这里是我的个人网站： https://endlesslethe.com/perceptron-with-python.html 有更多总结分享，最新更新也只会发布在我的个人网站上。排版也可能会更好看一点=v=
前言
本来想写一个关于感知机的总结，但如果要深入探讨，涉及的东西实在太多。仅仅浅尝辄止的话，那我就相当于照搬原文，违背了我写文章的初衷。
所以就单纯地把我自己写的感知机实现代码发上来，辅助大家学习。 我还提供了一个数据生成器，可以生成训练模型所需要的数据。
简单地对结果做了可视化，具体绘制代码见文末提供的github地址。跪求star=v=
感知机模型
感知机算法用于计算得到划分可二分数据集的超平面S。
我们定义优化函数为损失函数： L=误分类点到超平面S的距离和
\(d = \frac{1}{{\left| w \right|}}|w \bullet {x_i} + b|\)
\(L = - \sum\limits_N {{y_i}} (w \bullet {x_i} + b)\)
采用随机梯度下降算法
\(\frac{{dL}}{{dw}} = - \sum\limits_N {{y_i}} {x_i}\)
故对于每一个误分类点
\(w = w + \eta {y_i}{x_i}\)
算法流程
输入：w, b； 训练：f(x)=sign(wx+b)
选取初值w0, b0随机选取数据(xi, yi)如果为误分类点，则更新
import numpy as np
import matplotlib.pyplot as plt
np.random.seed(
1)
def sign(x):
if x >
0:
return 1;
return -
1
def svg(x, y, w, b, learning_rate):
i = np.random.randint(
0, x.shape[
0])
if y[i] * (np.dot(w, x[i]) + b) <=
0:
w = w + learning_rate * x[i].T * y[i]
b = b + learning_rate * y[i]
params = {
'w':w,
'b':b}
return params
预测
输入：x 输出：y=sign(wx+b)
def predict(x, w, b):
return sign(np.dot(w, x) + b)
小数据训练
dim =
2 #属性数量
dataSize =
10 #数据集大小
learning_rate =
0.1 #学习率
ITERATE =
1000 #迭代次数
x_train = np.array(
[[-1, 1], [-2, 0], [-1, 0], [-0.5, 0.5], [0, 0.5],[1, 3], [2, 3], [1, 1], [1, -0.5], [1, 0]])
x_train = x_train.reshape(
10, dim,
1)
y_train = np.array([
1,
1,
1,
1,
1, -
1, -
1, -
1, -
1, -
1])
#
print(x_train.shape)
#
print(x_train[
0].shape)
w = np.zeros((
1, dim))
b =
0
assert(x_train.shape == (dataSize, dim,
1))
assert(x_train[
0].shape == (dim,
1))
assert(w.shape == (
1, dim))
for x
in range(ITERATE):
params = svg(x_train, y_train, w, b, learning_rate)
w = params[
'w']
b = params[
'b']
print(w)
print(b)
训练结果
数据生成器
def getData(rg, dim, size):
w = np.array([
1,
1])
b =
2.5
x = []
y = []
for i
in range(size):
x_i = np.random.rand(dim,
1) * rg - rg/
2
y_i = -
1
if np.dot(w, x_i) + b >
0:
y_i =
1
x.append(x_i)
y.append(y_i)
x = np.array(x)
y = np.array(y)
data = {
"x":x,
"y":y}
return data
大数据测试
rangeOfNumber =
10 #随机数的范围
dim =
2 #属性数量
dataSize =
1000 #数据集大小
testSize =
2000 #测试集大小
learning_rate =
0.05 #学习率
ITERATE =
1000 #迭代次数
data_train = getData(rangeOfNumber,
dim, dataSize)
x_train = data_train[
"x"]
y_train = data_train[
"y"]
# print(x_train.shape)
# print(x_train[0].shape)
w = np.zeros((
1,
dim))
b =
0
assert(x_train.shape == (dataSize,
dim,
1))
assert(x_train[
0].shape == (
dim,
1))
assert(w.shape == (
1,
dim))
for x
in range(ITERATE):
params = svg(x_train, y_train, w, b, learning_rate)
w = params[
b = params[
print(w)
print(b)
训练结果
对测试集预测
data_test = getData(rangeOfNumber, dim, testSize)
x_test = data_test[
"x"]
y_test = data_test[
"y"]
y_predict = []
for i
in range(testSize):
y_predict.append(predict(x_test[i], w, b))
cnt =
0
for i
in range(testSize):
if y_test[i] == y_predict[i]:
cnt = cnt +
1
print(
"Accuracy:%d" % (cnt / testSize *
100))
误分类样本分布
完整代码
戳我的github
