1.1 感知机perceptron
20 世纪五六十年代，科学家Frank Rosenblatt 发明了感知机，其受到了 Warren McCulloch 和 Walter Pitts 早期研究的影响。
what's weighted sum in perceptron?
In the context of the perceptron algorithm, the weighted sum refers to the linear combination of the input features and their corresponding weights. Specifically, given an input vector x = [x1, x2, ..., xn] and weight vector w = [w1, w2, ..., wn], the weighted sum is computed as:
z = w1*x1 + w2*x2 + ... + wn*xnThis is the linear combination of the input features x with their corresponding weights w. The weighted sum is then passed through an activation function, typically a step function, to produce the output of the perceptron. In other words, the weighted sum determines whether the perceptron should fire (output 1) or not (output 0) based on the input.
The weighted sum can also be expressed in vector notation as the dot product of the input vector x and the weight vector w:
z = w.dot(x)In this form, the weighted sum is a concise way of representing the linear combination of the input features and their corresponding weights.
感知机接收若干个二进制输入 x1,x2,x3,...，并生成一个二进制输出，如图 1-3 所示。
图 1-3 中的感知机有 3 个输入 x1,x2,x3，一般来说输入还可以更多或更少。Rosenblatt 提出了
一条计算输出的简单规则。他引入权重 w1,w2,w3，用这些实数来表示输入对于输出的重要性。神
经元的输出究竟是 0 还是 1，则由加权和 小于或大于某个阈值来决定。