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hw2_run.py
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hw2_run.py
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from cvxopt.solvers import qp
from cvxopt.base import matrix
import numpy as np
import pylab as pl
import random as r
import math as m
def solve_for_alpha(P, q, G, h):
r = qp(matrix(P), matrix(q), matrix(G), matrix(h))
return list(r['x'])
def linearkernel(x1, x2):
# print(np.dot(x1, x2))
return np.dot(x1, x2) + 1
def polynomialkernel(x1, x2, power):
# print(pow(np.dot(x1, x2)+1, power))
if power > 0:
#print(np.dot(x1, x2) + 1)
return pow(np.dot(x1, x2) + 1, power) + 1
def radialkernel(x1, x2, sigma):
# print(pow(np.dot(x1, x2)+1, power))
# print(2 * sigma**2)
#print(np.asarray(x1))
#print(np.asarray(x2))
#print(np.linalg.norm(np.subtract(x1,x2)));
diff = -1 * np.power( np.linalg.norm(np.subtract(x1,x2)), 2)
#print(diff)
return m.exp(-(np.dot(diff, diff) / (2 * sigma ** 2))) + 1
def sigmoidkernel(x1, x2, k, delta):
# print(pow(np.dot(x1, x2)+1, power))
# print(k*np.dot(x1, x2) - delta)
return m.tanh((k * np.dot(x1, x2) - delta) * m.pi / 180.0) + 1
def testlinearkernel():
x1 = np.array([1, 2, 3])
# print(x1)
x2 = np.array([3, 2, 1])
# print(x2)
return linearkernel(x1, x2)
def testpolynomialkernel(power):
x1 = np.array([1, 2, 3])
# print(x1)
x2 = np.array([3, 2, 1])
# print(x2)
return polynomialkernel(x1, x2, power)
def testradialkernel(sigma):
x1 = np.array([2, 3, 1])
# print(x1)
x2 = np.array([3, 2, 1])
# print(x2)
return radialkernel(x1, x2, sigma)
def testsigmoidkernel(k, delta):
x1 = np.array([2, 3, 1])
# print(x1)
x2 = np.array([3, 2, 1])
# print(x2)
return sigmoidkernel(x1, x2, k, delta)
def testkernels():
print(testlinearkernel())
print(testpolynomialkernel(2))
print(testradialkernel(1))
print(testsigmoidkernel(1, 0))
# linear kernel
def buildP(data, func, *args):
datasize = len(data);
#print(datasize);
P = np.zeros((datasize, datasize));
#print(type(P));
#print(P);
for i in range(0,datasize):
for j in range(0,datasize):
P[i][j] = data[i][2] * data[j][2] * func(data[i][0:2], data[j][0:2], *args);
return P
def buildq(data):
return -1 * np.ones(len(data));
def buildh(data):
return np.zeros(len(data));
def buildG(data):
G = np.zeros((len(data), len(data)));
np.fill_diagonal(G, -1);
return G;
def generateData(size):
classA = [(r.normalvariate(-1.5, 1), r.normalvariate(0.5, 1), 1.0) for i in range(int(size / 2))] + \
[(r.normalvariate(1.5, 1), r.normalvariate(0.5, 1), 1.0) for i in range(int(size / 2))];
classB = [(r.normalvariate(0.0, 0.5), r.normalvariate(-0.5, 0.5), -1.0) for i in range(size)];
data = classA + classB;
r.shuffle(data);
return data
def generateData2(size):
classA = [(r.normalvariate(-1.0, .5), r.normalvariate(0.5, 1), 1.0) for i in range(int(size / 2))] + \
[(r.normalvariate(1.0, .8), r.normalvariate(0.5, 1), 1.0) for i in range(int(size / 2))];
classB = [(r.normalvariate(0.0, 0.5), r.normalvariate(-0.5, 0.5), -1.0) for i in range(size)];
data = classA + classB;
r.shuffle(data);
return data
def generateData3(size):
classA = [(r.normalvariate(-1.0, .5), r.normalvariate(0.5, 1), 1.0) for i in range(int(size))]
classB = [(r.normalvariate(0.0, 0.5), r.normalvariate(-0.5, 0.5), -1.0) for i in range(size)];
data = classA + classB;
r.shuffle(data);
return data
def plotData(data):
pl.hold(True);
pl.plot([d[0] for d in data if d[2] == 1], [d[1] for d in data if d[2] == 1], 'bo');
pl.plot([d[0] for d in data if d[2] == -1], [d[1] for d in data if d[2] == -1], 'ro');
#pl.show();
pass
def indicator(testpoint, data, alphas, func, *args):
sum = 0;
for i in range(0, len(data)):
sum = sum + alphas[i] * data[i][2] * func(testpoint, data[i][0:2], *args);
return 1 if sum >=0 else -1;
def plotDecisionB(data, alphas, kernel, func, *args):
xrange = np.arange(-4, 4, 0.05);
yrange = np.arange(-4, 4, 0.05);
grid = matrix([[indicator((x,y), data, alphas, func, *args) for y in yrange] for x in xrange]);
#print(grid);
pl.contour(xrange, yrange, grid, (-1.0, 0.0, 1.0), colors = ('red', 'black', 'blue'), linewidths = (1,3,1));
pl.xlabel('x1');
pl.ylabel('x2');
if(kernel == 'linear'):
pl.title('Linear Kernel');
elif(kernel == 'polynomial'):
pl.title('Polynomial Kernel');
elif(kernel == 'radial'):
pl.title('Radial Kernel');
elif(kernel == 'sigmoidal'):
pl.title('Sigmoidal Kernel');
pl.show();
def run1(dataSize, dataSetNum, kernel):
print('run 1');
if (dataSetNum ==1):
data = generateData(dataSize);
elif(dataSetNum ==2):
data = generateData2(dataSize);
if(kernel == 'linear'):
P = buildP(data, linearkernel);
elif(kernel == 'polynomial'):
P = buildP(data, polynomialkernel, 3);
elif(kernel == 'radial'):
P = buildP(data, radialkernel, 4);
elif(kernel == 'sigmoidal'):
P = buildP(data, sigmoidkernel, 3, 2);
# print(matrix(P).size);
q = buildq(data);
# print(matrix(q).size);
h = buildh(data);
# print(matrix(h).size);
G = buildG(data);
# print(matrix(G).size);
alphas = solve_for_alpha(P, q, G, h);
alphas = [x for x in alphas if x > 10 ^-5]
# print("alphas > 0 :" + alphas.__str__());
# print(len(alphas))
#print(len(data[0]))
#testpoints = np.zeros((5, len(data[0])));
#testpoints[0] = [5,5,1];
#testtarget = indicator(testpoints[0], data, alphas, radialkernel, 2 );
#print(testtarget);
plotData(data);
if(kernel == 'linear'):
plotDecisionB(data, alphas, kernel, linearkernel);
elif(kernel == 'polynomial'):
plotDecisionB(data, alphas, kernel, polynomialkernel, 3);
elif(kernel == 'radial'):
plotDecisionB(data, alphas, kernel, radialkernel, 2 );
elif(kernel == 'sigmoidal'):
plotDecisionB(data, alphas, kernel, sigmoidkernel, 2, 3 );
pass
def run2(dataSize, dataSetNum, kernel):
print('run 2');
if (dataSetNum ==1):
data = generateData(dataSize);
elif(dataSetNum ==2):
data = generateData2(dataSize);
if(kernel == 'linear'):
P = buildP(data, linearkernel);
elif(kernel == 'polynomial'):
P = buildP(data, polynomialkernel, 7);
elif(kernel == 'radial'):
P = buildP(data, radialkernel, 8);
elif(kernel == 'sigmoidal'):
P = buildP(data, sigmoidkernel, 1, 6);
# print(matrix(P).size);
q = buildq(data);
# print(matrix(q).size);
h = buildh(data);
# print(matrix(h).size);
G = buildG(data);
# print(matrix(G).size);
alphas = solve_for_alpha(P, q, G, h);
alphas = [x for x in alphas if x > 10 ^-5]
# print("alphas > 0 :" + alphas.__str__());
# print(len(alphas))
#print(len(data[0]))
#testpoints = np.zeros((5, len(data[0])));
#testpoints[0] = [5,5,1];
#testtarget = indicator(testpoints[0], data, alphas, radialkernel, 2 );
#print(testtarget);
plotData(data);
if(kernel == 'linear'):
plotDecisionB(data, alphas, kernel, linearkernel);
elif(kernel == 'polynomial'):
plotDecisionB(data, alphas, kernel, polynomialkernel, 3);
elif(kernel == 'radial'):
plotDecisionB(data, alphas, kernel, radialkernel, 2 );
elif(kernel == 'sigmoidal'):
plotDecisionB(data, alphas, kernel, sigmoidkernel, 3, 2 );
pass
def run3(dataSize, dataSetNum, kernel):
print('run 3');
if (dataSetNum ==1):
data = generateData(dataSize);
elif(dataSetNum ==2):
data = generateData2(dataSize);
elif(dataSetNum ==3):
data = generateData3(dataSize);
if(kernel == 'linear'):
P = buildP(data, linearkernel);
elif(kernel == 'polynomial'):
P = buildP(data, polynomialkernel, 3);
elif(kernel == 'radial'):
P = buildP(data, radialkernel, 2);
elif(kernel == 'sigmoidal'):
P = buildP(data, sigmoidkernel, 1, 6);
# print(matrix(P).size);
q = buildq(data);
# print(matrix(q).size);
h = buildh(data);
# print(matrix(h).size);
G = buildG(data);
# print(matrix(G).size);
alphas = solve_for_alpha(P, q, G, h);
alphas = [x for x in alphas if x > 10 ^-5]
# print("alphas > 0 :" + alphas.__str__());
# print(len(alphas))
#print(len(data[0]))
#testpoints = np.zeros((5, len(data[0])));
#testpoints[0] = [5,5,1];
#testtarget = indicator(testpoints[0], data, alphas, radialkernel, 2 );
#print(testtarget);
plotData(data);
if(kernel == 'linear'):
plotDecisionB(data, alphas, kernel, linearkernel);
elif(kernel == 'polynomial'):
plotDecisionB(data, alphas, kernel, polynomialkernel, 3);
elif(kernel == 'radial'):
plotDecisionB(data, alphas, kernel, radialkernel, 2 );
elif(kernel == 'sigmoidal'):
plotDecisionB(data, alphas, kernel, sigmoidkernel, 3, 2 );
pass
# main
#testkernels();
#run1(dataSize=10,dataSetNum = 1, kernel = 'radial');
run2(dataSize=10,dataSetNum = 2, kernel = 'polynomial');
#run3(dataSize=10,dataSetNum = 3, kernel = 'linear');
#kernel = 'polynomial';
#kernel = 'radial';
#kernel = 'sigmoidal';