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demo_ELM_2D.py
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demo_ELM_2D.py
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# -*- coding: utf-8 -*-
"""
Basic implementation of ELM
@date: 31/01/2020
@author: mjflores
"""
#==================================================
# Implementacion de ELM
# Autor: MFlores, Enero 2020
#==================================================
# Datos
# i | x_i | y_i
#-------------------
# 1 (-2,-2) (1,0)
# 2 (-1,-1) (1,0)
# 3 (-2,-4) (1,0)
# 4 (-3,-3) (1,0)
# 5 (-2,-3) (0,1)
# 6 (+1,+1) (0,1)
# 7 (+2,+2) (0,1)
# 8 (+2,+4) (0,1)
# 9 (+3,+3) (0,1)
# 10 (+2,+3) (0,1)
#-------------------------------------------
# Notacion
# N = Tamano datos de entrenamiento
# L = Numero de nodos de la capa oculta
# d = Dimension del vector x_i
# m = Numero de clases en t_i
#
#==================================================
# Referencia
# An insight into Extreme Learning Machines: Random
# Neurons, Random Features and Kernels
# by Guang-Bin Huang, 2014
import matplotlib.pyplot as plt
import random as rn
import numpy as np
#-------------------------------------------
def generar_a_b(row_d,col_L):
a = np.random.uniform(-1,1,size=(row_d,col_L))
b = np.random.uniform(-1,1,size=(col_L,1))
return a, b
#-------------------------------------------
def generar_H(a,b,X,N,L):
H = np.zeros((N,L))
for i in range(N):
for j in range(L):
#print(a[:,j])
H[i,j] = funcion_Sigmoid(a[:,j],b[j],X[i,:])
return H, H.transpose()
#-------------------------------------------
def funcion_Sigmoid(a,b,x):
aux = np.dot(a,x) + b
return 1.0/(1.0+np.exp(-aux))
#=================================================
#=================================================
# Datos de entrenamiento
X = np.array([[-2,-2],
[-1,-1],
[-2,-4],
[-3,-3],
[-2,-3],
[1,1],
[2,2],
[2,4],
[3,3],
[2,4],])
T = np.array([[1,0],
[1,0],
[1,0],
[1,0],
[1,0],
[0,1],
[0,1],
[0,1],
[0,1],
[0,1]])
#-------------------------------------------
plt.scatter(X[:,0], X[:,1])
plt.title('Datos para ajustar ELM')
plt.xtitle('X')
plt.ytitle('Y')
plt.show()
#-------------------------------------------
L = 70 # numero de capas ocultas 5e06 no puede operar
N,d = X.shape
m = T.shape[1]
a, b = generar_a_b(d,L)
#print("Dimension a: ",a.shape)
H, H_tr = generar_H(a,b,X,N,L)
C = .10
beta = []
# Version cuando N grande
if N>L:
# Eq (11)
I1 = np.identity(L)/C
aux1 = np.linalg.inv((I1 + np.matmul(H_tr,H)))
aux2 = np.matmul(H_tr,T)
beta1 = np.matmul(aux1,aux2)
beta = beta1
# Version cuando N pequeño
else:
I2 = np.identity(N)/C
aux1 = np.linalg.inv((I2 + np.matmul(H,H_tr)))
aux2 = np.matmul(H_tr,aux1)
beta2 = np.matmul(aux2,T)
beta = beta2
#-------------------------------------------
def fx(xnew):
hx = np.zeros(L)
for j in range(L):
hx[j] = funcion_Sigmoid(a[:,j],b[j],xnew)
#print(hx.shape)
fx1 = np.matmul(hx,beta1)
return fx1
#-------------------------------------------
#-------------------------------------------
# Datos de prueba
#-------------------------------------------
#-------------------------------------------
xnew1 = np.array([-3,-3])
xnew2 = np.array([+0,+2])
fx1 = fx(xnew1)
fx2 = fx(xnew2)
print("fx1 = ",fx1)
print("fx2 = ",fx2)