神经元的实现

本文将使用python实现一个神经元(感知器).

本文来自https://www.zybuluo.com/hanbingtao/note/433855

理论请参考上文.下面是python2和3的实现

python2

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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。
        激活函数的类型为double -> double
        '''
        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, w): x * w,  
                       zip(input_vec, self.weights))
                , 0.0) + self.bias)
    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
        '''
        # 把input_vec[x1,x2,x3,...]和weights[w1,w2,w3,...]打包在一起
        # 变成[(x1,w1),(x2,w2),(x3,w3),...]
        # 然后利用感知器规则更新权重
        delta = label - output
        self.weights = map(
            lambda (x, w): w + rate * delta * x,
            zip(input_vec, self.weights))
        # 更新bias
        self.bias += rate * delta

def f(x):
    '''
    定义激活函数f
    '''
    return 1 if x > 0 else 0
def get_training_dataset():
    '''
    基于and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]]
    # 期望的输出列表，注意要与输入一一对应
    # [1,1] -> 1, [0,0] -> 0, [1,0] -> 0, [0,1] -> 0
    labels = [1, 0, 0, 0]
    return input_vecs, labels    
def train_and_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（因为and是二元函数），激活函数为f
    p = Perceptron(2, f)
    # 训练，迭代10轮, 学习速率为0.1
    input_vecs, labels = get_training_dataset()
    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
    and_perception = train_and_perceptron()
    # 打印训练获得的权重
    print and_perception
    # 测试
    print '1 and 1 = %d' % and_perception.predict([1, 1])
    print '0 and 0 = %d' % and_perception.predict([0, 0])
    print '1 and 0 = %d' % and_perception.predict([1, 0])
    print '0 and 1 = %d' % and_perception.predict([0, 1])

python3

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from functools import reduce


class Perceptron(object):
    def __init__(self, input_num, activator):
        self.activator = activator
        self.weights = [0.0 for _ in range(input_num)]
        self.bias = 0.0

    def train(self, input_vec, iteration, labels, rate):
        for _ in range(iteration):
            self._one_iteration(input_vec, labels, rate)

    def _one_iteration(self, input_vec, labels, rate):
        samples = zip(input_vec, labels)
        for (vec, label) in samples:
            output = self.predict(vec)
            self._update_weights(vec, output, label, rate)

    def predict(self, vec):
        return self.activator(
            reduce(
                lambda a, b: a + b,
                list(map(
                    lambda x, w: x * w,
                    vec, self.weights
                )), 0.0
            ) + self.bias
        )

    def _update_weights(self, vec, output, label, rate):
        delta = label - output
        self.weights = list(map(
            lambda x, w: w + rate * delta * x,  # 在python2里是用的(x,w)形式
            vec, self.weights
        ))
        self.bias += rate * delta

    def __str__(self):
        return 'weights: %s\nbias: %s\n' % (self.weights, self.bias)


def activator(x):
    return 1 if x > 0 else 0


def get_data_sets():
    x = [[0, 1], [1, 0], [1, 1], [0, 0]]
    labels = [0, 0, 1, 0]
    return x, labels


def train():
    p = Perceptron(2, activator)
    x, labels = get_data_sets()
    p.train(x, 20, labels, 0.05)
    return p


if __name__ == '__main__':
    p = train()
    print(p)
    # 测试
    print('1 and 1 = %d' % p.predict([1, 1]))
    print('0 and 0 = %d' % p.predict([0, 0]))
    print('1 and 0 = %d' % p.predict([1, 0]))
    print('0 and 1 = %d' % p.predict([0, 1]))

结果

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weights: [0.1, 0.05]
bias: -0.1

1 and 1 = 1
0 and 0 = 0
1 and 0 = 0
0 and 1 = 0

其实上面就是梯度下降的过程.