Neural network (BP) algorithm Python implementation and application

This article mainly introduces the implementation of neural network (BP) algorithm and simple application in Python in detail. It has certain reference value. Interested friends can refer to it.

The examples in this article are shared with everyone. The specific code for implementing neural network algorithms and applications in Python is provided for your reference. The specific content is as follows

First use Python to implement a simple neural network algorithm:

import numpy as np


# 定义tanh函数
def tanh(x):
  return np.tanh(x)


# tanh函数的导数
def tan_deriv(x):
  return 1.0 - np.tanh(x) * np.tan(x)


# sigmoid函数
def logistic(x):
  return 1 / (1 + np.exp(-x))


# sigmoid函数的导数
def logistic_derivative(x):
  return logistic(x) * (1 - logistic(x))


class NeuralNetwork:
  def __init__(self, layers, activation='tanh'):
    """
    神经网络算法构造函数
    :param layers: 神经元层数
    :param activation: 使用的函数（默认tanh函数）
    :return:none
    """
    if activation == 'logistic':
      self.activation = logistic
      self.activation_deriv = logistic_derivative
    elif activation == 'tanh':
      self.activation = tanh
      self.activation_deriv = tan_deriv

    # 权重列表
    self.weights = []
    # 初始化权重（随机）
    for i in range(1, len(layers) - 1):
      self.weights.append((2 * np.random.random((layers[i - 1] + 1, layers[i] + 1)) - 1) * 0.25)
      self.weights.append((2 * np.random.random((layers[i] + 1, layers[i + 1])) - 1) * 0.25)

  def fit(self, X, y, learning_rate=0.2, epochs=10000):
    """
    训练神经网络
    :param X: 数据集（通常是二维）
    :param y: 分类标记
    :param learning_rate: 学习率（默认0.2）
    :param epochs: 训练次数（最大循环次数，默认10000）
    :return: none
    """
    # 确保数据集是二维的
    X = np.atleast_2d(X)

    temp = np.ones([X.shape[0], X.shape[1] + 1])
    temp[:, 0: -1] = X
    X = temp
    y = np.array(y)

    for k in range(epochs):
      # 随机抽取X的一行
      i = np.random.randint(X.shape[0])
      # 用随机抽取的这一组数据对神经网络更新
      a = [X[i]]
      # 正向更新
      for l in range(len(self.weights)):
        a.append(self.activation(np.dot(a[l], self.weights[l])))
      error = y[i] - a[-1]
      deltas = [error * self.activation_deriv(a[-1])]

      # 反向更新
      for l in range(len(a) - 2, 0, -1):
        deltas.append(deltas[-1].dot(self.weights[l].T) * self.activation_deriv(a[l]))
        deltas.reverse()
      for i in range(len(self.weights)):
        layer = np.atleast_2d(a[i])
        delta = np.atleast_2d(deltas[i])
        self.weights[i] += learning_rate * layer.T.dot(delta)

  def predict(self, x):
    x = np.array(x)
    temp = np.ones(x.shape[0] + 1)
    temp[0:-1] = x
    a = temp
    for l in range(0, len(self.weights)):
      a = self.activation(np.dot(a, self.weights[l]))
    return a

Use your own defined neural network algorithm to implement some simple functions:

Small case:

10 Close to 1

Second example: Identify numbers in pictures

Import data:

from NN.NeuralNetwork import NeuralNetwork
import numpy as np

nn = NeuralNetwork([2, 2, 1], 'tanh')
temp = [[0, 0], [0, 1], [1, 0], [1, 1]]
X = np.array(temp)
y = np.array([0, 1, 1, 0])
nn.fit(X, y)
for i in temp:
  print(i, nn.predict(i))

Observe: size (1797, 64)

Number 0

The next code is to identify them:

from sklearn.datasets import load_digits
import pylab as pl

digits = load_digits()
print(digits.data.shape)
pl.gray()
pl.matshow(digits.images[0])
pl.show()

Result:

The diagonal of the matrix represents the number of correct predictions, and it is found that the correct rate is many

This table more intuitively shows the prediction accuracy:

A total of 450 cases, the success rate is 94%

Related recommendations:

kNN algorithm Python implementation and simple number recognition method

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