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robustFisherLDA.py
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robustFisherLDA.py
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import sys
import numpy as np
from cvxopt import matrix
import log
import load
import util
import QCQP
def estimate(trainX, trainY, resample_num):
sample_pos_means = []
sample_pos_covs = []
sample_neg_means = []
sample_neg_covs = []
for i in xrange(resample_num):
[sampledX, sampledY] = util.resample(trainX, trainY)
[positiveX, negativeX] = util.split(sampledX, sampledY)
sample_pos_means.append(np.mean(positiveX, 0))
sample_neg_means.append(np.mean(negativeX, 0))
sample_pos_covs.append(np.cov(np.array(positiveX).T))
sample_neg_covs.append(np.cov(np.array(negativeX).T))
nominal_pos_mean = np.mean(sample_pos_means, 0)
nominal_neg_mean = np.mean(sample_neg_means, 0)
nominal_pos_cov = np.mean(sample_pos_covs, 0)
nominal_neg_cov = np.mean(sample_neg_covs, 0)
sample_pos_means_cov = np.cov(np.array(sample_pos_means).T)
sample_neg_means_cov = np.cov(np.array(sample_neg_means).T)
#log(sample_pos_means_cov)
#log(sample_neg_means_cov)
np.linalg.cholesky(sample_pos_means_cov+ np.eye(sample_pos_means_cov.shape[0]) * 1e-8)
np.linalg.cholesky(sample_neg_means_cov+ np.eye(sample_neg_means_cov.shape[0]) * 1e-8)
P_pos = np.linalg.inv(sample_pos_means_cov + np.eye(sample_pos_means_cov.shape[0]) * 1e-8) / len(trainX)
P_neg = np.linalg.inv(sample_neg_means_cov + np.eye(sample_pos_means_cov.shape[0]) * 1e-8) / len(trainX)
np.linalg.cholesky(P_pos+ np.eye(sample_neg_means_cov.shape[0]) * 1e-3)
np.linalg.cholesky(P_neg+ np.eye(sample_neg_means_cov.shape[0]) * 1e-3)
rho_pos = 0
rho_neg = 0
for cov_matrix in sample_pos_covs:
dis = util.F_norm(cov_matrix - nominal_pos_cov)
rho_pos = max(dis, rho_pos)
for cov_matrix in sample_neg_covs:
dis = util.F_norm(cov_matrix - nominal_neg_cov)
rho_neg = max(dis, rho_neg)
return [nominal_pos_mean, P_pos, nominal_neg_mean, P_neg,
nominal_pos_cov, rho_pos, nominal_neg_cov, rho_neg]
def mainRobustFisherLDAtest(dataset, alpha, resample_num=100, split_token=','):
data_file = dataset + '/' + dataset + '.data'
data_loader = load.loader(file_name = data_file, split_token = split_token)
[dataX, dataY] = data_loader.load()
dimension = data_loader.dimension
[trainX, trainY, testX, testY] = util.divide(dataX, dataY, alpha)
[pos_mean, pos_P, neg_mean, neg_P, pos_cov, pos_rho, neg_cov, neg_rho] = estimate(trainX, trainY, resample_num)
M = pos_cov + neg_cov + np.eye(dimension) * (pos_rho + neg_rho)
M0 = np.linalg.inv(M)
# minus = np.concatenate((np.eye(dimension), -np.eye(dimension)), axis = 1)
# choose_pos = np.concatenate((np.eye(dimension), np.zeros([dimension, dimension])), axis = 1)
# choose_neg = np.concatenate((np.zeros([dimension, dimension]), np.eye(dimension)), axis = 1)
# M0 = np.dot(minus.T, np.dot(M, minus))
# M1 = np.dot(choose_pos.T, np.dot(pos_P, choose_pos))
# M2 = np.dot(choose_neg.T, np.dot(neg_P, choose_neg))
# sol = QCQP.qcqprel(P = {'P0':matrix(M0), 'b0':None, 'c0':0.0},
# G = {'P':[matrix(M1), matrix(M2)], 'b':[None] * 2, 'c':[0.0,] * 2,
# 'Peq':[], 'beq':[], 'ceq':[]})
# sol_array = np.array(sol['RQCQPx'])
# x_pos_star = sol_array[:dimension]
# x_neg_star = sol_array[dimension:]
# w = np.dot(M, x_pos_star - x_neg_star)
M1 = pos_P
M2 = neg_P
[train_pos_X, train_neg_X] = util.split(trainX, trainY)
k1 = np.mean(train_pos_X, axis = 0).reshape(dimension, 1)
k2 = np.mean(train_neg_X, axis = 0).reshape(dimension, 1)
k1 = k1 / np.linalg.norm(k1)
k2 = k2 / np.linalg.norm(k2)
k1_norm = util.M_norm(M1, k1)
k2_norm = util.M_norm(M2, k2)
x1 = k1 / k1_norm
x2 = k2 / k2_norm
pos_mean = pos_mean.reshape(dimension, 1)
neg_mean = neg_mean.reshape(dimension, 1)
while True:
tail = np.dot(M0, x1 - x2 + pos_mean - neg_mean)
k1_head = (np.eye(dimension) * k1_norm ** 2 - np.dot(M1, np.dot(k1, k1.T))) / (k1_norm ** 3)
k2_head = - (np.eye(dimension) * k2_norm ** 2 - np.dot(M2, np.dot(k2, k2.T))) / (k2_norm ** 3)
k1_gradient = np.dot(k1_head, tail)
k2_gradient = np.dot(k2_head, tail)
k1 -= k1_gradient * 0.01
k2 -= k2_gradient * 0.01
#print ('%.9f\t %.9f\t %.9f\t %.9f \t%.9f')% (util.M_norm(M0, x1 + pos_mean - x2 - neg_mean), np.linalg.norm(np.concatenate((k1_gradient, k2_gradient), axis = 0)), util.M_norm(M1, x1), util.M_norm(M2, x2), util.F_norm(x1 + pos_mean - x2 - neg_mean))
if np.linalg.norm(np.concatenate((k1_gradient, k2_gradient), axis = 0)) < 1e-5:
break
k1_norm = util.M_norm(M1, k1)
k2_norm = util.M_norm(M2, k2)
x1 = k1 / k1_norm
x2 = k2 / k2_norm
w = np.dot(M0, x1 - x2 + pos_mean - neg_mean).reshape(dimension)
train_pos_mean = np.mean(train_pos_X, axis = 0)
train_neg_mean = np.mean(train_neg_X, axis = 0)
threshold = np.dot(w, (train_pos_mean + train_neg_mean) / 2.0)
positive_lower = True if np.dot(train_pos_mean - train_neg_mean, w) > 0 else False
predict = np.zeros(len(testY))
testNum = len(testY)
for i in xrange(testNum):
value = np.dot(testX[i], w)
if (value > threshold) == positive_lower:
predict[i] = 1
else:
predict[i] = -1
rightNum = 0
for i in xrange(testNum):
if predict[i] == testY[i]:
rightNum += 1
#print 'Right Radio: %.5f'% (float(rightNum)/float(testNum))
return float(rightNum)/float(testNum)
if __name__ == '__main__':
dataset = ['ionosphere', 'sonar'] # choose the dataset
dataset = dataset[0]
sol = mainRobustFisherLDAtest(dataset, 0.5)
print sol