一、問題描述
利用SVM、KNN、bp神經網絡等算法進行集成學習，基於MNIST數據集進行手寫識別的訓練和測試。
二、算法核心思想分析
集成學習是將幾個弱分類器結合起來，得到更好的分類結果。使用SVM、KNN和bp神經網絡分別訓練，將分類結果進行投票，得出最後集成分類器的結果。
三、題目分析
首先讀取MNIST數據集，分別對分類器進行訓練，測試時，將三個分類器的結果進行投票，最終得出的結果即爲集成分類器的結果。其中SVM使用LibSVM。
四、代碼及運行結果
mnist_reader.py
# -*- coding: utf-8 -*-
import numpy as np
import struct
import matplotlib.pyplot as plt
# 訓練集文件
train_images_idx3_ubyte_file = 'mnist/train-images.idx3-ubyte'
# 訓練集標籤文件
train_labels_idx1_ubyte_file = 'mnist/train-labels.idx1-ubyte'
# 測試集文件
test_images_idx3_ubyte_file = 'mnist/t10k-images.idx3-ubyte'
# 測試集標籤文件
test_labels_idx1_ubyte_file = 'mnist/t10k-labels.idx1-ubyte'
def decode_idx3_ubyte(idx3_ubyte_file):
"""
解析idx3文件的通用函數
:param idx3_ubyte_file: idx3文件路徑
:return: 數據集
"""
# 讀取二進制數據
bin_data = open(idx3_ubyte_file, 'rb').read()
# 解析文件頭信息，依次爲魔數、圖片數量、每張圖片高、每張圖片寬
offset = 0
fmt_header = '>iiii'
magic_number, num_images, num_rows, num_cols = struct.unpack_from(fmt_header, bin_data, offset)
print('魔數:%d, 圖片數量: %d張, 圖片大小: %d*%d' % (magic_number, num_images, num_rows, num_cols))
# 解析數據集
image_size = num_rows * num_cols
offset += struct.calcsize(fmt_header)
fmt_image = '>' + str(image_size) + 'B'
images = np.empty((num_images, num_rows, num_cols))
for i in range(num_images):
if (i + 1) % 10000 == 0:
print('已解析 %d' % (i + 1) + '張')
images[i] = np.array(struct.unpack_from(fmt_image, bin_data, offset)).reshape((num_rows, num_cols))
offset += struct.calcsize(fmt_image)
return images
def decode_idx1_ubyte(idx1_ubyte_file):
"""
解析idx1文件的通用函數
:param idx1_ubyte_file: idx1文件路徑
:return: 數據集
"""
# 讀取二進制數據
bin_data = open(idx1_ubyte_file, 'rb').read()
# 解析文件頭信息，依次爲魔數和標籤數
offset = 0
fmt_header = '>ii'
magic_number, num_images = struct.unpack_from(fmt_header, bin_data, offset)
print('魔數:%d, 圖片數量: %d張' % (magic_number, num_images))
# 解析數據集
offset += struct.calcsize(fmt_header)
fmt_image = '>B'
labels = np.empty(num_images)
for i in range(num_images):
if (i + 1) % 10000 == 0:
print('已解析 %d' % (i + 1) + '張')
labels[i] = struct.unpack_from(fmt_image, bin_data, offset)[0]
offset += struct.calcsize(fmt_image)
return labels
def load_train_images(idx_ubyte_file=train_images_idx3_ubyte_file):
"""
TRAINING SET IMAGE FILE (train-images-idx3-ubyte):
[offset] [type] [value] [description]
0000 32 bit integer 0x00000803(2051) magic number
0004 32 bit integer 60000 number of images
0008 32 bit integer 28 number of rows
0012 32 bit integer 28 number of columns
0016 unsigned byte ?? pixel
0017 unsigned byte ?? pixel
........
xxxx unsigned byte ?? pixel
Pixels are organized row-wise. Pixel values are 0 to 255. 0 means background (white), 255 means foreground (black).
:param idx_ubyte_file: idx文件路徑
:return: n*row*col維np.array對象，n爲圖片數量
"""
return decode_idx3_ubyte(idx_ubyte_file)
def load_train_labels(idx_ubyte_file=train_labels_idx1_ubyte_file):
"""
TRAINING SET LABEL FILE (train-labels-idx1-ubyte):
[offset] [type] [value] [description]
0000 32 bit integer 0x00000801(2049) magic number (MSB first)
0004 32 bit integer 60000 number of items
0008 unsigned byte ?? label
0009 unsigned byte ?? label
........
xxxx unsigned byte ?? label
The labels values are 0 to 9.
:param idx_ubyte_file: idx文件路徑
:return: n*1維np.array對象，n爲圖片數量
"""
return decode_idx1_ubyte(idx_ubyte_file)
def load_test_images(idx_ubyte_file=test_images_idx3_ubyte_file):
"""
TEST SET IMAGE FILE (t10k-images-idx3-ubyte):
[offset] [type] [value] [description]
0000 32 bit integer 0x00000803(2051) magic number
0004 32 bit integer 10000 number of images
0008 32 bit integer 28 number of rows
0012 32 bit integer 28 number of columns
0016 unsigned byte ?? pixel
0017 unsigned byte ?? pixel
........
xxxx unsigned byte ?? pixel
Pixels are organized row-wise. Pixel values are 0 to 255. 0 means background (white), 255 means foreground (black).
:param idx_ubyte_file: idx文件路徑
:return: n*row*col維np.array對象，n爲圖片數量
"""
return decode_idx3_ubyte(idx_ubyte_file)
def load_test_labels(idx_ubyte_file=test_labels_idx1_ubyte_file):
"""
TEST SET LABEL FILE (t10k-labels-idx1-ubyte):
[offset] [type] [value] [description]
0000 32 bit integer 0x00000801(2049) magic number (MSB first)
0004 32 bit integer 10000 number of items
0008 unsigned byte ?? label
0009 unsigned byte ?? label
........
xxxx unsigned byte ?? label
The labels values are 0 to 9.
:param idx_ubyte_file: idx文件路徑
:return: n*1維np.array對象，n爲圖片數量
"""
return decode_idx1_ubyte(idx_ubyte_file)
def run():
train_images = load_train_images()
train_labels = load_train_labels()
# test_images = load_test_images()
# test_labels = load_test_labels()
# zipper = zip(train_images, train_labels)
# for x, y in zipper:
# print((x, y))
# 查看前十個數據及其標籤以讀取是否正確
len = 10
for i in range(len):
print("label\n", train_labels[i])
print("image\n", train_images[i])
plt.subplot((len-1)/5 + 1, 5, i+1)
plt.imshow(train_images[i], cmap='gray')
# plt.show()
plt.show()
print('done')
def getdataset():
X_train = load_train_images()
y_train = load_train_labels()
X_test = load_test_images()
y_test = load_test_labels()
return X_train, y_train, X_test, y_test
def showMinist():
y_train = load_train_labels()
X_train = load_train_images()
# 看看數據集中的一些樣本：每個類別展示一些
classes = ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9']
num_classes = len(classes)
samples_per_class = 7
for y, cls in enumerate(classes):
idxs = np.flatnonzero(y_train == y)
# 一個類別中挑出一些
idxs = np.random.choice(idxs, samples_per_class, replace=False)
for i, idx in enumerate(idxs):
plt_idx = i * num_classes + y + 1
plt.subplot(samples_per_class, num_classes, plt_idx)
plt.imshow(X_train[idx].astype('uint8'))
plt.axis('off')
if i == 0:
plt.title(cls)
plt.show()
if __name__ == '__main__':
# run()
showMinist()
svm.py
from libsvm.python.svmutil import *
from libsvm.python.svm import *
import mnist_reader as reader
import numpy as np
import random
class SVM(object):
def __init__(self):
self.X_train, self.y_train, self.X_test, self.y_test = reader.getdataset()
self.X_train = self.X_train/256
self.X_test = self.X_test/256
self.y_train = self.y_train.astype(int)
self.y_test = self.y_test.astype(int)
def dropsomepicture(self, trainm=5000, testm=500):
# 下采樣
num_training = trainm
mask = range(num_training)
self.X_train = self.X_train[mask]
self.y_train = self.y_train[mask]
num_test = testm
mask = range(num_test)
self.X_test = self.X_test[mask]
self.y_test = self.y_test[mask]
# 預處理：把數據展成一列
self.X_train = np.reshape(self.X_train, (self.X_train.shape[0], -1))
self.X_test = np.reshape(self.X_test, (self.X_test.shape[0], -1))
def train(self):
train_images = self.X_train.tolist()
train_labels = self.y_train.tolist()
test_images = self.X_test.tolist()
test_labels = self.y_test.tolist()
self.model = svm_train(train_labels, train_images)
def test(self):
test_images = self.X_test.tolist()
test_labels = self.y_test.tolist()
p_label, p_acc, p_val = svm_predict(test_labels, test_images, self.model)
print(p_acc)
def predict(self, label, image, model):
p_label, p_acc, p_val = svm_predict(label, image, model)
return int(p_label[0])
if __name__ == '__main__':
svm = SVM()
# svm.dropsomepicture(5000, 10000)
# svm.train()
# svm.test()
## predict
svm.dropsomepicture(5000, 10)
svm.train()
test_images = svm.X_test.tolist()
test_labels = svm.y_test.tolist()
svm_label = [test_labels[0]]
svm_image = [test_images[0]]
print(svm_label)
print(svm.predict(svm_label, svm_image, svm.model))
knn.py
from shaomingshan.classifiers.k_nearest_neighbor import KNearestNeighbor
import numpy as np
import matplotlib.pyplot as plt
import mnist_reader as reader
import time
def time_function(f, *args):
tic = time.time()
f(*args)
toc = time.time()
return toc - tic
class KNN(object):
def __init__(self):
self.X_train, self.y_train, self.X_test, self.y_test = reader.getdataset()
self.y_train = self.y_train.astype(int)
self.y_test = self.y_test.astype(int)
def dropsomepicture(self, trainm=5000, testm=500):
# 下采樣
num_training = trainm
mask = range(num_training)
self.X_train = self.X_train[mask]
self.y_train = self.y_train[mask]
num_test = testm
mask = range(num_test)
self.X_test = self.X_test[mask]
self.y_test = self.y_test[mask]
def show(self):
# 加載數據集
X_train, y_train, X_test, y_test = self.X_train, self.y_train, self.X_test, self.y_test
print('Training data shape: ', X_train.shape)
print('Training labels shape: ', y_train.shape)
print('Test data shape: ', X_test.shape)
print('Test labels shape: ', y_test.shape)
# 咱們把圖像數據展開成一個向量的形式
X_train = np.reshape(X_train, (X_train.shape[0], -1))
X_test = np.reshape(X_test, (X_test.shape[0], -1))
print(
X_train.shape, X_test.shape)
# 調用一下KNN分類器，然後訓練(其實就是把樣本都記下來)
classifier = KNearestNeighbor()
classifier.train(X_train, y_train)
# 一層for循環的方式，高效一點
dists_two = classifier.compute_distances_no_loops(X_test)
no_loop_time = time_function(classifier.compute_distances_no_loops, X_test)
print('No loop version took %f seconds' % no_loop_time)
pass
# 交叉驗證
def num_folds_cross(self):
X_train, y_train, X_test, y_test = self.X_train, self.y_train, self.X_test, self.y_test
X_test = np.reshape(X_test, (X_test.shape[0], -1))
X_train = np.reshape(X_train, (X_train.shape[0], -1))
num_folds = 5
k_choices = [1, 3, 5, 8, 10, 12, 15, 20, 50, 100]
X_train_folds = []
y_train_folds = []
idxes = range(len(X_train))
idx_folds = np.array_split(idxes, num_folds)
for idx in idx_folds:
# mask = np.ones(num_training, dtype=bool)
# mask[idx] = False
# X_train_folds.append( (X_train[mask], X_train[~mask]) )
# y_train_folds.append( (y_train[mask], y_train[~mask]) )
X_train_folds.append(X_train[idx])
y_train_folds.append(y_train[idx])
k_to_accuracies = {}
import sys
classifier = KNearestNeighbor()
Verbose = False
for k in k_choices:
if Verbose:
print("processing k=%f" % k)
else:
sys.stdout.write('.')
k_to_accuracies[k] = list()
for num in range(num_folds):
if Verbose:
print("processing fold#%i/%i" % (num, num_folds))
X_cv_train = np.vstack([X_train_folds[x] for x in range(num_folds) if x != num])
y_cv_train = np.hstack([y_train_folds[x].T for x in range(num_folds) if x != num])
X_cv_test = X_train_folds[num]
y_cv_test = y_train_folds[num]
# 訓練KNN分類器
classifier.train(X_cv_train, y_cv_train)
# 計算和訓練集之間圖片的距離
dists = classifier.compute_distances_no_loops(X_cv_test)
y_cv_test_pred = classifier.predict_labels(dists, k=k)
# 計算和預測
num_correct = np.sum(y_cv_test_pred == y_cv_test)
k_to_accuracies[k].append(float(num_correct) / y_cv_test.shape[0])
# 輸出計算的準確率
for k in sorted(k_to_accuracies):
for accuracy in k_to_accuracies[k]:
print(
'k = %d, accuracy = %f' % (k, accuracy))
for k in k_choices:
accuracies = k_to_accuracies[k]
plt.scatter([k] * len(accuracies), accuracies)
accuracies_mean = np.array([np.mean(v) for k,v in sorted(k_to_accuracies.items())])
accuracies_std = np.array([np.std(v) for k,v in sorted(k_to_accuracies.items())])
plt.errorbar(k_choices, accuracies_mean, yerr=accuracies_std)
plt.title('Cross-validation on k')
plt.xlabel('k')
plt.ylabel('Cross-validation accuracy')
plt.show()
def test(self,best_k = 3):
X_train, y_train, X_test, y_test = self.X_train, self.y_train, self.X_test, self.y_test
X_test = np.reshape(X_test, (X_test.shape[0], -1))
X_train = np.reshape(X_train, (X_train.shape[0], -1))
classifier = KNearestNeighbor()
classifier.train(X_train, y_train)
y_test_pred = classifier.predict(X_test, k = best_k)
# 輸出準確度
num_correct = np.sum(y_test_pred == y_test)
accuracy = float(num_correct) / len(X_test)
print('Got %d / %d correct => accuracy: %f' % (num_correct, len(X_test), accuracy))
def predictone(self, image, k=5):
X_train, y_train, X_test, y_test = self.X_train, self.y_train, self.X_test, self.y_test
X_test = np.array([image])
X_test = np.reshape(X_test, (X_test.shape[0], -1))
X_train = np.reshape(X_train, (X_train.shape[0], -1))
classifier = KNearestNeighbor()
classifier.train(X_train, y_train)
return classifier.predict(X_test, k)[0]
def predictdist(self, dist, k=5):
X_train, y_train, X_test, y_test = self.X_train, self.y_train, self.X_test, self.y_test
X_test = np.array(dist)
X_test = np.reshape(X_test, (X_test.shape[0], -1))
X_train = np.reshape(X_train, (X_train.shape[0], -1))
classifier = KNearestNeighbor()
classifier.train(X_train, y_train)
return classifier.predict(X_test, k)
if __name__ == '__main__':
k = KNN()
k.dropsomepicture(5000, 500)
k.show()
# k.num_folds_cross()
k.test(1)
# print(k.predictdist(k.X_test[0:5], 5))
# print(k.y_test[0:5])
mnist_loader.py
"""
mnist_loader
~~~~~~~~~~~~
A library to load the MNIST image data. For details of the data
structures that are returned, see the doc strings for ``load_data``
and ``load_data_wrapper``. In practice, ``load_data_wrapper`` is the
function usually called by our neural network code.
"""
# Libraries
# Standard library
import pickle
import gzip
# Third-party libraries
import numpy as np
def load_data():
"""Return the MNIST data as a tuple containing the training data,
the validation data, and the test data.
The ``training_data`` is returned as a tuple with two entries.
The first entry contains the actual training images. This is a
numpy ndarray with 50,000 entries. Each entry is, in turn, a
numpy ndarray with 784 values, representing the 28 * 28 = 784
pixels in a single MNIST image.
The second entry in the ``training_data`` tuple is a numpy ndarray
containing 50,000 entries. Those entries are just the digit
values (0...9) for the corresponding images contained in the first
entry of the tuple.
The ``validation_data`` and ``test_data`` are similar, except
each contains only 10,000 images.
This is a nice data format, but for use in neural networks it's
helpful to modify the format of the ``training_data`` a little.
That's done in the wrapper function ``load_data_wrapper()``, see
below.
"""
f = gzip.open('mnist.pkl.gz', 'rb')
training_data, validation_data, test_data = pickle.load(f, encoding='bytes')
f.close()
return training_data, validation_data, test_data
def load_data_wrapper():
"""Return a tuple containing ``(training_data, validation_data,
test_data)``. Based on ``load_data``, but the format is more
convenient for use in our implementation of neural networks.
In particular, ``training_data`` is a list containing 50,000
2-tuples ``(x, y)``. ``x`` is a 784-dimensional numpy.ndarray
containing the input image. ``y`` is a 10-dimensional
numpy.ndarray representing the unit vector corresponding to the
correct digit for ``x``.
``validation_data`` and ``test_data`` are lists containing 10,000
2-tuples ``(x, y)``. In each case, ``x`` is a 784-dimensional
numpy.ndarry containing the input image, and ``y`` is the
corresponding classification, i.e., the digit values (integers)
corresponding to ``x``.
Obviously, this means we're using slightly different formats for
the training data and the validation / test data. These formats
turn out to be the most convenient for use in our neural network
code."""
tr_d, va_d, te_d = load_data()
training_inputs = [np.reshape(x, (784, 1)) for x in tr_d[0]]
training_results = [vectorized_result(y) for y in tr_d[1]]
training_data = zip(training_inputs, training_results)
validation_inputs = [np.reshape(x, (784, 1)) for x in va_d[0]]
validation_data = zip(validation_inputs, va_d[1])
test_inputs = [np.reshape(x, (784, 1)) for x in te_d[0]]
test_data = zip(test_inputs, te_d[1])
return training_data, validation_data, test_data
def vectorized_result(j):
"""Return a 10-dimensional unit vector with a 1.0 in the jth
position and zeroes elsewhere. This is used to convert a digit
(0...9) into a corresponding desired output from the neural
network."""
e = np.zeros((10, 1))
e[j] = 1.0
return e
bp_network.py
import random
import numpy as np
class Network(object):
def __init__(self, sizes):
self.num_layers = len(sizes)
self.sizes = sizes
self.biases = [np.random.randn(y, 1) for y in sizes[1:]]
self.weights = [np.random.randn(y, x)
for x, y in zip(sizes[:-1], sizes[1:])]
def feedforward(self, a):
for b, w in zip(self.biases, self.weights):
a = sigmoid(np.dot(w, a)+b)
return a
def SGD(self, training_data, epochs, mini_batch_size, eta,
test_data=None):
if test_data:
test_data = list(test_data)
n_test = len(test_data)
training_data = list(training_data)
n = len(training_data)
for j in range(epochs):
random.shuffle(training_data)
mini_batches = [
training_data[k:k+mini_batch_size]
for k in range(0, n, mini_batch_size)]
for mini_batch in mini_batches:
self.update_mini_batch(mini_batch, eta)
if test_data:
print("Epoch {0}: {1} / {2}".format(j, self.evaluate(test_data), n_test))
else:
print("Epoch {0} complete".format(j))
def update_mini_batch(self, mini_batch, eta):
nabla_b = [np.zeros(b.shape) for b in self.biases]
nabla_w = [np.zeros(w.shape) for w in self.weights]
for x, y in mini_batch:
delta_nabla_b, delta_nabla_w = self.backprop(x, y)
nabla_b = [nb+dnb for nb, dnb in zip(nabla_b, delta_nabla_b)]
nabla_w = [nw+dnw for nw, dnw in zip(nabla_w, delta_nabla_w)]
self.weights = [w-(eta/len(mini_batch))*nw
for w, nw in zip(self.weights, nabla_w)]
self.biases = [b-(eta/len(mini_batch))*nb
for b, nb in zip(self.biases, nabla_b)]
def backprop(self, x, y):
nabla_b = [np.zeros(b.shape) for b in self.biases]
nabla_w = [np.zeros(w.shape) for w in self.weights]
# feedforward
activation = x
activations = [x] # list to store all the activations, layer by layer
zs = [] # list to store all the z vectors, layer by layer
for b, w in zip(self.biases, self.weights):
z = np.dot(w, activation)+b
zs.append(z)
activation = sigmoid(z)
activations.append(activation)
# backward pass
delta = self.cost_derivative(activations[-1], y) * \
sigmoid_prime(zs[-1])
nabla_b[-1] = delta
nabla_w[-1] = np.dot(delta, activations[-2].transpose())
for l in range(2, self.num_layers):
z = zs[-l]
sp = sigmoid_prime(z)
delta = np.dot(self.weights[-l+1].transpose(), delta) * sp
nabla_b[-l] = delta
nabla_w[-l] = np.dot(delta, activations[-l-1].transpose())
return nabla_b, nabla_w
def evaluate(self, test_data):
test_results = [(np.argmax(self.feedforward(x)), y)
for (x, y) in test_data]
return sum(int(x == y) for (x, y) in test_results)
def cost_derivative(self, output_activations, y):
return output_activations-y
def sigmoid(z):
return 1.0/(1.0+np.exp(-z))
def sigmoid_prime(z):
return sigmoid(z)*(1-sigmoid(z))
ensemble_learning.py
from SVM import *
from KNN import *
import bp_network
import mnist_reader as reader
import mnist_loader as mnist_loader
import numpy as np
# SVM
svm = SVM()
svm.dropsomepicture(5000, 500)
svm.train()
# KNN
k = KNN()
k.dropsomepicture(5000, 500)
# bp network
training_data, validation_data, test_data = mnist_loader.load_data_wrapper()
net = bp_network.Network([784, 30, 10])
net.SGD(training_data, 30, 10, 3.0, test_data=test_data)
X_train, y_train, X_test, y_test = reader.getdataset()
mask = 10000
X_test = X_test[range(mask)]
y_test = y_test[range(mask)]
X_train = np.reshape(X_train, (X_train.shape[0], -1))
X_test = np.reshape(X_test, (X_test.shape[0], -1))
test_images = X_test.tolist()
test_labels = y_test.tolist()
right = 0
for i in range(len(test_images)):
svm_label = [test_labels[i]]
svm_image = [test_images[i]]
pre_svm = int(svm.predict(svm_label, svm_image, svm.model))
pre_knn = int(k.predictone(test_images[i], 1))
pre_bp = int(np.argmax(net.feedforward(X_test[i].reshape((784, 1)))))
result = -1
if pre_svm == pre_knn:
result = pre_svm
elif pre_svm == pre_bp:
result = pre_svm
elif pre_bp == pre_knn:
result = pre_bp
else:
result = pre_bp
if test_labels[i] == result:
right += 1
print(i, "true")
else:
print(i, "false")
print("Accuracy:", right/mask)
1、SVM
準確率90.86%
2、KNN
交叉驗證發現，k最佳值爲1
使用500張圖片測試結果爲90.6%
3、bp network
迭代30次，準確率爲94.98%
4、集成學習
準確率93.76%
五、總結
本實驗中SVM、KNN、神經網絡算法的精確度都不算差，所以單純進行投票的方式並不會有顯著提升。
如有錯誤請指正