深度學習——神經網絡

目錄

線性界線：

N維界線：

感知器：

​感知器算法實現：

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線性界線：

 ———— （），W：權重，b：偏差

y = label: 0 or 1

predection:

N維界線：

n維：

n - 1維超平面的方程：

predection:

感知器：

1、它是神經網絡的基礎構成組件。

2、

3、整個數據集中的每一個點都會把分類的結果提供給感知器（分類函數），並調整感知器。——這就是計算機在神經網絡算法中，找尋最優感知器的原理。

4、

感知器算法實現：

import numpy as np
# Setting the random seed, feel free to change it and see different solutions.
np.random.seed(42)

def stepFunction(t):
    if t >= 0:
        return 1
    return 0

def prediction(X, W, b):
    return stepFunction((np.matmul(X,W)+b)[0])

# TODO: Fill in the code below to implement the perceptron trick.
# The function should receive as inputs the data X, the labels y,
# the weights W (as an array), and the bias b,
# update the weights and bias W, b, according to the perceptron algorithm,
# and return W and b.
def perceptronStep(X, y, W, b, learn_rate = 0.01):
    # Fill in code
    for i in range(len(X)):
        y_hat = prediction(X[i], W, b)
        if y[i] - y_hat == 1:   #分類爲負，標籤爲正
            W[0] += X[i][0] * learn_rate
            W[1] += X[i][1] * learn_rate
            b += learn_rate
        if y[i] - y_hat == -1:
            W[0] -= X[i][0] * learn_rate
            W[1] -= X[i][1] * learn_rate
            b -= learn_rate
    return W, b
    
# This function runs the perceptron algorithm repeatedly on the dataset,
# and returns a few of the boundary lines obtained in the iterations,
# for plotting purposes.
# Feel free to play with the learning rate and the num_epochs,
# and see your results plotted below.
def trainPerceptronAlgorithm(X, y, learn_rate = 0.01, num_epochs = 25):
    x_min, x_max = min(X.T[0]), max(X.T[0])
    y_min, y_max = min(X.T[1]), max(X.T[1])
    W = np.array(np.random.rand(2,1))
    b = np.random.rand(1)[0] + x_max
    # These are the solution lines that get plotted below.
    boundary_lines = []
    for i in range(num_epochs):
        # In each epoch, we apply the perceptron step.
        W, b = perceptronStep(X, y, W, b, learn_rate)
        boundary_lines.append((-W[0]/W[1], -b/W[1]))
    return boundary_lines