#!/usr/bin/python """ A Framework of Back Propagation Neural Network (BP) model Easy to use: * add many layers as you want ! ! ! * clearly see how the loss decreasing Easy to expand: * more activation functions * more loss functions * more optimization method Author: Stephen Lee Github : https://github.com/RiptideBo Date: 2017.11.23 """ import numpy as np from matplotlib import pyplot as plt def sigmoid(x: np.ndarray) -> np.ndarray: return 1 / (1 + np.exp(-x)) class DenseLayer: """ Layers of BP neural network """ def __init__( self, units, activation=None, learning_rate=None, is_input_layer=False ): """ common connected layer of bp network :param units: numbers of neural units :param activation: activation function :param learning_rate: learning rate for paras :param is_input_layer: whether it is input layer or not """ self.units = units self.weight = None self.bias = None self.activation = activation if learning_rate is None: learning_rate = 0.3 self.learn_rate = learning_rate self.is_input_layer = is_input_layer def initializer(self, back_units): rng = np.random.default_rng() self.weight = np.asmatrix(rng.normal(0, 0.5, (self.units, back_units))) self.bias = np.asmatrix(rng.normal(0, 0.5, self.units)).T if self.activation is None: self.activation = sigmoid def cal_gradient(self): # activation function may be sigmoid or linear if self.activation == sigmoid: gradient_mat = np.dot(self.output, (1 - self.output).T) gradient_activation = np.diag(np.diag(gradient_mat)) else: gradient_activation = 1 return gradient_activation def forward_propagation(self, xdata): self.xdata = xdata if self.is_input_layer: # input layer self.wx_plus_b = xdata self.output = xdata return xdata else: self.wx_plus_b = np.dot(self.weight, self.xdata) - self.bias self.output = self.activation(self.wx_plus_b) return self.output def back_propagation(self, gradient): gradient_activation = self.cal_gradient() # i * i 维 gradient = np.asmatrix(np.dot(gradient.T, gradient_activation)) self._gradient_weight = np.asmatrix(self.xdata) self._gradient_bias = -1 self._gradient_x = self.weight self.gradient_weight = np.dot(gradient.T, self._gradient_weight.T) self.gradient_bias = gradient * self._gradient_bias self.gradient = np.dot(gradient, self._gradient_x).T # upgrade: the Negative gradient direction self.weight = self.weight - self.learn_rate * self.gradient_weight self.bias = self.bias - self.learn_rate * self.gradient_bias.T # updates the weights and bias according to learning rate (0.3 if undefined) return self.gradient class BPNN: """ Back Propagation Neural Network model """ def __init__(self): self.layers = [] self.train_mse = [] self.fig_loss = plt.figure() self.ax_loss = self.fig_loss.add_subplot(1, 1, 1) def add_layer(self, layer): self.layers.append(layer) def build(self): for i, layer in enumerate(self.layers[:]): if i < 1: layer.is_input_layer = True else: layer.initializer(self.layers[i - 1].units) def summary(self): for i, layer in enumerate(self.layers[:]): print(f"------- layer {i} -------") print("weight.shape ", np.shape(layer.weight)) print("bias.shape ", np.shape(layer.bias)) def train(self, xdata, ydata, train_round, accuracy): self.train_round = train_round self.accuracy = accuracy self.ax_loss.hlines(self.accuracy, 0, self.train_round * 1.1) x_shape = np.shape(xdata) for _ in range(train_round): all_loss = 0 for row in range(x_shape[0]): _xdata = np.asmatrix(xdata[row, :]).T _ydata = np.asmatrix(ydata[row, :]).T # forward propagation for layer in self.layers: _xdata = layer.forward_propagation(_xdata) loss, gradient = self.cal_loss(_ydata, _xdata) all_loss = all_loss + loss # back propagation: the input_layer does not upgrade for layer in self.layers[:0:-1]: gradient = layer.back_propagation(gradient) mse = all_loss / x_shape[0] self.train_mse.append(mse) self.plot_loss() if mse < self.accuracy: print("----达到精度----") return mse return None def cal_loss(self, ydata, ydata_): self.loss = np.sum(np.power((ydata - ydata_), 2)) self.loss_gradient = 2 * (ydata_ - ydata) # vector (shape is the same as _ydata.shape) return self.loss, self.loss_gradient def plot_loss(self): if self.ax_loss.lines: self.ax_loss.lines.remove(self.ax_loss.lines[0]) self.ax_loss.plot(self.train_mse, "r-") plt.ion() plt.xlabel("step") plt.ylabel("loss") plt.show() plt.pause(0.1) def example(): rng = np.random.default_rng() x = rng.normal(size=(10, 10)) y = np.asarray( [ [0.8, 0.4], [0.4, 0.3], [0.34, 0.45], [0.67, 0.32], [0.88, 0.67], [0.78, 0.77], [0.55, 0.66], [0.55, 0.43], [0.54, 0.1], [0.1, 0.5], ] ) model = BPNN() for i in (10, 20, 30, 2): model.add_layer(DenseLayer(i)) model.build() model.summary() model.train(xdata=x, ydata=y, train_round=100, accuracy=0.01) if __name__ == "__main__": example()