Nearest Neighbor分类器

L1距离计算：

$I_{1}$ 与 $I_{2}$ 分别代表训练与测试图像，对两图像逐个像素做差，所得结果即为L1值（如下图所示）

L1插值越大，代表test图片与train图片差异越大。

L2距离公式：

代码笔记：

1.notbook 导入包设置plt

# 此处为notebook部分代码import random
import numpy as np
from cs231n.data_utils import load_CIFAR10
import matplotlib.pyplot as plt             # matplotlib 是款画图使用的插件
%matplotlib inline #使用%matplotlib命令可以将matplotlib的图表直接嵌入到Notebook之中
plt.rcParams['figure.figsize'] = (10.0, 8.0) # 设置图像尺寸
plt.rcParams['image.interpolation'] = 'nearest' # 最近邻差值: 像素为正方形
plt.rcParams['image.cmap'] = 'gray' # 输出为灰色# Some more magic so that the notebook will reload external python modules;
# see http://stackoverflow.com/questions/1907993/autoreload-of-modules-in-ipython
%load_ext autoreload
%autoreload 2

matplotlib更多设置可见此处： http://t.csdn.cn/TPgOh

2.加载数据集

#notebook部分第二块代码
# Load the raw CIFAR-10 data.
cifar10_dir = 'cs231n/datasets/cifar-10-batches-py' #此处为cifar数据集存放地址，可以
# 手动下载放置其中，cs231n在assignment1目录之下# Cleaning up variables to prevent loading data multiple times (which may
# cause memory issue)
try:del X_train, y_train  #del函数可以清除后续变量中的内容，在存储上是解绑变量与内存del X_test, y_testprint('Clear previously loaded data.')
except:passX_train, y_train, X_test, y_test = load_CIFAR10(cifar10_dir) #载入数据集，在
# data_utils中可以找到# As a sanity check, we print out the size of the training and test data.
print('Training data shape: ', X_train.shape)
print('Training labels shape: ', y_train.shape)
print('Test data shape: ', X_test.shape)
print('Test labels shape: ', y_test.shape)#输出结果为下
#Training data shape:  (50000, 32, 32, 3)
#Training labels shape:  (50000,)
#Test data shape:  (10000, 32, 32, 3)
#Test labels shape:  (10000,)

3.展示部分数据集

flatnonzero()，与random.choice()函数详细解析http://t.csdn.cn/abuYJ

#notebook部分第三块代码
# Visualize some examples from the dataset.
# We show a few examples of training images from each class.
classes = ['plane', 'car', 'bird', 'cat', 'deer', 'dog', 'frog', 'horse', 'ship',
'truck']
#classes是分类的标签
num_classes = len(classes) #记录标签数
samples_per_class = 7 #展示图片数设定
for y, cls in enumerate(classes):  # 遍历y为标签位置，cls为标签值如 y=1,cls=planeidxs = np.flatnonzero(y_train == y) # 筛选出y_train中值为y的数据地址idxs = np.random.choice(idxs, samples_per_class, replace=False)#  从idxs中抽取samples_per_class张图片组成新数组for i, idx in enumerate(idxs):plt_idx = i * num_classes + y + 1 #计算索引位置，i为行位置，y为列位置（可见显示矩阵）plt.subplot(samples_per_class, num_classes, plt_idx)plt.imshow(X_train[idx].astype('uint8'))plt.axis('off')if i == 0:plt.title(cls)
plt.show()

图片显示如下：

4.二次采样

#notebook部分第四块代码
# Subsample the data for more efficient code execution in this exercise
# 使用mask数组划分训练集，测试集
num_training = 5000
mask = list(range(num_training))
X_train = X_train[mask]
y_train = y_train[mask]num_test = 500
mask = list(range(num_test))
X_test = X_test[mask]
y_test = y_test[mask]# Reshape the image data into rows
# 将图片数据转化为行
X_train = np.reshape(X_train, (X_train.shape[0], -1)) # 转化为行数为X_train.shape[0]的形状
X_test = np.reshape(X_test, (X_test.shape[0], -1))
print(X_train.shape, X_test.shape)#输出结果
#(5000, 3072) (500, 3072)

5.导入 k_nearest_neighbor

#notebook部分第五块代码
from cs231n.classifiers import KNearestNeighbor
# 导入k_nearest_neighbor.py程序中的KNearestNeighbor类# Create a kNN classifier instance.
# Remember that training a kNN classifier is a noop:
# the Classifier simply remembers the data and does no further processing
classifier = KNearestNeighbor()
classifier.train(X_train, y_train)

k_nearest_neighbor.py模块代码如下：

from builtins import range
from builtins import object
import numpy as np
from past.builtins import xrangeclass KNearestNeighbor(object):""" a kNN classifier with L2 distance """def __init__(self):passdef train(self, X, y):"""Train the classifier. For k-nearest neighbors this is justmemorizing the training data.Inputs:- X: A numpy array of shape (num_train, D) containing the training dataconsisting of num_train samples each of dimension D.- y: A numpy array of shape (N,) containing the training labels, wherey[i] is the label for X[i]."""self.X_train = Xself.y_train = ydef predict(self, X, k=1, num_loops=0):"""Predict labels for test data using this classifier.Inputs:- X: A numpy array of shape (num_test, D) containing test data consistingof num_test samples each of dimension D.- k: The number of nearest neighbors that vote for the predicted labels.- num_loops: Determines which implementation to use to compute distancesbetween training points and testing points.Returns:- y: A numpy array of shape (num_test,) containing predicted labels for thetest data, where y[i] is the predicted label for the test point X[i]."""if num_loops == 0:dists = self.compute_distances_no_loops(X)elif num_loops == 1:dists = self.compute_distances_one_loop(X)elif num_loops == 2:dists = self.compute_distances_two_loops(X)else:raise ValueError('Invalid value %d for num_loops' % num_loops)return self.predict_labels(dists, k=k)

L2(self, X)距离函数代码如下，公式为：

$\sqrt{\sum_{p}^{}(I_{1}^{p} - I_{2}^{p})^{2}}$

此为2层循环代码

 def compute_distances_two_loops(self, X):"""Compute the distance between each test point in X and each training pointin self.X_train using a nested loop over both the training data and thetest data.Inputs:- X: A numpy array of shape (num_test, D) containing test data.Returns:- dists: A numpy array of shape (num_test, num_train) where dists[i, j]is the Euclidean distance between the ith test point and the jth trainingpoint."""num_test = X.shape[0]num_train = self.X_train.shape[0]dists = np.zeros((num_test, num_train))for i in range(num_test):for j in range(num_train):###################################################################### TODO:                                                             ## Compute the l2 distance between the ith test point and the jth    ## training point, and store the result in dists[i, j]. You should   ## not use a loop over dimension, nor use np.linalg.norm().          ####################################################################### *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****dists[i][j] = np.sqrt(np.sum((X[i]-self.X_train[j]) ** 2))# dists[i][j] = np.linalg.norm(X[i]-self.X_train[j])pass# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****return dists

使用单次循环，代码如下

def compute_distances_one_loop(self, X):"""Compute the distance between each test point in X and each training pointin self.X_train using a single loop over the test data.Input / Output: Same as compute_distances_two_loops"""num_test = X.shape[0]num_train = self.X_train.shape[0]dists = np.zeros((num_test, num_train))for i in range(num_test):######################################################################## TODO:                                                               ## Compute the l2 distance between the ith test point and all training ## points, and store the result in dists[i, :].                        ## Do not use np.linalg.norm().                                        ######################################################################### *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****#dists[i, :] = np.sqrt(np.sum((self.X_train-X[i])**2, axis=1))dists[i, :] = np.sqrt(np.sum(np.square((self.X_train-X[i])), axis=1))pass# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****return dists

无循环代码推导公式，详情http://t.csdn.cn/upPdB

代码如下：

def compute_distances_no_loops(self, X):"""Compute the distance between each test point in X and each training pointin self.X_train using no explicit loops.Input / Output: Same as compute_distances_two_loops"""num_test = X.shape[0]num_train = self.X_train.shape[0]dists = np.zeros((num_test, num_train))########################################################################## TODO:                                                                 ## Compute the l2 distance between all test points and all training      ## points without using any explicit loops, and store the result in      ## dists.                                                                ##                                                                       ## You should implement this function using only basic array operations; ## in particular you should not use functions from scipy,                ## nor use np.linalg.norm().                                             ##                                                                       ## HINT: Try to formulate the l2 distance using matrix multiplication    ##       and two broadcast sums.                                         ########################################################################### *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****# hmmm... reference: https://mlxai.github.io/2017/01/03/finding-distances-between-data-points-with-numpy.htmldists = X.dot(self.X_train.T)X_square = np.sum(np.square(X), axis=1) X_train_square = np.square(self.X_train).sum(axis=1)dists = np.sqrt(X_square[:, np.newaxis] + X_train_square - 2*dists)#np.newaxis用于扩展维度# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****return dists

预测标签函数代码如下，其中argsort详情参考http://t.csdn.cn/UZ9oe：

 def predict_labels(self, dists, k=1):"""Given a matrix of distances between test points and training points,predict a label for each test point.Inputs:- dists: A numpy array of shape (num_test, num_train) where dists[i, j]gives the distance betwen the ith test point and the jth training point.Returns:- y: A numpy array of shape (num_test,) containing predicted labels for thetest data, where y[i] is the predicted label for the test point X[i]."""num_test = dists.shape[0]y_pred = np.zeros(num_test)for i in range(num_test):# A list of length k storing the labels of the k nearest neighbors to# the ith test point.closest_y = []########################################################################## TODO:                                                                 ## Use the distance matrix to find the k nearest neighbors of the ith    ## testing point, and use self.y_train to find the labels of these       ## neighbors. Store these labels in closest_y.                           ## Hint: Look up the function numpy.argsort.                             ########################################################################### *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****closest_y = self.y_train[np.argsort(dists[i])][0:k] #argsort将图像从小到大排序，并输出前k个的类型pass# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****########################################################################## TODO:                                                                 ## Now that you have found the labels of the k nearest neighbors, you    ## need to find the most common label in the list closest_y of labels.   ## Store this label in y_pred[i]. Break ties by choosing the smaller     ## label.                                                                ########################################################################### *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****y_pred[i] = max(closest_y, key=list(closest_y).count)#对得到的k个数进行投票，选取出现次数最多的类别作为最后的预测类别pass# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****return y_pred

6.交叉验证部分

交叉验证思维导图如下

num_folds = 5
k_choices = [1, 3, 5, 8, 10, 12, 15, 20, 50, 100]X_train_folds = []
y_train_folds = []
################################################################################
# TODO:                                                                        #
# Split up the training data into folds. After splitting, X_train_folds and    #
# y_train_folds should each be lists of length num_folds, where                #
# y_train_folds[i] is the label vector for the points in X_train_folds[i].     #
# Hint: Look up the numpy array_split function.                                #
################################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****y_train=y_train.reshape(-1,1)
X_train_folds = np.array_split(X_train, num_folds)
y_train_folds = np.array_split(y_train, num_folds)
# 将X_train，y_train分割成五个数组# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****# A dictionary holding the accuracies for different values of k that we find
# when running cross-validation. After running cross-validation,
# k_to_accuracies[k] should be a list of length num_folds giving the different
# accuracy values that we found when using that value of k.
k_to_accuracies = {}################################################################################
# TODO:                                                                        #
# Perform k-fold cross validation to find the best value of k. For each        #
# possible value of k, run the k-nearest-neighbor algorithm num_folds times,   #
# where in each case you use all but one of the folds as training data and the #
# last fold as a validation set. Store the accuracies for all fold and all     #
# values of k in the k_to_accuracies dictionary.                               #
################################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****num_fold_test = y_train_folds[0].shape[0]for k in k_choices:classifier = KNearestNeighbor()k_to_accuracies[k] = []for test_idx in range(num_folds):# print(np.concatenate(np.delete(X_train_folds, k, 0), axis=0).shape)classifier.train(np.concatenate(np.delete(X_train_folds, test_idx, 0)), np.concatenate(np.delete(y_train_folds, test_idx, 0)))#np.concatenate的作用是将np.delete处理后的数组拼接成一个数组#np.delete是对X_train_folds矩阵的test_idx索引按行删除dists = classifier.compute_distances_no_loops(X_train_folds[test_idx])k_to_accuracies[k].append(np.sum(classifier.predict_labels(dists, k) == y_train_folds[test_idx]) / num_fold_test*1.0)#计算交叉验证准确率# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****# Print out the computed accuracies
for k in sorted(k_to_accuracies):for accuracy in k_to_accuracies[k]:print('k = %d, accuracy = %f' % (k, accuracy))

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