用KNN做手写数字识别(mnist)

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一. KNN的原理

KNN的主要思想是找到与待测样本最接近的k个样本，然后把这k个样本出现次数最多的类别作为待测样本的类别。

二. 数据源

mnist数据集，包含42000张28*28的图片，可以从网盘下载http://pan.baidu.com/s/1kVi1nc7，下载完解压后如下图所示：

三. 处理方法

1. 把图片读取到一个28*28的矩阵里，然后对图片进行一个简单的二值化，这里选择127为一个界限，大于127的像素点为1，小于等于127的像素点为0，二值化之后的手写数字如下图所示：

2. 把28*28的矩阵直接转成一个784维的向量，直接去欧氏距离作为度量进行KNN算法，代码如下：

import osimport Imageimport numpy as npdef binaryzation(data):row = data.shape[1]col = data.shape[2]ret = np.empty(row * col)for i in range(row):for j in range(col):ret[i * col + j] = 0if(data[0][i][j] > 127):ret[i * col + j] = 1return retdef load_data(data_path, split):files = os.listdir(data_path)file_num = len(files)idx = np.random.permutation(file_num)selected_file_num = 42000selected_files = []for i in range(selected_file_num):selected_files.append(files[idx[i]])img_mat = np.empty((selected_file_num, 1, 28, 28), dtype = "float32")data = np.empty((selected_file_num, 28 * 28), dtype = "float32")label = np.empty((selected_file_num), dtype = "uint8")print "loading data..."for i in range(selected_file_num):print i,"/",selected_file_num,"\r",file_name = selected_files[i]file_path = os.path.join(data_path, file_name)img_mat[i] = Image.open(file_path)data[i] = binaryzation(img_mat[i])label[i] = int(file_name.split('.')[0])print ""div_line = (int)(split * selected_file_num)idx = np.random.permutation(selected_file_num)train_idx, test_idx = idx[:div_line], idx[div_line:]train_data, test_data = data[train_idx], data[test_idx]train_label, test_label = label[train_idx], label[test_idx]return train_data, train_label, test_data, test_labeldef KNN(test_vec, train_data, train_label, k):train_data_size = train_data.shape[0]dif_mat = np.tile(test_vec, (train_data_size, 1)) - train_datasqr_dif_mat = dif_mat ** 2sqr_dis = sqr_dif_mat.sum(axis = 1)sorted_idx = sqr_dis.argsort()class_cnt = {}maxx = 0best_class = 0for i in range(k):tmp_class = train_label[sorted_idx[i]]tmp_cnt = class_cnt.get(tmp_class, 0) + 1class_cnt[tmp_class] = tmp_cntif(tmp_cnt > maxx):maxx = tmp_cntbest_class = tmp_classreturn best_classif __name__=="__main__":np.random.seed(123456)train_data, train_label, test_data, test_label = load_data("mnist_data", 0.7)tot = test_data.shape[0]err = 0print "testing..."for i in range(tot):print i,"/",tot,"\r",best_class = KNN(test_data[i], train_data, train_label, 3)if(best_class != test_label[i]):err = err + 1.0print ""print "accuracy"print 1 - err / tot

四. 实验结果

实验取70%的数据作为训练，30%的数据作为测试，准确率为95%，结果截图如下：

如有错误，请指正

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