用KNN做手寫數字識別(mnist)

一. KNN的原理

KNN的主要思想是找到與待測樣本最接近的k個樣本，然後把這k個樣本出現次數最多的類別作爲待測樣本的類別。

二. 數據源

mnist數據集，包含42000張28*28的圖片，可以從網盤下載http://pan.baidu.com/s/1kVi1nc7，下載完解壓後如下圖所示：

三. 處理方法

1. 把圖片讀取到一個28*28的矩陣裏，然後對圖片進行一個簡單的二值化，這裏選擇127爲一個界限，大於127的像素點爲1，小於等於127的像素點爲0，二值化之後的手寫數字如下圖所示：

2. 把28*28的矩陣直接轉成一個784維的向量，直接去歐氏距離作爲度量進行KNN算法，代碼如下：

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. 實驗結果

實驗取70%的數據作爲訓練，30%的數據作爲測試，準確率爲95%，結果截圖如下：

如有錯誤，請指正