# Como implementar um perceptron de Rosenblatt?

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## 1 Resposta

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respondida Jun 10, 2016 por (5,456 pontos)

Abaixo apresento a implementação em Python seguindo as linhas gerais da seção 4.1.7 do livro Pattern Recognition and Machine Learning - Christopher Bishop:

import matplotlib.pyplot as plt
import numpy as np
from sklearn import linear_model
np.random.seed(50)

fig=plt.figure(num=None, figsize=(8, 4), dpi=80, facecolor='w', edgecolor='k')

step_function = lambda x: 0 if x < 0 else 1

def plot_classificator(beta0,beta1,beta2,x1):
minx1=np.min(x1)
maxx1=np.max(x1)

minx2=(beta1*minx1+beta0)/(-beta2)
maxx2=(beta1*maxx1+beta0)/(-beta2)

plt.plot([minx1,maxx1],[minx2,maxx2],'k-')

def data_generation(n,beta0,beta1,beta2):
x1=np.random.normal(1,0.64,n) # Primeiro regressor
x2=np.random.normal(1,0.36,n) # Segundo regressor
z=beta0*np.ones(n)+beta1*x1+beta2*x2 # Variavel latente
y=np.empty([n])
for i in range(n):
if(z[i]>0): # In order to ensure that in average each class has the same number of points
y[i]=1
else:
y[i]=-1
return y,x1,x2

class Perceptron():
def __init__(self,inputData,target):
self.numberOfInputs=np.shape(inputData)[0]
self.numberOfWeights=np.shape(inputData)[1]+1
self.inputData=np.concatenate((np.ones([self.numberOfInputs,1]), x),axis=1)
self.target=target
self.numberOfWeights=np.shape(inputData)[1]+1
self.weights=np.random.normal(0,1,[self.numberOfWeights])
def train_weights(self,numberOfEpochs,eta):
error=np.zeros([numberOfEpochs])
for epoch in range(numberOfEpochs):
print "epoch: ",epoch
for i in range(self.numberOfInputs):
if(np.dot(self.weights,self.inputData[i,:])*self.target[i]<0):
self.weights=self.weights+eta*self.inputData[i]*self.target[i]
for i in range(self.numberOfInputs):
if(np.dot(self.weights,self.inputData[i,:])*self.target[i]<0):
error[epoch]=error[epoch]-np.dot(self.weights,self.inputData[i,:])*self.target[i]
print error[epoch]
#Error Evaluation
return error
def fit(self,x):
x=np.vstack((x,np.ones([1])))
return step_function(np.dot(self.weights,x))

if __name__ == '__main__':
n=100 # numero de observacoes
beta0=2.5
beta1=-1.5
beta2=-1

# Case 1

ax=plt.subplot(121)

[y,x1,x2]=data_generation(n,beta0,beta1,beta2)
x=np.stack(( x1.T,x2.T),axis=1)
myPerceptron=Perceptron(x,y)
error=myPerceptron.train_weights(10,0.01)
myWeights=myPerceptron.weights
myBeta0=myWeights[0]
myBeta1=myWeights[1]
myBeta2=myWeights[2]

for i in range(n):
if(y[i]==1):
plt.plot(x1[i],x2[i],u'ro',markersize=5, markeredgewidth=0)
else:
plt.plot(x1[i],x2[i],u'bo',markersize=5, markeredgewidth=0)
ax.set_xlabel('$x_1$')
ax.set_ylabel('$x_2$')
ax.set_title('Perceptron')

plot_classificator(myBeta0,myBeta1,myBeta2,x1)

ax=plt.subplot(122)

plt.plot(range(np.size(error)),error,'r-')
ax.set_xlabel('Epochs')
ax.set_ylabel('Error')
ax.set_title('Perceptron')

fig.savefig("perceptronClassificator.jpg")
# Example Fit
x=np.ones([2,1])
print "The output of the perceptron is: ",myPerceptron.fit(x)


Esse código gera as seguintes figuras: