Conv2D(filters=
50,kernel_size=(
5,
5),padding=
'same',activation=
'relu'),
-
tf.keras.layers.MaxPool2D(pool_size=(
2,
2), strides=
2),
-
tf.keras.layers.Flatten(),
-
tf.keras.layers.Dense(
500, activation=
'relu'),
-
tf.keras.layers.Dense(
21,activation=
'softmax')])
-
-
model.
compile(optimizer=
'adam',loss=
'sparse_categorical_crossentropy',metrics=[
'accuracy'])
-
model.fit(train_face, train_label, epochs=
5)
#训练模型
-
model.evaluate(test_face, test_label, batch_size=
32,verbose=
2)
-
结果
转载：https://blog.csdn.net/qq_51831335/article/details/127587495
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