This article is based on the English article The Perceptron .
A perceptron is a classifier and one of the simplest kinds of Artificial Neural Network . The goal is to take the characteristics of a biological neural network and replicate it as an algorithm.
The following figure shows a neural network with two inputs; each input has its weight, then they are summed and the activation function generates an output.
The mathematical equation would be something like:
y = FuncionActivacion(x1*w1+x2*w2)The activation function for a square wave is:
Where the activation function can be a square wave (there are more activation functions).
Here is another perceptron with 5 input signals.
The code is shown below:
#!/usr/bin/env python3
# coding: utf-8
# # Importar librerías
from pylab import rand,plot,show,norm
# # Clase Perceptron
class Perceptron:
def __init__(self):
""" inicialización del perceptron """
self.w = rand(2)*2-1 # pesos
self.tasaAprendizaje = 0.1
def respuesta(self,x):
""" saldia del perceptron """
y = x[0]*self.w[0]+x[1]*self.w[1] # producto punto entre w y x
if y >= 0:
return 1
else:
return -1
def actualizarPesos(self,x,iterError):
"""
Actualizar estatus de los pesos, w en un tiempo t+1 es w(t+1)= w(t) + learningRate*(d-r)*x
donde d es la salida deseada y r la respuesta del perceptro, iteError es la diferencia entre
d y r (d-r).
"""
self.w[0] += self.tasaAprendizaje*iterError*x[0]
self.w[1] += self.tasaAprendizaje*iterError*x[1]
def entrenamiento(self,data):
"""
Entra todo el vector en los datos, cada vector en los datos debe tener 3 elementos,
el tercer elemento (x[2]) debe ser etiquetado (salida deseada)
"""
learned = False
iteration = 0
while not learned:
globalError = 0.0
for x in data: # por cada muestra
r = self.respuesta(x)
if x[2] != r: # si tenemos un respuesta equivocada
iterError = x[2] - r # respuesta deseada-respuesta actual
self.actualizarPesos(x,iterError)
globalError += abs(iterError)
iteration += 1
if globalError == 0.0 or iteration >= 100: # detiene por el criterio
print ('iterations {}'.format(iteration))
learned = True # detiene el aprendizaje
def datosGenerados(n):
"""
genera un conjunto de datos, de dos dimensiones, linealmente separados con
n muestras. El tercer elemento de la muestra es la etiqueta.
"""
xb = (rand(n)*2-1)/2-0.5
yb = (rand(n)*2-1)/2+0.5
xr = (rand(n)*2-1)/2+0.5
yr = (rand(n)*2-1)/2-0.5
inputs = []
for i in range(len(xb)):
inputs.append([xb[i],yb[i],1])
inputs.append([xr[i],yr[i],-1])
return inputs
trainset = datosGenerados(30) # generación de datos para entrenar
perceptron = Perceptron() # Instancia del perceptron
perceptron.entrenamiento(trainset) # Entrenamiento con el conjunto de datos
testset = datosGenerados(20) # conjunto de datos para el test.
# Prueba del perceptron
for x in testset:
r = perceptron.respuesta(x)
if r != x[2]: # Si la respuesta no es correcta
print ('error')
if r == 1:
plot(x[0],x[1],'ob')
else:
plot(x[0],x[1],'or')
# Se gráfica una línea de separación, la cual es ortogonal a w.
n = norm(perceptron.w)
ww = perceptron.w/n
ww1 = [ww[1],-ww[0]]
ww2 = [-ww[1],ww[0]]
plot([ww1[0], ww2[0]],[ww1[1], ww2[1]],'--k')
show()
# ##
When you run the script you get the following plot:
The blue dots belong to the first class and the red ones belong to the second. The dotted line is the separation line that the perceptron learned during training.
In upcoming articles we will keep working with the perceptron but using libraries such as scikit-learn and tensorflow.
You can download the python script and the jupyter notebook from github.
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