In [1]:

    

from PIL import Image
import numpy as np


    

In [2]:

    

import os
import urllib
from urllib.request import urlretrieve
dataset = 'mnist.pkl.gz'
def reporthook(a,b,c):
    print("\rdownloading: %5.1f%%"%(a*b*100.0/c), end="")
    
if not os.path.isfile(dataset):
        origin = "https://github.com/mnielsen/neural-networks-and-deep-learning/raw/master/data/mnist.pkl.gz"
        print('Downloading data from %s' % origin)
        urlretrieve(origin, dataset, reporthook=reporthook)


    

In [3]:

    

import gzip
import pickle
with gzip.open(dataset, 'rb') as f:
    train_set, valid_set, test_set = pickle.load(f, encoding='latin1')


    

In [4]:

    

print("train_set", train_set[0].shape, train_set[1].shape)
print("valid_set", valid_set[0].shape, valid_set[1].shape)
print("test_set", test_set[0].shape, test_set[1].shape)


    

    




train_set (50000, 784) (50000,)
valid_set (10000, 784) (10000,)
test_set (10000, 784) (10000,)

In [5]:

    

# 訓練資料， Y 的前 20 筆
train_set[1][:20]


    

    
Out[5]:





array([5, 0, 4, 1, 9, 2, 1, 3, 1, 4, 3, 5, 3, 6, 1, 7, 2, 8, 6, 9])

In [6]:

    

# 訓練資料， X 的前 20 筆
int_X = (train_set[0][:20]*255).clip(0,255).astype('uint8')
int_X_reshape = int_X.reshape(-1,28,28).swapaxes(0,1).reshape(28,-1)
Image.fromarray(int_X_reshape)


    

    
Out[6]:

In [7]:

    

# 資料正規化
train_X  = train_set[0]
train_X  = train_X / np.linalg.norm(train_X, axis=1, keepdims=True)
test_X  = test_set[0]
test_X  = test_X / np.linalg.norm(test_X, axis=1, keepdims=True)


    

In [8]:

    

# 矩陣乘法
A = test_X @ train_X.T


    

In [9]:

    

A.argmax(axis=1)


    

    
Out[9]:





array([44566, 28882, 15224, ...,  3261,  1311, 22424])

In [10]:

    

y_predict = train_set[1][A.argmax(axis=1)]


    

In [11]:

    

# 測試資料， X 的前 20 筆
int_X = (test_set[0][:20]*255).clip(0,255).astype('uint8')
int_X_reshape = int_X.reshape(-1,28,28).swapaxes(0,1).reshape(28,-1)
Image.fromarray(int_X_reshape)


    

    
Out[11]:

In [13]:

    

# 猜測的 Y 前20筆
y_predict[:20]


    

    
Out[13]:





array([7, 2, 1, 0, 4, 1, 4, 9, 5, 9, 0, 6, 9, 0, 1, 5, 9, 7, 3, 4])

In [14]:

    

#測試資料的 Y 前 20 筆
test_set[1][:20]


    

    
Out[14]:





array([7, 2, 1, 0, 4, 1, 4, 9, 5, 9, 0, 6, 9, 0, 1, 5, 9, 7, 3, 4])

In [15]:

    

# 正確率
(y_predict == test_set[1]).mean()


    

    
Out[15]:





0.9708

In [16]:

    

# 用 PCA 降低維度到 60
from sklearn.decomposition import PCA
pca = PCA(n_components=60)
train_X = pca.fit_transform(train_set[0])
test_X = pca.transform(test_set[0])


    

In [17]:

    

train_X /= np.linalg.norm(train_X, axis=1, keepdims=True)
test_X /= np.linalg.norm(test_X, axis=1, keepdims=True)


    

In [18]:

    

# 矩陣乘法
A = test_X @ train_X.T


    

In [19]:

    

y_predict = train_set[1][A.argmax(axis=1)]


    

In [20]:

    

# 正確率
(y_predict == test_set[1]).mean()


    

    
Out[20]:





0.97030000000000005

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