一般knn算法识别mnist数据集（代码）

本来是想弄个kd tree来玩玩knn的，但是mnist这样的数据集真是不好按维切分。把数据打印出来看了下，貌似灰度值大于3的都算是手写的印迹，着实不能取中值。既然这样，先拿一般的knn方法识别一下，看看效果和执行效率，再想办法这算一下mnist，玩玩kd tree吧。knn的基本原理在k-means、GMM聚类、KNN原理概述 有介绍，比较全的原理介绍在http://www.hankcs.com/ml/k-nearest-neighbor-method.html
下面是用knn 识别mnist数据集的代码，代码包括mnist的下载和抽取，以及knn测试，并计算了测试1000张图片所花费的时间。

#coding:utf-8import numpy as npimport osimport gzipfrom six.moves import urllibimport operatorfrom datetime import datetimeSOURCE_URL = 'http://yann.lecun.com/exdb/mnist/'TRAIN_IMAGES = 'train-images-idx3-ubyte.gz'TRAIN_LABELS = 'train-labels-idx1-ubyte.gz'TEST_IMAGES = 't10k-images-idx3-ubyte.gz'TEST_LABELS = 't10k-labels-idx1-ubyte.gz'#下载mnist数据集，仿照tensorflow的base.py中的写法。def maybe_download(filename, path, source_url):    if not os.path.exists(path):        os.makedirs(path)    filepath = os.path.join(path, filename)    if not os.path.exists(filepath):        urllib.request.urlretrieve(source_url, filepath)    return filepath#按32位读取，主要为读校验码、图片数量、尺寸准备的#仿照tensorflow的mnist.py写的。def _read32(bytestream):    dt = np.dtype(np.uint32).newbyteorder('>')    return np.frombuffer(bytestream.read(4), dtype=dt)[0]#抽取图片，并按照需求，可将图片中的灰度值二值化，按照需求，可将二值化后的数据存成矩阵或者张量#仿照tensorflow中mnist.py写的def extract_images(input_file, is_value_binary, is_matrix):    with gzip.open(input_file, 'rb') as zipf:        magic = _read32(zipf)        if magic !=2051:            raise ValueError('Invalid magic number %d in MNIST image file: %s' %(magic, input_file.name))        num_images = _read32(zipf)        rows = _read32(zipf)        cols = _read32(zipf)        print magic, num_images, rows, cols        buf = zipf.read(rows * cols * num_images)        data = np.frombuffer(buf, dtype=np.uint8)        if is_matrix:            data = data.reshape(num_images, rows*cols)        else:            data = data.reshape(num_images, rows, cols)        if is_value_binary:            return np.minimum(data, 1)        else:            return data#抽取标签#仿照tensorflow中mnist.py写的def extract_labels(input_file):    with gzip.open(input_file, 'rb') as zipf:        magic = _read32(zipf)        if magic != 2049:            raise ValueError('Invalid magic number %d in MNIST label file: %s' % (magic, input_file.name))        num_items = _read32(zipf)        buf = zipf.read(num_items)        labels = np.frombuffer(buf, dtype=np.uint8)        return labels# 一般的knn分类，跟全部数据同时计算一般距离，然后找出最小距离的k张图，并找出这k张图片的标签，标签占比最大的为newInput的label#copy大神http://blog.csdn.net/zouxy09/article/details/16955347的def kNNClassify(newInput, dataSet, labels, k):    numSamples = dataSet.shape[0] # shape[0] stands for the num of row    init_shape = newInput.shape[0]    newInput = newInput.reshape(1, init_shape)    #np.tile(A,B)：重复A B次，相当于重复[A]*B    #print np.tile(newInput, (numSamples, 1)).shape    diff = np.tile(newInput, (numSamples, 1)) - dataSet # Subtract element-wise    squaredDiff = diff ** 2 # squared for the subtract    squaredDist = np.sum(squaredDiff, axis = 1) # sum is performed by row    distance = squaredDist ** 0.5    sortedDistIndices = np.argsort(distance)    classCount = {} # define a dictionary (can be append element)    for i in xrange(k):        ## step 3: choose the min k distance        voteLabel = labels[sortedDistIndices[i]]        ## step 4: count the times labels occur        # when the key voteLabel is not in dictionary classCount, get()        # will return 0        classCount[voteLabel] = classCount.get(voteLabel, 0) + 1    ## step 5: the max voted class will return    maxCount = 0    maxIndex = 0    for key, value in classCount.items():        if value > maxCount:            maxCount = value            maxIndex = key    return maxIndexmaybe_download('train_images', 'data/mnist', SOURCE_URL+TRAIN_IMAGES)maybe_download('train_labels', 'data/mnist', SOURCE_URL+TRAIN_LABELS)maybe_download('test_images', 'data/mnist', SOURCE_URL+TEST_IMAGES)maybe_download('test_labels', 'data/mnist', SOURCE_URL+TEST_LABELS)# 主函数，先读图片，然后用于测试手写数字#copy大神http://blog.csdn.net/zouxy09/article/details/16955347的def testHandWritingClass():    ## step 1: load data    print "step 1: load data..."    train_x = extract_images('data/mnist/train_images', True, True)    train_y = extract_labels('data/mnist/train_labels')    test_x = extract_images('data/mnist/test_images', True, True)    test_y = extract_labels('data/mnist/test_labels')    ## step 2: training...    print "step 2: training..."    pass    ## step 3: testing    print "step 3: testing..."    a = datetime.now()    numTestSamples = test_x.shape[0]    matchCount = 0    test_num = numTestSamples/10    for i in xrange(test_num):        predict = kNNClassify(test_x[i], train_x, train_y, 3)        if predict == test_y[i]:            matchCount += 1        if i % 100 == 0:            print "完成%d张图片"%(i)    accuracy = float(matchCount) / test_num    b = datetime.now()    print "一共运行了%d秒"%((b-a).seconds)    ## step 4: show the result    print "step 4: show the result..."    print 'The classify accuracy is: %.2f%%' % (accuracy * 100)if __name__ == '__main__':    testHandWritingClass()

执行后的结果如下：

step 1: load data...2051 60000 28 282051 10000 28 28step 2: training...step 3: testing...完成0张图片完成100张图片完成200张图片完成300张图片完成400张图片完成500张图片完成600张图片完成700张图片完成800张图片完成900张图片一共运行了234秒step 4: show the result...The classify accuracy is: 96.20%

1000张图片运行时间234秒，时间开销大于简单的cnn，识别率高于96.2%，仅高于softmax回归，后者只有92%，多层感知机能达到98%的识别率，且训练速度快，测试更快。