Created
February 27, 2016 04:05
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a sample of Perceptron Learning Algorithm
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import numpy as np | |
import random | |
import os, subprocess | |
class Perceptron: | |
def __init__(self, N): | |
# Random linearly separated data | |
xA,yA,xB,yB = [random.uniform(-1, 1) for i in range(4)] | |
self.V = np.array([xB*yA-xA*yB, yB-yA, xA-xB]) | |
self.X = self.generate_points(N) | |
def generate_points(self, N): | |
X = [] | |
for i in range(N): | |
x1,x2 = [random.uniform(-1, 1) for i in range(2)] | |
x = np.array([1,x1,x2]) | |
s = int(np.sign(self.V.T.dot(x))) | |
X.append((x, s)) | |
return X | |
def plot(self, mispts=None, vec=None, save=False): | |
fig = plt.figure(figsize=(5,5)) | |
plt.xlim(-1,1) | |
plt.ylim(-1,1) | |
V = self.V | |
a, b = -V[1]/V[2], -V[0]/V[2] | |
l = np.linspace(-1,1) | |
plt.plot(l, a*l+b, 'k-') | |
cols = {1: 'r', -1: 'b'} | |
for x,s in self.X: | |
plt.plot(x[1], x[2], cols[s]+'o') | |
if mispts: | |
for x,s in mispts: | |
plt.plot(x[1], x[2], cols[s]+'.') | |
if vec != None: | |
aa, bb = -vec[1]/vec[2], -vec[0]/vec[2] | |
plt.plot(l, aa*l+bb, 'g-', lw=2) | |
if save: | |
if not mispts: | |
plt.title('N = %s' % (str(len(self.X)))) | |
else: | |
plt.title('N = %s with %s test points' \ | |
% (str(len(self.X)),str(len(mispts)))) | |
plt.savefig('p_N%s' % (str(len(self.X))), \ | |
dpi=200, bbox_inches='tight') | |
def classification_error(self, vec, pts=None): | |
# Error defined as fraction of misclassified points | |
if not pts: | |
pts = self.X | |
M = len(pts) | |
n_mispts = 0 | |
for x,s in pts: | |
if int(np.sign(vec.T.dot(x))) != s: | |
n_mispts += 1 | |
error = n_mispts / float(M) | |
return error | |
def choose_miscl_point(self, vec): | |
# Choose a random point among the misclassified | |
pts = self.X | |
mispts = [] | |
for x,s in pts: | |
if int(np.sign(vec.T.dot(x))) != s: | |
mispts.append((x, s)) | |
return mispts[random.randrange(0,len(mispts))] | |
def pla(self, save=False): | |
# Initialize the weigths to zeros | |
w = np.zeros(3) | |
X, N = self.X, len(self.X) | |
it = 0 | |
# Iterate until all points are correctly classified | |
while self.classification_error(w) != 0: | |
it += 1 | |
# Pick random misclassified point | |
x, s = self.choose_miscl_point(w) | |
# Update weights | |
w += s*x | |
if save: | |
self.plot(vec=w) | |
plt.title('N = %s, Iteration %s\n' \ | |
% (str(N),str(it))) | |
plt.savefig('p_N%s_it%s' % (str(N),str(it)), \ | |
dpi=200, bbox_inches='tight') | |
self.w = w | |
def check_error(self, M, vec): | |
check_pts = self.generate_points(M) | |
return self.classification_error(vec, pts=check_pts) |
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