深度学习笔记--单层感知机原理及代码实现

╰半橙微兮° 2022-04-10 13:41 548阅读 0赞

**本文作者：合肥工业大学 管理学院 钱洋 email：1563178220@qq.com 。  
以下内容是个人的学习笔记，内容可能有不到之处，欢迎交流。未经本人允许禁止转载。**

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# python3实现简单的感知器 #

下面使用python3实现or运算：

#-*- coding:utf-8 -*-
    from functools import reduce
    class Perceptron(object):
        def __init__(self, input_num, activator):
            ''' 初始化感知器，设置输入参数的个数，以及激活函数。 '''
            self.activator = activator
            # 权重向量初始化为0
            self.weights = [0.0 for _ in range(input_num)]
            # 偏置项初始化为0
            self.bias = 0.0
        def __str__(self):
            ''' 打印学习到的权重、偏置项 '''
            return 'weights\t:%s\nbias\t:%f\n' % (self.weights, self.bias)
        def predict(self, input_vec):
            ''' 输入向量，输出感知器的计算结果 '''
            # 把input_vec[x1,x2,x3...]和weights[w1,w2,w3,...]打包在一起
            # 变成[(x1,w1),(x2,w2),(x3,w3),...]
            # 然后利用map函数计算[x1*w1, x2*w2, x3*w3]
            # 最后利用reduce求和
            return self.activator(reduce(lambda a,b:a+b,map(lambda x:x[0]*x[1],zip(input_vec,self.weights)),0.0)+self.bias)#0.0为reduce的初始计算值
        def train(self, input_vecs, labels, iteration, rate):
            ''' 输入训练数据：一组向量、与每个向量对应的label；以及训练轮数、学习率 '''
            for i in range(iteration):
                self._one_iteration(input_vecs, labels, rate)
    
        def _one_iteration(self, input_vecs, labels, rate):
            ''' 一次迭代，把所有的训练数据过一遍 '''
            # 把输入和输出打包在一起，成为样本的列表[(input_vec, label), ...]
            # 而每个训练样本是(input_vec, label)
            samples = zip(input_vecs, labels)
            # 对每个样本，按照感知器规则更新权重
            for input_vec, label in samples:
                # 计算感知器在当前权重下的输出
                output = self.predict(input_vec)
                # 更新权重
                self._update_weights(input_vec, output, label, rate)
        def _update_weights(self, input_vec, output, label, rate):
            ''' 按照感知器规则更新权重 '''
            delta = label - output
            self.weights = list(map(lambda x:x[1]+rate*delta*x[0],zip(input_vec,self.weights)))
            # 更新bias
            self.bias += rate * delta
    
    def f(x):
        ''' 激活函数f '''
        return 1 if x > 0 else 0
    def get_training_data():
        ''' 基于or真值表构建训练数据 '''
        # 构建训练数据
        # 输入向量列表
        input_vecs = [[1,1], [0,0], [1,0], [0,1]]
        labels = [1, 0, 1, 1]
        return input_vecs, labels
    def train_perceptron():
        ''' 使用and真值表训练感知器 '''
        # 创建感知器，输入参数个数为2，激活函数为f
        p = Perceptron(2, f)
        # 获取数据集
        input_vecs, labels = get_training_data()   # 训练，迭代10轮, 学习速率为0.1
        p.train(input_vecs, labels, 10, 0.1)
        #返回训练好的感知器
        return p
    if __name__ == '__main__':
        # 训练and感知器
        perception = train_perceptron()
        # 打印训练获得的权重
        print (perception)
        # 测试
        print('1 and 1 = %d' % perception.predict([1, 1]))
        print('0 and 0 = %d' % perception.predict([0, 0]))
        print('1 and 0 = %d' % perception.predict([1, 0]))
        print('0 and 1 = %d' % perception.predict([0, 1]))

程序的输出结果为：  
![在这里插入图片描述][20190111103100733.png]  
参考内容：  
[https://towardsdatascience.com/what-the-hell-is-perceptron-626217814f53][https_towardsdatascience.com_what-the-hell-is-perceptron-626217814f53]  
[https://towardsdatascience.com/activation-functions-neural-networks-1cbd9f8d91d6][https_towardsdatascience.com_activation-functions-neural-networks-1cbd9f8d91d6]  
[http://hagan.okstate.edu/NNDesign.pdf][http_hagan.okstate.edu_NNDesign.pdf]  
[https://www.zybuluo.com/hanbingtao/note/433855][https_www.zybuluo.com_hanbingtao_note_433855]

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[20190111103100733.png]: /images/20220328/1f1ca1e3dfe64bfd8339dd74279911bb.png
[https_towardsdatascience.com_what-the-hell-is-perceptron-626217814f53]: https://towardsdatascience.com/what-the-hell-is-perceptron-626217814f53
[https_towardsdatascience.com_activation-functions-neural-networks-1cbd9f8d91d6]: https://towardsdatascience.com/activation-functions-neural-networks-1cbd9f8d91d6
[http_hagan.okstate.edu_NNDesign.pdf]: http://hagan.okstate.edu/NNDesign.pdf
[https_www.zybuluo.com_hanbingtao_note_433855]: https://www.zybuluo.com/hanbingtao/note/433855