Monadic linear function perceptron: Rosenblatt perceptron

1. Data files

Write a first py file , Define a dataset ：

import numpy as np

def get_beans(counts):
	xs = np.random.rand(counts)
	xs = np.sort(xs)
	ys = [1.2*x+np.random.rand()/10 for x in xs]
	return xs,ys

Function description ：

# np.random.rand(counts) establish counts I'm obedient “0~1” Uniform distribution 
#  Random sample value of cloth . The range of random samples is [0,1), barring 1.
counts = 5
xs = np.random.rand(counts)
[0.70491788 0.42003216 0.65673763 0.76751605 0.47131048]

# np.sort(a,axis) The function sorts the elements of a given array 
# a： Array to sort 
# axis： Specify by what sort , Default axis = 1  Sort by row , axis = 0  Sort by column 
xs = np.sort(xs)
[0.42003216 0.47131048 0.65673763 0.70491788 0.76751605]

#  For generating a list ys, And xs The relationship is 1.2*xs+np.random.rand()/10
ys = [1.2*x+np.random.rand()/10 for x in xs]
[0.05303335450122437, 0.6920008171892412, 0.8394550531216658, 0.8587572065335468, 1.1020587170327967]

2. rosenblatt perceptron

Create a py file , Name it rosenblatt.py

import dataset
from matplotlib import pyplot as plt
xs, ys = dataset.get_beans(100)

plt.title("size-toxicity function", fontsize = 12)
plt.xlabel("bean size")
plt.ylabel("toxicity")
plt.scatter(xs,ys)   # scatter Used to draw scatter plots 


#  The initial prediction model of this scatter diagram is y = 0.5*x
w = 0.5

for m in range(100):
	for i in range(100):
		x = xs[i]
		y = ys[i]
		y_pre = w * x
		e = y - y_pre
		alpha = 0.05
		w = w + alpha * e * x

#  here  dataset The random number in is numpy Realized 
#  When a number is multiplied by an array ,
#  Automatically broadcast this number to each element in the array , Multiply 
#  This is it. numpy Broadcasting mechanism in 
y_pre = w * xs
print(y_pre)


plt.plot(xs, y_pre)
plt.show()

3. Predicted results

D:\lesson1>python rosenblatt.py
[0.03780218 0.04059785 0.0477705  0.0855943  0.12874181 0.13685395
 0.14489358 0.15819581 0.15873595 0.17213861 0.18243123 0.18766552
 0.19346648 0.19838957 0.20573188 0.20668577 0.24096686 0.24422348
 0.24707373 0.25030397 0.26286694 0.26648086 0.31443808 0.35684708
 0.3591003  0.39489619 0.39817362 0.40656083 0.41692886 0.41976208
 0.42143049 0.43370606 0.44166334 0.44266134 0.44797852 0.50634899
 0.54419973 0.54498475 0.56182277 0.5891967  0.59048749 0.61811849
 0.63202426 0.63321798 0.63505258 0.64797476 0.64997838 0.65315589
 0.67106602 0.67516753 0.67553516 0.7157855  0.73822292 0.75061685
 0.75788042 0.76475806 0.79805265 0.80329171 0.81531963 0.81951605
 0.83349578 0.84459298 0.84777837 0.84847466 0.84959395 0.85415659
 0.8768467  0.87854525 0.87910801 0.8931603  0.89518502 0.90568107
 0.92065886 0.93747641 0.94244445 0.96398146 0.97403517 1.01397134
 1.02901236 1.03930353 1.05150133 1.06272852 1.06790564 1.07580509
 1.07822583 1.08778958 1.11816681 1.12882552 1.13526779 1.14116164
 1.14473274 1.16009282 1.16715462 1.17221958 1.1767737  1.18421983
 1.19188772 1.19945019 1.21415735 1.24617466]