From a58d26aa4ce55903f80a8c0fd9eb02d9c9c74146 Mon Sep 17 00:00:00 2001
From: scxixixi <1310503779@qq.com>
Date: Fri, 22 May 2020 22:08:01 +0800
Subject: [PATCH] First project
---
README.md | 1 +
face.rec.klda.homework.py | 222 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
2 files changed, 223 insertions(+)
create mode 100644 face.rec.klda.homework.py
diff --git a/README.md b/README.md
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+++ b/README.md
@@ -0,0 +1 @@
+#Homework is submit here
diff --git a/face.rec.klda.homework.py b/face.rec.klda.homework.py
new file mode 100644
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+++ b/face.rec.klda.homework.py
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+"""
+==============================================================
+基于 Kernel LDA + KNN 的人脸识别
+使用 Kernel Discriminant Analysis 做特征降维
+使用 K-Nearest-Neighbor 做分类
+
+数据:
+ 人脸图像来自于 Olivetti faces data-set from AT&T (classification)
+ 数据集包含 40 个人的人脸图像, 每个人都有 10 张图像
+ 我们只使用其中标签(label/target)为 0 和 1 的前 2 个人的图像
+
+算法:
+ 需要自己实现基于 RBF Kernel 的 Kernel Discriminant Analysis 用于处理两个类别的数据的特征降维
+ 代码的框架已经给出, 需要学生自己补充 KernelDiscriminantAnalysis 的 fit() 和 transform() 函数的内容
+==============================================================
+"""
+
+# License: BSD 3 clause
+
+import numpy as np
+import matplotlib.pyplot as plt
+from sklearn import datasets
+from sklearn.model_selection import train_test_split
+from sklearn.datasets import fetch_olivetti_faces
+from sklearn.neighbors import KNeighborsClassifier
+from sklearn.pipeline import make_pipeline
+from sklearn.preprocessing import StandardScaler
+
+print(__doc__)
+################################################
+"""
+Scikit-learn-compatible Kernel Discriminant Analysis.
+"""
+
+import numpy as np
+from scipy import linalg
+from sklearn.base import BaseEstimator, ClassifierMixin, TransformerMixin
+from sklearn.preprocessing import OneHotEncoder
+from sklearn.utils.validation import check_array, check_is_fitted, check_X_y
+from scipy.spatial.distance import pdist, squareform
+
+class KernelDiscriminantAnalysis(BaseEstimator, ClassifierMixin,
+ TransformerMixin):
+ """Kernel Discriminant Analysis.
+
+ Parameters
+ ----------
+ n_components: integer.
+ The dimension after transform.
+ gamma: float.
+ Parameter to RBF Kernel
+ lmb: float (>= 0.0), default=0.001.
+ Regularization parameter
+
+ """
+
+ def __init__(self, n_components, gamma, lmb=0.001):
+ self.n_components = n_components
+ self.gamma = gamma
+ self.lmb = lmb
+ self.X = None # 用于存放输入的训练数据的 X
+ self.K = None # 用于存放训练数据 X 产生的 Kernel Matrix
+ self.M = None # 用于存放 Kernel LDA 最优化公式中的 M
+ self.N = None # 用于存放 Kernel LDA 最优化公式中的 N
+ self.EigenVectors = None # 用于存放 Kernel LDA 最优化公式中的 M 对应的广义特征向量, 每一列为一个特征向量, 按照对应特征值大小排序
+
+ def fit(self, X, y):
+ """Fit KDA model.
+
+ Parameters
+ ----------
+ X: numpy array of shape [n_samples, n_features]
+ Training set.
+ y: numpy array of shape [n_samples]
+ Target values. Only works for 2 classes with label/target 0 and 1.
+
+ Returns
+ -------
+ self
+
+ """
+ self.X = X
+
+ # calculate the euclidean matrix
+ distance_matrix = self.find_distance_matrix(X)
+ self.K = np.exp(-self.gamma * distance_matrix)
+
+ # calculate indexes of data points of two class
+ K1 = self.K[:,y==0]
+ K2 = self.K[:,y==1]
+
+ # calculate A = I - 1_{l_j} for calc of N
+ l1, l2 = K1.shape[1], K2.shape[1]
+ A1 = np.identity(l1) - (1 / float(l1)) * np.ones((l1, l1))
+ A2 = np.identity(l2) - (1 / float(l2)) * np.ones((l2, l2))
+
+ # calculate within calss scatter matrix N
+ N1 = np.dot(A1, K1.T)
+ N1 = np.dot(K1, N1)
+
+ N2 = np.dot(A2, K2.T)
+ N2 = np.dot(K2, N2)
+
+ self.N = N1 + N2 + self.lmb * np.identity(len(N1))
+
+ M1 = np.sum(K1,axis=1)/float(l1)
+ M2 = np.sum(K2,axis=1)/float(l2)
+
+ # calculate alpha
+ M_diff = M1 - M2
+ self.M = np.outer(M_diff.transpose(), M_diff)
+
+ _, vecs = linalg.eig(self.M, self.N)
+ self.EigenVectors = vecs
+
+ return self
+
+
+ def find_distance_matrix(self, data):
+ sq_dists = pdist(data.reshape(10,64*64), 'sqeuclidean')
+ mat_sq_dists = squareform(sq_dists)
+ return mat_sq_dists
+
+ def transform(self, X_test):
+ """Transform data with the trained KernelLDA model.
+
+ Parameters
+ ----------
+ X_test: numpy array of shape [n_samples, n_features]
+ The input data.
+
+ Returns
+ -------
+ y_pred: array-like, shape (n_samples, n_components)
+ Transformations for X.
+
+ """
+ test_kernel_matrix = []
+ for test_item in X_test:
+ dist = np.array([np.sum((test_item - row)**2) for row in self.X])
+ k = np.exp(-self.gamma * dist)
+ test_kernel_matrix.append(k)
+
+ # print(len(test_kernel_matrix))
+
+ # projecting data
+ y_pred = np.zeros((len(X_test), self.n_components))
+ for i in range(0, self.n_components):
+ alpha_i = self.EigenVectors[:, i]
+ for j in range(len(test_kernel_matrix)):
+ test_kernel = test_kernel_matrix[j]
+ y_pred[j, i] = np.dot(alpha_i.transpose(),test_kernel)
+
+ return y_pred
+
+
+################################################
+
+# 指定 KNN 中最近邻的个数 (k 的值)
+n_neighbors = 3
+
+# 设置随机数种子让实验可以复现
+random_state = 0
+
+# 现在人脸数据集
+faces = fetch_olivetti_faces()
+targets = faces.target
+
+# show sample images
+images = faces.images[targets < 2] # save images
+
+features = faces.data # features
+targets = faces.target # targets
+
+fig = plt.figure() # create a new figure window
+for i in range(20): # display 20 images
+ # subplot : 4 rows and 5 columns
+ img_grid = fig.add_subplot(4, 5, i+1)
+ # plot features as image
+ img_grid.imshow(images[i], cmap='gray')
+
+plt.show()
+
+# Prepare data, 只限于处理类别 0 和 1 的人脸
+X, y = faces.data[targets < 2], faces.target[targets < 2]
+
+# Split into train/test
+X_train, X_test, y_train, y_test = \
+ train_test_split(X, y, test_size=0.5, stratify=y,
+ random_state=random_state)
+
+
+# Reduce dimension to 2 with KernelDiscriminantAnalysis
+# can adjust the value of 'gamma' as needed.
+kda = make_pipeline(StandardScaler(),
+ KernelDiscriminantAnalysis(n_components=2, gamma = 0.000005))
+
+# Use a nearest neighbor classifier to evaluate the methods
+knn = KNeighborsClassifier(n_neighbors=n_neighbors)
+
+
+plt.figure()
+# plt.subplot(1, 3, i + 1, aspect=1)
+
+# Fit the method's model
+kda.fit(X_train, y_train)
+
+# Fit a nearest neighbor classifier on the embedded training set
+knn.fit(kda.transform(X_train), y_train)
+
+# Compute the nearest neighbor accuracy on the embedded test set
+acc_knn = knn.score(kda.transform(X_test), y_test)
+
+# Embed the data set in 2 dimensions using the fitted model
+X_embedded = kda.transform(X)
+
+# Plot the projected points and show the evaluation score
+plt.scatter(X_embedded[:, 0], X_embedded[:, 1], c=y, s=30, cmap='Set1')
+plt.title("{}, KNN (k={})\nTest accuracy = {:.2f}".format('kda',
+ n_neighbors,
+ acc_knn))
+plt.show()
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