4、权重参数矩阵初始化

读者需要了解神经网络的基础知识可以参考神经网络深度学习计算机视觉得分函数损失函数前向传播反向传播激活函数

本文为大家详细的描述了实现神经网络的逻辑代码。

并且用手写识别来实验结果基本实现了神经网络的要求。

二、神经网络架构

Neural_Network_Lab.utils.features

import

Neural_Network_Lab.utils.hypothesis

import

features_split[1](num_examples_1,

num_features_1)

dataset_1.shape(num_examples_2,

num_features_2)

normalize(polynomials)[0]return

polynomialsimport

sinusoid_degree):sin(x).num_examples

0))for

normalize(features):features_normalized

np.copy(features).astype(float)#

计算均值features_mean

防止除以0features_deviation[features_deviation

1features_normalized

normalize_data:(data_normalized,features_mean,features_deviation)

normalize(data_processed)data_processed

data_normalized#

generate_sinusoids(data_normalized,

np.concatenate((data_processed,

sinusoids),

generate_polynomials(data_normalized,

polynomial_degree,

np.concatenate((data_processed,

polynomials),

np.hstack((np.ones((num_examples,

1)),

初始化数据标签网络层次(用列表表示如三层[784,25,10]表示输入层784个神经元25个隐藏层神经元10个输出层神经元)数据是否标准化处理。

class

__init__(self,data,labels,layers,normalize_dataFalse):data_processed

prepare_for_training(data,normalize_datanormalize_data)[0]self.data

labelsself.layers

MultilayerPerceptron.thetas_init(layers)3、训练函数

输入迭代次数学习率进行梯度下降算法更新权重参数矩阵得到最终的权重参数矩阵和损失值。

矩阵不好进行更新操作可以把它拉成向量。

def

MultilayerPerceptron.thetas_unroll(self.thetas)(optimized_theta,

cost_history)

MultilayerPerceptron.gradient_descent(self.data,self.labels,unrolled_theta,self.layers,max_ietrations,alpha)self.thetas

MultilayerPerceptron.thetas_roll(optimized_theta,self.layers)return

4、权重参数矩阵初始化

初始值小#这里需要考虑偏置项偏置的个数与输出的个数一样thetas[layer_index]np.random.rand(out_count,in_count1)

0.05

thetas_unroll(thetas):#拼接成一个向量num_theta_layers

np.array([])for

range(num_theta_layers):unrolled_theta

np.hstack((unrolled_theta,thetas[theta_layer_index].flatten()))return

unrolled_theta

thetas_roll(unrolled_theta,layers):num_layers

len(layers)thetas

thetas_volumelayer_theta_unrolled

unrolled_theta[start_index:end_index]thetas[layer_index]

layer_theta_unrolled.reshape((thetas_height,thetas_width))unrolled_shift

unrolled_shift

feedforword_propagation(data,thetas,layers):num_layers

data.shape[0]in_layer_activation

data

thetas[layer_index]out_layer_activation

sigmoid(np.dot(in_layer_activation,theta.T))

#输出层#

np.hstack((np.ones((num_examples,1)),out_layer_activation))in_layer_activation

out_layer_activation#返回输出层结果,不要偏置项return

损失函数

cost_function(data,labels,thetas,layers):num_layers

MultilayerPerceptron.feedforword_propagation(data,thetas,layers)#制作标签每一个样本的标签都是one-dotbitwise_labels

np.zeros((num_examples,num_labels))for

example_index

range(num_examples):bitwise_labels[example_index][labels[example_index][0]]

np.sum(np.log(predictions[bitwise_labels

1]))bit_not_set_cost

(bit_set_costbit_not_set_cost)return

cost

在梯度下降的过程中要实现参数矩阵的更新必须要实现反向传播。

利用上述的公式进行运算即可得到。

staticmethoddef

back_propagation(data,labels,thetas,layers):num_layers

len(layers)(num_examples,num_features)

layers[-1]deltas

np.zeros((out_count,in_count1))

#25

range(num_examples):layers_inputs

{}layers_activations

data[example_index,:].reshape((num_features,1))layers_activations[0]

layer_index

np.dot(layer_theta,layers_activation)

第一次

np.vstack((np.array([[1]]),sigmoid(layer_input)))

#完成激活函数加上一个偏置参数layers_inputs[layer_index1]

layer_input

后一层计算结果layers_activations[layer_index

layers_activation

后一层完成激活的结果output_layer_activation

layers_activation[1:,:]#计算输出层和结果的差异delta

{}#标签处理bitwise_label

np.zeros((num_label_types,1))bitwise_label[labels[example_index][0]]

1#计算输出结果和真实值之间的差异delta[num_layers-1]

bitwise_label

layers_inputs[layer_index]layer_input

np.vstack((np.array((1)),layer_input))#按照公式计算delta[layer_index]

np.dot(layer_theta.T,next_delta)*sigmoid(layer_input)#过滤掉偏置参数delta[layer_index]

delta[layer_index][1:,:]#计算梯度值for

layer_index

range(num_layers-1):layer_delta

np.dot(delta[layer_index1],layers_activations[layer_index].T)

deltas[layer_index]

range(num_layers-1):deltas[layer_index]

deltas[layer_index]

gradient_step(data,labels,optimized_theta,layers):theta

MultilayerPerceptron.thetas_roll(optimized_theta,layers)#反向传播BPthetas_rolled_gradinets

MultilayerPerceptron.back_propagation(data,labels,theta,layers)thetas_unrolled_gradinets

MultilayerPerceptron.thetas_unroll(thetas_rolled_gradinets)return

实现梯度下降

gradient_descent(data,labels,unrolled_theta,layers,max_ietrations,alpha):#1.

计算损失值#2.

MultilayerPerceptron.cost_function(data,labels,MultilayerPerceptron.thetas_roll(optimized_theta,layers),layers)cost_history.append(cost)theta_gradient

MultilayerPerceptron.gradient_step(data,labels,optimized_theta,layers)optimized_theta

optimized_theta

predict(self,data):data_processed

prepare_for_training(data,normalize_data

self.normalize_data)[0]num_examples

data_processed.shape[0]predictions

MultilayerPerceptron.feedforword_propagation(data_processed,self.thetas,self.layers)return

np.argmax(predictions,axis1).reshape((num_examples,1))

四、完整代码

Neural_Network_Lab.utils.features

import

Neural_Network_Lab.utils.hypothesis

import

__init__(self,data,labels,layers,normalize_dataFalse):data_processed

prepare_for_training(data,normalize_datanormalize_data)[0]self.data

labelsself.layers

MultilayerPerceptron.thetas_init(layers)def

predict(self,data):data_processed

prepare_for_training(data,normalize_data

self.normalize_data)[0]num_examples

data_processed.shape[0]predictions

MultilayerPerceptron.feedforword_propagation(data_processed,self.thetas,self.layers)return

np.argmax(predictions,axis1).reshape((num_examples,1))def

1000,alpha

MultilayerPerceptron.thetas_unroll(self.thetas)(optimized_theta,

cost_history)

MultilayerPerceptron.gradient_descent(self.data,self.labels,unrolled_theta,self.layers,max_ietrations,alpha)self.thetas

MultilayerPerceptron.thetas_roll(optimized_theta,self.layers)return

self.thetas,cost_historystaticmethoddef

gradient_descent(data,labels,unrolled_theta,layers,max_ietrations,alpha):#1.

计算损失值#2.

MultilayerPerceptron.cost_function(data,labels,MultilayerPerceptron.thetas_roll(optimized_theta,layers),layers)cost_history.append(cost)theta_gradient

MultilayerPerceptron.gradient_step(data,labels,optimized_theta,layers)optimized_theta

optimized_theta

optimized_theta,cost_historystaticmethoddef

gradient_step(data,labels,optimized_theta,layers):theta

MultilayerPerceptron.thetas_roll(optimized_theta,layers)#反向传播BPthetas_rolled_gradinets

MultilayerPerceptron.back_propagation(data,labels,theta,layers)thetas_unrolled_gradinets

MultilayerPerceptron.thetas_unroll(thetas_rolled_gradinets)return

thetas_unrolled_gradinetsstaticmethoddef

back_propagation(data,labels,thetas,layers):num_layers

len(layers)(num_examples,num_features)

layers[-1]deltas

np.zeros((out_count,in_count1))

#25

range(num_examples):layers_inputs

{}layers_activations

data[example_index,:].reshape((num_features,1))layers_activations[0]

layer_index

np.dot(layer_theta,layers_activation)

第一次

np.vstack((np.array([[1]]),sigmoid(layer_input)))

#完成激活函数加上一个偏置参数layers_inputs[layer_index1]

layer_input

后一层计算结果layers_activations[layer_index

layers_activation

后一层完成激活的结果output_layer_activation

layers_activation[1:,:]#计算输出层和结果的差异delta

{}#标签处理bitwise_label

np.zeros((num_label_types,1))bitwise_label[labels[example_index][0]]

1#计算输出结果和真实值之间的差异delta[num_layers-1]

bitwise_label

layers_inputs[layer_index]layer_input

np.vstack((np.array((1)),layer_input))#按照公式计算delta[layer_index]

np.dot(layer_theta.T,next_delta)*sigmoid(layer_input)#过滤掉偏置参数delta[layer_index]

delta[layer_index][1:,:]#计算梯度值for

layer_index

range(num_layers-1):layer_delta

np.dot(delta[layer_index1],layers_activations[layer_index].T)

deltas[layer_index]

range(num_layers-1):deltas[layer_index]

deltas[layer_index]

cost_function(data,labels,thetas,layers):num_layers

MultilayerPerceptron.feedforword_propagation(data,thetas,layers)#制作标签每一个样本的标签都是one-dotbitwise_labels

np.zeros((num_examples,num_labels))for

example_index

range(num_examples):bitwise_labels[example_index][labels[example_index][0]]

np.sum(np.log(predictions[bitwise_labels

1]))bit_not_set_cost

(bit_set_costbit_not_set_cost)return

coststaticmethoddef

feedforword_propagation(data,thetas,layers):num_layers

data.shape[0]in_layer_activation

data

thetas[layer_index]out_layer_activation

sigmoid(np.dot(in_layer_activation,theta.T))

#输出层#

np.hstack((np.ones((num_examples,1)),out_layer_activation))in_layer_activation

out_layer_activation#返回输出层结果,不要偏置项return

in_layer_activation[:,1:]staticmethoddef

thetas_roll(unrolled_theta,layers):num_layers

len(layers)thetas

thetas_volumelayer_theta_unrolled

unrolled_theta[start_index:end_index]thetas[layer_index]

layer_theta_unrolled.reshape((thetas_height,thetas_width))unrolled_shift

unrolled_shift

thetas_unroll(thetas):#拼接成一个向量num_theta_layers

np.array([])for

range(num_theta_layers):unrolled_theta

np.hstack((unrolled_theta,thetas[theta_layer_index].flatten()))return

len(layers)thetas

初始值小#这里需要考虑偏置项偏置的个数与输出的个数一样thetas[layer_index]np.random.rand(out_count,in_count1)

0.05

共一万个样本第一列为标签值一列表示像素点的值共28*28共784个像素点。

import

Neural_Network_Lab.Multilayer_Perceptron

import

pd.read_csv(../Neural_Network_Lab/data/mnist-demo.csv)

#展示数据

math.ceil(math.sqrt(numbers_to_display))

for

range(numbers_to_display):digit

data[plot_index:plot_index1].valuesdigit_label

int(math.sqrt(digit_pixels.shape[0]))frame

digit_pixels.reshape((image_size,image_size))plt.subplot(num_cells,num_cells,plot_index1)plt.imshow(frame,cmap

plt.subplots_adjust(wspace0.5,hspace0.5)

plt.show()train_data

data.drop(train_data.index)train_data

train_data.values

test_data.valuesnum_training_examples

8000X_train

train_data[:num_training_examples,1:]

y_train

train_data[:num_training_examples,[0]]X_test

test_data[:,1:]

MultilayerPerceptron(X_train,y_train,layers,normalize_data)

multilayerperceptron.train(max_iteration,alpha)

plt.plot(range(len(cost_history)),cost_history)

plt.xlabel(Grident

multilayerperceptron.predict(X_train)

y_test_predictions

multilayerperceptron.predict(X_test)train_p

y_train)

print(测试集准确率,test_p)numbers_to_display

num_cells

math.ceil(math.sqrt(numbers_to_display))

for

range(numbers_to_display):digit_label

y_test[plot_index,0]digit_pixels

X_test[plot_index,:]predicted_label

y_test_predictions[plot_index][0]image_size

int(math.sqrt(digit_pixels.shape[0]))frame

digit_pixels.reshape((image_size,image_size))plt.subplot(num_cells,num_cells,plot_index1)color_map

Greens

color_map)plt.title(predicted_label)plt.tick_params(axisboth,whichboth,bottomFalse,leftFalse,labelbottomFalse)plt.subplots_adjust(wspace0.5,hspace0.5)

plt.show()

这里准确率不高读者可以自行调整参数改变迭代次数网络层次都可以哦。