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December 10, 2015 15:39
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Logistic regression (linear separable classes)
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# - Logistic regression implementation | |
# - Linear hypothesis and linearly separable classes | |
# Copyright (C) 2015 Eric Aislan Antonelo | |
# This program is free software: you can redistribute it and/or modify | |
# it under the terms of the GNU General Public License as published by | |
# the Free Software Foundation, either version 3 of the License, or | |
# (at your option) any later version. | |
############################# | |
using Gadfly | |
using Distributions | |
############################# | |
## classes linearmente separaveis linear | |
n = 40 | |
sigma = 5 | |
d1 = Normal(0,sigma) | |
d2 = Normal(20,sigma) | |
# classe 1 | |
x1 = rand(d1,n) | |
x2 = rand(d1,n) | |
samples = [x1 x2 zeros(n)] | |
# classe 2 | |
x1 = rand(d2,n) | |
x2 = rand(d2,n) | |
samples = [x; x1 x2 ones(n)] | |
plot(layer(x=samples[:,1],y=samples[:,2],Geom.point)) | |
# layer(x=1:n,y=ysample2,Geom.point)) | |
############################# | |
MAX_EPISODES = 500 | |
function cost(examples, theta) | |
err = 0 | |
for (x,y) in examples | |
err += y * log(hypothesis(x, theta)) + (1-y) * log(1-hypothesis(x, theta)) | |
end | |
- err/length(examples) | |
end | |
function gradient_descent(examples, theta; learning_rate=0.05) | |
err = 10000 | |
# learning_rate = 0.05 | |
max_episodes = MAX_EPISODES | |
i = 0 | |
while err > 0.005 && i < max_episodes | |
println("Episode $i") | |
theta = theta - learning_rate * gradient(examples, theta) | |
println("theta: $theta") | |
err = cost(examples, theta) | |
println("cost: $err") | |
i += 1 | |
end | |
theta | |
end | |
function gradient(examples, theta) | |
grad = zeros(size(theta)) | |
for (x,y) in examples | |
#println(x," __ ",y) | |
#println(hypothesis(x, theta)[1] -y) | |
#println((hypothesis(x, theta) - y) * [1 x]') | |
grad = grad + (hypothesis(x, theta) - y) * hypothesis_features(x) | |
end | |
grad/length(examples) | |
end | |
function sigmoid(x) | |
1/(1+exp(-x)) | |
end | |
function hypothesis(x, theta) | |
y = hypothesis_features(x)' * theta | |
sigmoid(y[1]) | |
end | |
# Plota resultados | |
function plot_results() | |
h_ = zeros(size(samples,1)) | |
for i in 1:size(samples,1) | |
h_[i] = hypothesis(samples[i,1:2]', theta) | |
end | |
#x = -10:0.5:30 | |
#y = [hypothesis(x_, theta) for x_ in x] | |
x1 = -10:0.5:30 | |
x2 = [hypothesis_curve(x_, theta) for x_ in x1] | |
#plot(layer(x=x1, y=x2, Geom.point, Theme(default_color=color("red")))) | |
plot(layer(x=x1, y=x2, Geom.point, Theme(default_color=color("red"))), | |
layer(x=samples[:,1],y=samples[:,2],Geom.point)) | |
# hypothesis in red | |
# plot(layer(x=x, y=h_, Geom.point, Theme(default_color=color("red"))), | |
# layer(x=x, y=y, Geom.point), | |
# layer(x=x, y=ysample, Geom.point, Theme(default_color=color("black")))) | |
end | |
############################# | |
# para hipotese linear | |
function hypothesis_features(x) | |
[1; x;] | |
end | |
function hypothesis_curve(x1, theta) | |
- (theta[1] + theta[2] * x1) / theta[3] | |
end | |
theta_ini = ones(3) * 0.01 | |
dataset = [(samples[i,1:2]',samples[i,3]) for i in 1:size(samples,1)] | |
theta = gradient_descent(dataset, theta_ini, learning_rate=0.1) | |
println("Theta $theta") | |
plot_results() | |
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