用KNN做手写数字识别(mnist)
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 os
import Image
import numpy as np
def 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] = 0
if(data[0][i][j] > 127):
ret[i * col + j] = 1
return ret
def load_data(data_path, split):
files = os.listdir(data_path)
file_num = len(files)
idx = np.random.permutation(file_num)
selected_file_num = 42000
selected_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_label
def 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_data
sqr_dif_mat = dif_mat ** 2
sqr_dis = sqr_dif_mat.sum(axis = 1)
sorted_idx = sqr_dis.argsort()
class_cnt = {}
maxx = 0
best_class = 0
for i in range(k):
tmp_class = train_label[sorted_idx[i]]
tmp_cnt = class_cnt.get(tmp_class, 0) + 1
class_cnt[tmp_class] = tmp_cnt
if(tmp_cnt > maxx):
maxx = tmp_cnt
best_class = tmp_class
return best_class
if __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 = 0
print "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 + 1.0
print ""
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：
