cs231n课程作业assignment1(KNN)
2016-11-25 09:52
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前言:
以斯坦福cs231n课程的python编程任务为主线,展开对该课程主要内容的理解和部分数学推导。该课程相关笔记参考自知乎-CS231n官方笔记授权翻译总集篇发布
k-Nearest Neighbor分类器简介:
k-Nearest Neighbor,简称KNN,翻译过来的意思就是k邻近分类,一个测试与已知的训练集中的数据进行求欧氏距离运算,取前K个距离最短的数据,然后根据前K个数据中标签出现次数最多的便为该测试的标签,更高的k值可以让分类的效果更平滑,使得分类器对于异常值更有抵抗力。KNN原理
图像分类数据集:CIFAR-10。这个数据集包含了60000张32X32的小图像。每张图像都有10种分类标签中的一种。这60000张图像被分为包含50000张图像的训练集和包含10000张图像的测试集。在下图中你可以看见10个类的10张随机图片。![](http://upload-images.jianshu.io/upload_images/3817674-c0bc9991a4444356.jpg?imageMogr2/auto-orient/strip%7CimageView2/2/w/1240)
最简单的求两个数据差异化的方法就是把每个像素相减求平方和,即计算欧氏距离。若不考虑平方的放大效果,可直接做差求和,换句话说,就是将两张图片先转化为两个向量,然后计算他们的距离d:
过程如下:
![](https://pic2.zhimg.com/95cfe7d9efb83806299c218e0710a6c5_r.jpg)
根据测试图像和已知数据进行比较后可以的得出当前test image和training image的距离关系,在高维度下不好表示,我们将其想象成二维的im(x,y)。然后我们找出距离最近的K个training image的标签,标签出现次数最多的就是当前test image的标签了。
![](http://upload-images.jianshu.io/upload_images/3817674-c94b1e01ed94aca2.jpg?imageMogr2/auto-orient/strip%7CimageView2/2/w/1240)
Python实现过程
k_nearest_neighbor.py#coding: utf-8 import numpy as np class KNearestNeighbor(object): def __init__(self): pass def train(self, X, y): """ Train the classifier. For k-nearest neighbors this is just memorizing the training data. Inputs: - X: A numpy array of shape (num_train, D) containing the training data consisting of num_train samples each of dimension D. - y: A numpy array of shape (N,) containing the training labels, where y[i] is the label for X[i]. """ self.X_train = X self.y_train = y def 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 consisting of 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 distances between training points and testing points. Returns: - y: A numpy array of shape (num_test,) containing predicted labels for the test 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) def compute_distances_two_loops(self, X): """ Compute the distance between each test point in X and each training point in self.X_train using a nested loop over both the training data and the test 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 training point. """ num_test = X.shape[0] num_train = self.X_train.shape[0] dists = np.zeros((num_test, num_train)) for i in xrange(num_test): for j in xrange(num_train): train = self.X_train[j,:] test = X[i,:] distence = np.sqrt(np.sum((test-train)**2))#Calculate the eyclidean distance dists[i,j]=distence return dists def compute_distances_one_loop(self, X): """ Compute the distance between each test point in X and each training point in 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 xrange(num_test): dis_array = X[i,:]-self.X_train dists[i,:] = np.sqrt(np.sum(dis_array**2)) return dists def compute_distances_no_loops(self, X): """ Compute the distance between each test point in X and each training point in 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)) M = np.dot(X, self.X_train.T) te = np.square(X).sum(axis = 1) tr = np.square(self.X_train).sum(axis = 1) dists = np.sqrt(-2*M+tr+np.matrix(te).T) dists = np.array(dists) return dists 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 the test 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 xrange(num_test): # A list of length k storing the labels of the k nearest neighbors to # the ith test point. closest_y = [] idx = np.argsort(dists[i,:],-1) closest_y = self.y_train[idx[:k]] closest_set = set(closest_y)#find max label for idx,item in enumerate(closest_set): y_pred[i]= item if idx == 0: break return y_pred
详细测试部分:
TryKNN.py# coding:utf-8 import random import numpy as np from data_utils import load_CIFAR10 import matplotlib.pyplot as plt plt.rcParams['figure.figsize'] = (10.0, 8.0) # set default size of plots plt.rcParams['image.interpolation'] = 'nearest' plt.rcParams['image.cmap'] = 'gray' cifar10_dir = 'datasets/cifar-10-batches-py'#data_path X_train, y_train, X_test, y_test = load_CIFAR10(cifar10_dir) 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 num_training = 5000 #the trainning number mask = range(num_training) #create range number X_train = X_train[mask] y_train = y_train[mask] num_test = 500 #the test number mask = range(num_test) X_test = X_test[mask] y_test = y_test[mask] # Reshape the image data into rows X_train = np.reshape(X_train, (X_train.shape[0], -1))#-1 mean auto number X_test = np.reshape(X_test, (X_test.shape[0], -1)) print X_train.shape, X_test.shape from classifiers import KNearestNeighbor#import classifier = KNearestNeighbor() #classifier.train(X_train, y_train)#data and lable #dists = classifier.compute_distances_no_loops(X_test) #print dists.shape #classifier the test and mark the label #y_test_pred = classifier.predict_labels(dists, k=7) #num_correct = np.sum(y_test_pred == y_test) #accuracy = float(num_correct) / num_test #print 'Got %d / %d correct => accuracy: %f' % (num_correct, num_test, accuracy) #compare the different function def time_function(f, *args): """ Call a function f with args and return the time (in seconds) that it took to execute. """ import time tic = time.time() f(*args) toc = time.time() return toc - tic #two_loop_time = time_function(classifier.compute_distances_two_loops, X_test) #print 'Two loop version took %f seconds' % two_loop_time #one_loop_time = time_function(classifier.compute_distances_one_loop, X_test) #print 'One loop version took %f seconds' % one_loop_time #the faster than anyother #no_loop_time = time_function(classifier.compute_distances_no_loops, X_test) #print 'No loop version took %f seconds' % no_loop_time num_folds = 5 k_choices = [1, 3, 5, 8, 10, 12, 15, 20, 50, 100] X_train_folds = [] y_train_folds = [] X_train_folds = np.array_split(X_train, num_folds);#split the array y_train_folds = np.array_split(y_train, num_folds); k_to_accuracies = {} for k in k_choices: k_to_accuracies[k] = [] for k in k_choices:#find the best k-value for i in range(num_folds): X_train_cv = np.vstack(X_train_folds[:i]+X_train_folds[i+1:]) X_test_cv = X_train_folds[i] y_train_cv = np.hstack(y_train_folds[:i]+y_train_folds[i+1:]) #size:4000 y_test_cv = y_train_folds[i] classifier.train(X_train_cv, y_train_cv) dists_cv = classifier.compute_distances_no_loops(X_test_cv) y_test_pred = classifier.predict_labels(dists_cv, k) num_correct = np.sum(y_test_pred == y_test_cv) accuracy = float(num_correct) / y_test_cv.shape[0] k_to_accuracies[k].append(accuracy) for k in sorted(k_to_accuracies): for accuracy in k_to_accuracies[k]: print 'k = %d, accuracy = %f' % (k, accuracy) # plot the raw observations for k in k_choices: accuracies = k_to_accuracies[k] plt.scatter([k] * len(accuracies), accuracies) # plot the trend line with error bars that correspond to standard deviation accuracies_mean = np.array([np.mean(v) for k,v in sorted(k_to_accuracies.items())]) accuracies_std = np.array([np.std(v) for k,v in sorted(k_to_accuracies.items())]) plt.errorbar(k_choices, accuracies_mean, yerr=accuracies_std) plt.title('Cross-validation on k') plt.xlabel('k') plt.ylabel('Cross-validation accuracy') plt.show() # Based on the cross-validation results above, choose the best value for k, # retrain the classifier using all the training data, and test it on the test # data. You should be able to get above 28% accuracy on the test data. best_k = 1 classifier = KNearestNeighbor() classifier.train(X_train, y_train) y_test_pred = classifier.predict(X_test, k=best_k) # Compute and display the accuracy num_correct = np.sum(y_test_pred == y_test) accuracy = float(num_correct) / num_test print 'Got %d / %d correct => accuracy: %f' % (num_correct, num_test, accuracy)
![](http://upload-images.jianshu.io/upload_images/3817674-f98711a0e91e160f.png?imageMogr2/auto-orient/strip%7CimageView2/2/w/1240)
KNN分类器的优劣:
首先,Nearest Neighbor分类器易于理解,实现简单。其次,算法的训练不需要花时间,因为其训练过程只是将训练集数据存储起来。然而测试要花费大量时间计算,因为每个测试图像需要和所有存储的训练图像进行比较,这显然是一个缺点。
总体来说KNN分类器的训练花费非常小,而实际的识别开销非常大,在不进行特征提取的情况下很难运用到时间当中去。
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