最近忙里偷闲学习了一点机器学习的知识,看到神经网络算法时我和阿Kun便想到要将它用Python代码实现。我们用了两种不同的方法来编写它。这里只放出我的代码。
MNIST数据集基于美国国家标准与技术研究院的两个数据集构建而成。
训练集中包含250个人的手写数字,其中50%是高中生,50%来自人口调查局。
每个训练集的数字图片像素为28x28。
MNIST数据集可通过 下载链接 下载,它包含以下内容:
- 训练集图像:train-images-idx3-ubyte.gz,包含60000个样本
- 训练集类标:train-labels-idx1-ubyte.gz,包含60000个类标
- 测试集图像:t10k-images-idx3-ubyte.gz,包含10000个样本
- 测试集类标:t10k-labels-idx1-ubyte.gz,包含10000个类标
关于神经网络算法的详解太过复杂,本人水平有限便不再描述,我这里只给出我们两人的代码。若想了解详情请移步谷歌或者百度。
StarMan
github项目地址:https://github.com/MyBules/Neural-Network
import os
import numpy as np
import struct
import matplotlib.pyplot as plt
import sys
from scipy.special import expit
def load_mnist(path, kind = 'train'):
'''
读取数据
:param path: 路径
:param kind: 文件类型
:return: images: 60000*784
labels:手写数字对应的类标(整数0~9)
'''
labels_path = os.path.join(path, '%s-labels-idx1-ubyte' % kind)
images_path = os.path.join(path, '%s-images-idx3-ubyte' % kind)
with open(labels_path, 'rb') as lbpath:
magic, n = struct.unpack('>II', lbpath.read(8))
labels = np.fromfile(lbpath, dtype=np.uint8)
with open(images_path, 'rb') as imgpath:
magic, num, rows, cols = struct.unpack(">IIII", imgpath.read(16))
images = np.fromfile(imgpath, dtype= np.uint8).reshape(len(labels), 784) # 28*28=784
return images, labels
class NeuralNetMLP(object):
def __init__(self, n_output, n_features, n_hidden=30, l1=0.0,
l2=0.0, epochs=500, eta=0.001, alpha=0.0, decrease_const=0.0,
shuffle=True, minibatches=1, random_state=None):
'''
:param n_output: 输出单元
:param n_features: 输入单元
:param n_hidden: 隐层单元
:param l1: L1正则化系数 lamda
:param l2: L2正则化系数 lamda
:param epochs: 遍历训练集的次数(迭代次数)
:param eta: 学习速率
:param alpha: 动量学习进度的参数,它在上一轮的基础上增加一个因子,用于加快权重更新的学习
:param decrease_const: 用于降低自适应学习速率 n 的常数 d ,随着迭代次数的增加而随之递减以更好地确保收敛
:param shuffle: 在每次迭代前打乱训练集的顺序,以防止算法陷入死循环
:param minibatches: 在每次迭代中,将训练数据划分为 k 个小的批次,为加速学习的过程,梯度由每个批次分别计算,而不是在整个训练集数据上进行计算。
:param random_state:
'''
np.random.seed(random_state)
self.n_output = n_output
self.n_features = n_features
self.n_hidden = n_hidden
self.w1, self.w2 = self._initialize_weights()
self.l1 = l1
self.l2 = l2
self.epochs = epochs
self.eta = eta
self.alpha = alpha
self.decrease_const = decrease_const
self.shuffle = shuffle
self.minibatches = minibatches
def _encode_labels(self, y, k):
'''
:param y:
:param k:
:return:
'''
onehot = np.zeros((k, y.shape[0]))
for idx, val, in enumerate(y):
onehot[val, idx] = 1.0
return onehot
def _initialize_weights(self):
'''
# 计算权重
:return: w1, w2
'''
w1 = np.random.uniform(-1.0, 1.0, size=self.n_hidden*(self.n_features + 1))
w1 = w1.reshape(self.n_hidden, self.n_features + 1)
w2 = np.random.uniform(-1.0, 1.0, size=self.n_output*(self.n_hidden + 1))
w2 = w2.reshape(self.n_output, self.n_hidden + 1)
return w1, w2
def _sigmoid(self, z):
'''
expit 等价于 1.0/(1.0 + np.exp(-z))
:param z:
:return: 1.0/(1.0 + np.exp(-z))
'''
return expit(z)
def _sigmoid_gradient(self, z):
sg = self._sigmoid(z)
return sg * (1 - sg)
def _add_bias_unit(self, X, how='column'):
if how == 'column':
X_new = np.ones((X.shape[0], X.shape[1] + 1))
X_new[:, 1:] = X
elif how =='row':
X_new = np.ones((X.shape[0]+1, X.shape[1]))
X_new[1:,:] = X
else:
raise AttributeError("'how' must be 'column' or 'row'")
return X_new
def _feedforward(self, X, w1, w2):
a1 = self._add_bias_unit(X, how='column')
z2 = w1.dot(a1.T)
a2 = self._sigmoid(z2)
a2 = self._add_bias_unit(a2, how='row')
z3 = w2.dot(a2)
a3 = self._sigmoid(z3)
return a1, z2, a2, z3, a3
def _L2_reg(self, lambda_, w1, w2):
return (lambda_/2.0) * (np.sum(w1[:, 1:] ** 2) + np.sum(w2[:, 1:] ** 2))
def _L1_reg(self, lambda_, w1, w2):
return (lambda_/2.0) * (np.abs(w1[:,1:]).sum() + np.abs(w2[:, 1:]).sum())
def _get_cost(self, y_enc, output, w1, w2):
term1 = -y_enc * (np.log(output))
term2 = (1 - y_enc) * np.log(1 - output)
cost = np.sum(term1 - term2)
L1_term = self._L1_reg(self.l1, w1, w2)
L2_term = self._L2_reg(self.l2, w1, w2)
cost = cost + L1_term + L2_term
return cost
def _get_gradient(self, a1, a2, a3, z2, y_enc, w2, w1):
# 反向传播
sigma3 = a3 - y_enc
z2 = self._add_bias_unit(z2, how='row')
sigma2 = w2.T.dot(sigma3) * self._sigmoid_gradient(z2)
sigma2 = sigma2[1:, :]
grad1 = sigma2.dot(a1)
grad2 = sigma3.dot(a2.T)
# 调整
grad1[:, 1:] += (w1[:, 1:] * (self.l1 + self.l2))
grad2[:, 1:] += (w2[:, 1:] * (self.l1 + self.l2))
return grad1, grad2
def predict(self, X):
a1, z2, a2, z3, a3 = self._feedforward(X, self.w1, self.w2)
y_pred = np.argmax(z3, axis=0)
return y_pred
def fit(self, X, y, print_progress=False):
self.cost_ = []
X_data, y_data = X.copy(), y.copy()
y_enc = self._encode_labels(y, self.n_output)
delta_w1_prev = np.zeros(self.w1.shape)
delta_w2_prev = np.zeros(self.w2.shape)
for i in range(self.epochs):
# 自适应学习率
self.eta /= (1 + self.decrease_const*i)
if print_progress:
sys.stderr.write('\rEpoch: %d/%d' % (i+1, self.epochs))
sys.stderr.flush()
if self.shuffle:
idx = np.random.permutation(y_data.shape[0])
X_data, y_data = X_data[idx], y_data[idx]
mini = np.array_split(range(y_data.shape[0]), self.minibatches)
for idx in mini:
# 前馈
a1, z2, a2, z3, a3 = self._feedforward(X[idx], self.w1, self.w2)
cost = self._get_cost(y_enc=y_enc[:, idx], output=a3, w1=self.w1, w2=self.w2)
self.cost_.append(cost)
# 通过反向传播计算梯度
grad1, grad2 = self._get_gradient(a1=a1, a2=a2, a3=a3, z2=z2, y_enc=y_enc[:, idx],
w1=self.w1, w2=self.w2)
# 更新权重
delta_w1, delta_w2 = self.eta * grad1, self.eta * grad2
self.w1 -= (delta_w1 + (self.alpha * delta_w1_prev))
self.w2 -= (delta_w2 + (self.alpha * delta_w2_prev))
delta_w1_prev, delta_w2_prev = delta_w1, delta_w2
return self
def costplt1(nn):
'''代价函数图象'''
plt.plot(range(len(nn.cost_)), nn.cost_)
plt.ylim([0, 2000])
plt.ylabel('Cost')
plt.xlabel('Epochs * 50')
plt.tight_layout()
plt.show()
def costplt2(nn):
'''代价函数图象'''
batches = np.array_split(range(len(nn.cost_)), 1000)
cost_ary = np.array(nn.cost_)
cost_avgs = [np.mean(cost_ary[i]) for i in batches]
plt.plot(range(len(cost_avgs)), cost_avgs, color='red')
plt.ylim([0, 10000])
plt.ylabel('Cost')
plt.xlabel('Epochs')
plt.tight_layout()
plt.show()
if __name__ == '__main__':
path = 'mnist' # 路径
# images, labels = load_mnist(path)
# print(np.shape(images), labels)
# 训练样本和测试样本
X_train, y_train = load_mnist(path, kind='train') # X_train : 60000*784
# print(np.shape(X_train),y_train)
X_test, y_test = load_mnist(path, kind='t10k') # X_test : 10000*784
# print(np.shape(X_test), y_test)
nn = NeuralNetMLP(n_output=10,
n_features=X_train.shape[1],
n_hidden=50,
l2=0.1,
l1=0.0,
epochs=1000,
eta=0.001,
alpha=0.001,
decrease_const=0.00001,
shuffle=True,
minibatches=50,
random_state=1)
nn.fit(X_train, y_train, print_progress=True)
costplt1(nn)
costplt2(nn)
y_train_pred = nn.predict(X_train)
acc = np.sum(y_train == y_train_pred, axis=0) / X_train.shape[0]
print('训练准确率: %.2f%%' % (acc * 100))
y_test_pred = nn.predict(X_test)
acc = np.sum(y_test == y_test_pred, axis=0) / X_test.shape[0]
print('测试准确率: %.2f%%' % (acc * 100))
# 错误样本
miscl_img = X_test[y_test != y_test_pred][:25]
correct_lab = y_test[y_test != y_test_pred][:25]
miscl_lab = y_test_pred[y_test != y_test_pred][:25]
fig, ax = plt.subplots(nrows=5, ncols=5, sharex=True, sharey=True,)
ax = ax.flatten()
for i in range(25):
img = miscl_img[i].reshape(28, 28)
ax[i].imshow(img, cmap='Greys', interpolation='nearest')
ax[i].set_title('%d) t: %d p: %d' % (i+1, correct_lab[i], miscl_lab[i]))
ax[0].set_xticks([])
ax[0].set_yticks([])
plt.tight_layout()
plt.show()
# 正确样本
unmiscl_img = X_test[y_test == y_test_pred][:25]
uncorrect_lab = y_test[y_test == y_test_pred][:25]
unmiscl_lab = y_test_pred[y_test == y_test_pred][:25]
fig, ax = plt.subplots(nrows=5, ncols=5, sharex=True, sharey=True, )
ax = ax.flatten()
for i in range(25):
img = unmiscl_img[i].reshape(28, 28)
ax[i].imshow(img, cmap='Greys', interpolation='nearest')
ax[i].set_title('%d) t: %d p: %d' % (i + 1, uncorrect_lab[i], unmiscl_lab[i]))
ax[0].set_xticks([])
ax[0].set_yticks([])
plt.tight_layout()
plt.show()
View Code
测试结果:
代价函数图像:
测试错误样本:
测试正确样本: