BP神经网络算法程序实现鸢尾花(iris)数据集分类

作者有话说

最近学习了一下BP神经网络，写篇随笔记录一下得到的一些结果和代码，该随笔会比较简略，对一些简单的细节不加以说明。

目录

• BP算法简要推导
• 应用实例
• PYTHON代码

BP算法简要推导

该部分用一个$2\times3\times 2\times1$的神经网络为例简要说明BP算法的步骤。

• 向前计算输出

• 反向传播误差

•  权重更新

 应用实例

鸢尾花数据集一共有150个样本，分为3个类别，每个样本有4个特征，（数据集链接：http://archive.ics.uci.edu/ml/datasets/Iris)。针对该数据集，选取如下神经网络结构和激活函数

• 神经网络组成

 

• 隐含层神经元个数对准确率的影响

调节隐含层神经元的个数，得到模型分类准确率的变化图像如下：

• 梯度更新步长对准确率的影响

调节梯度更新步长（学习率）的大小，得到模型分类准确率的变化图像如下：

 

可见准确率最高可达98.6666666666667%

PYTHON代码

BPNeuralNetwork.py

# coding=utf-8
import numpy as np


def tanh(x):
    return np.tanh(x)


def tanh_deriv(x):
    return 1.0 - np.tanh(x) * np.tanh(x)


def logistic(x):
    return 1.0 / (1.0 + np.exp(-x))


def logistic_derivative(x):
    return logistic(x) * (1.0 - logistic(x))


class NeuralNetwork:
    def __init__(self, layers, activation='tanh'):
        """
        """
        if activation == 'logistic':
            self.activation = logistic
            self.activation_deriv = logistic_derivative
        elif activation == 'tanh':
            self.activation = tanh
            self.activation_deriv = tanh_deriv

        self.weights = []
        self.weights.append((2 * np.random.random((layers[0] + 1, layers[1] - 1)) - 1) * 0.25)
        for i in range(2, len(layers)):
            self.weights.append((2 * np.random.random((layers[i - 1], layers[i])) - 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):
        X = np.atleast_2d(X)
        # atlest_2d函数:确认X至少二位的矩阵
        temp = np.ones([X.shape[0], X.shape[1] + 1])
        # 初始化矩阵全是1（行数，列数+1是为了有B这个偏向）
        temp[:, 0:-1] = X
        # 行全选，第一列到倒数第二列
        X = temp
        y = np.array(y)
        # 数据结构转换
        for k in range(epochs):
            # 抽样梯度下降epochs抽样
            i = np.random.randint(X.shape[0])
            a = [X[i]]
            # print(self.weights)

            for l in range(len(self.weights) - 1):
                b = self.activation(np.dot(a[l], self.weights[l]))
                b = b.tolist()
                b.append(1)
                b = np.array(b)
                a.append(b)

            a.append(self.activation(np.dot(a[-1], self.weights[-1])))

            # 向前传播，得到每个节点的输出结果
            error = y[i] - a[-1]
            # 最后一层错误率
            deltas = [error * self.activation_deriv(a[-1])]

            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) - 1):
                layer = np.atleast_2d(a[i])
                delta = np.atleast_2d(deltas[i])
                delta = delta[:, : -1]
                self.weights[i] += learning_rate * layer.T.dot(delta)
            layer = np.atleast_2d(a[-2])
            delta = np.atleast_2d(deltas[-1])
            # print('w=',self.weights[-1])
            # print('l=',layer)
            # print('d=',delta)
            self.weights[-1] += learning_rate * layer.T.dot(delta)

    def predict(self, x):
        x = np.atleast_2d(x)
        # atlest_2d函数:确认X至少二位的矩阵
        temp = np.ones(x.shape[1] + 1)
        # 初始化矩阵全是1（行数，列数+1是为了有B这个偏向）
        temp[:4] = x[0, :]
        a = temp
        # print(self.weights)

        for l in range(len(self.weights) - 1):
            b = self.activation(np.dot(a, self.weights[l]))
            b = b.tolist()
            b.append(1)
            b = np.array(b)
            a = b

        a = self.activation(np.dot(a, self.weights[-1]))
        return (a)

Text.py

from BPNeuralNetwork import NeuralNetwork
import numpy as np
from openpyxl import load_workbook
import xlrd

nn = NeuralNetwork([4, 12, 3], 'tanh')
x = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])
y = np.array([0, 1, 1, 0])
import openpyxl

# 打开excel文件,获取工作簿对象
data = xlrd.open_workbook('BbezdekIris.xlsx')
table = data.sheets()[0]
nrows = table.nrows  # 行数
ncols = table.ncols  # 列数
datamatrix = np.zeros((nrows, ncols - 1))
for k in range(ncols - 1):
    cols = table.col_values(k)
    minVals = min(cols)
    maxVals = max(cols)
    cols1 = np.matrix(cols)  # 把list转换为矩阵进行矩阵操作
    ranges = maxVals - minVals
    b = cols1 - minVals
    normcols = b / ranges  # 数据进行归一化处理
    datamatrix[:, k] = normcols  # 把数据进行存储
# print(datamatrix)
datalabel = table.col_values(ncols - 1)
for i in range(nrows):
    if datalabel[i] == 'Iris-setosa':
        datalabel[i] = [1, 0, 0]
    if datalabel[i] == 'Iris-versicolor':
        datalabel[i] = [0, 1, 0]
    if datalabel[i] == 'Iris-virginica':
        datalabel[i] = [0, 0, 1]
datamatrix1 = table.col_values(0)
for i in range(nrows):
    datamatrix1[i] = datamatrix[i]
x = datamatrix1
y = datalabel
nn.fit(x, y)
CategorySet = ['Iris-setosa', 'Iris-versicolor', 'Iris-virginica']
P = np.zeros((1, len(y)))
P = y

a = [0, 1, 3, 5, 4, 7, 8, 1, 5, 1, 5, 5, 1]
print(a.index(max(a)))
b = nn.predict(x[1])
b = b.tolist()
print(b.index(max(b)))

for i in range(len(y)):
    Predict = nn.predict(x[i])
    Predict = Predict.tolist()
    Index = Predict.index(max(Predict, key=abs))
    Real = y[i]
    Category = Real.index(max(Real, key=abs))
    if Index == Category:
        P[i] = 1
        print('样本', i + 1, ':', x[i], '   ', '实际类别', '：', CategorySet[Category], '   ', '预测类别', '：', CategorySet[Index],
              '   ', '预测正确')
    else:
        P[i] = 0
        print('样本', i + 1, ':', x[i], '   ', '实际类别', '：', CategorySet[Category], '   ', '预测类别', '：', CategorySet[Index],
              '   ', '预测错误')

print('准确率', ':', sum(P) / len(P))