def cca(X, Y):
# print '#### Canonical Correlation Analyais ####'
# print 'X\n', X
# print 'Y\n', Y
xsamples, n = X.shape
ysamples, m = Y.shape
# print 'xsamples=', xsamples, 'n=', n
# print 'ysamples=', ysamples, 'm=', m
if (xsamples != ysamples):
print 'The number of samples are inconsistent'
else:
nsamples = xsamples
XMean = sum(X) / float(nsamples)
YMean = sum(Y) / float(nsamples)
# print 'XMean', XMean
# print 'YMean', YMean
XX = X - XMean
YY = Y - YMean
SXX = np.dot(XX.T, XX) / float(nsamples - 1)
SYY = np.dot(YY.T, YY) / float(nsamples - 1)
SXY = np.dot(XX.T, YY) / float(nsamples - 1)
SYYinv = np.linalg.inv(SYY)
SXYYYXY = np.dot(SXY, np.dot(SYYinv, SXY.T))
Eval, Evec = klin.pencil(SXYYYXY, SXX)
idx = Eval.argsort()
Eval = Eval[idx][::-1]
Evec = Evec[:, idx][:, ::-1]
A = Evec
# print 'sqrt(Eval)', np.sqrt(Eval)
# print 'A\n', A
# U = np.dot(XX, A)
# print 'U\n', U
# print 'inv(Eval)', 1 / np.sqrt(Eval)
Evalinv = 1.0 / np.sqrt(Eval)
B = np.dot(np.dot(SYYinv, np.dot(SXY.T, A)), np.diag(Evalinv))
# print 'B\n', B
# V = np.dot(YY, B)
# print 'V\n', V
return (A, B, XMean, YMean)
def danal(data,label,K):
nr, nc = data.shape
ldim = np.minimum(nc, K-1)
# Total mean and Total covrainace matrix
# TMEAN = (sum(np.asarray(data,dtype=np.float))) / float(nr)
TMEAN = sum(data) / float(nr)
data_m = data - TMEAN
St = np.dot(data_m.T, data_m)/float(nr)
# print 'TMEAN'
# print TMEAN
# print 'Total Covaraince Matrix'
# print St
# # Class Means
# NS = np.zeros((K, 1))
XMEAN = np.zeros((K, nc))
#
# for i in range(nr):
# k = label[i];
# NS[k] = NS[k] + 1
# for j in range(nc):
# XMEAN[k,j] = XMEAN[k,j] + data[i,j]
#
# for k in range(K):
# omega = NS[k]
# for j in range(nc):
# XMEAN[k,j] = XMEAN[k,j] / omega
#
# print 'Class Means'
# print XMEAN
NE = np.zeros((K))
for k in range(K):
NE[k] = sum(label == k)
for k in range(K):
XMEAN[k,:] = np.dot(data[ label == k, :].T, np.ones((int(NE[k])))).T / float(NE[k])
# print 'Class Means'
# print XMEAN
# Between Class Covariance Matrix
# Sb = np.zeros((nc, nc))
# for k in range(K):
# omega = sum(label == k) / float(nr)
# for i in range(nc):
# for j in range(nc):
# Sb[i,j] = Sb[i,j] + omega * (XMEAN[k,i] - TMEAN[i]) * (XMEAN[k,j] - TMEAN[j])
#
# print 'Between Class Covariance Matrix'
# print Sb
# alpha = 0.001
Sb = np.zeros((nc, nc))
for k in range(K):
omega = float(NE[k]) / float(nr)
xmean_m = XMEAN[k,:] - TMEAN
Sb = Sb + omega * np.outer(xmean_m, xmean_m)
# print 'Between Class Covariance Matrix'
# print Sb.dtype
# print Sb
Sw = St - Sb
# Sw = Sw + alpha * np.eye(nc)
# print 'Within Class Covariance Matrix'
# print Sw.dtype
# print Sw
Eval, Evec = klin.pencil(Sb,Sw)
return (Eval[:ldim], Evec[:,:ldim], TMEAN, XMEAN)
def danal(data, label, K):
nr, nc = data.shape
ldim = np.minimum(nc, K - 1)
# Total mean and Total covrainace matrix
# TMEAN = (sum(np.asarray(data,dtype=np.float))) / float(nr)
TMEAN = sum(data) / float(nr)
data_m = data - TMEAN
St = np.dot(data_m.T, data_m) / float(nr)
# print 'TMEAN'
# print TMEAN
# print 'Total Covaraince Matrix'
# print St
# # Class Means
# NS = np.zeros((K, 1))
XMEAN = np.zeros((K, nc))
#
# for i in range(nr):
# k = label[i];
# NS[k] = NS[k] + 1
# for j in range(nc):
# XMEAN[k,j] = XMEAN[k,j] + data[i,j]
#
# for k in range(K):
# omega = NS[k]
# for j in range(nc):
# XMEAN[k,j] = XMEAN[k,j] / omega
#
# print 'Class Means'
# print XMEAN
NE = np.zeros((K))
for k in range(K):
NE[k] = sum(label == k)
for k in range(K):
XMEAN[k, :] = np.dot(data[label == k, :].T, np.ones(
(int(NE[k])))).T / float(NE[k])
# print 'Class Means'
# print XMEAN
# Between Class Covariance Matrix
# Sb = np.zeros((nc, nc))
# for k in range(K):
# omega = sum(label == k) / float(nr)
# for i in range(nc):
# for j in range(nc):
# Sb[i,j] = Sb[i,j] + omega * (XMEAN[k,i] - TMEAN[i]) * (XMEAN[k,j] - TMEAN[j])
#
# print 'Between Class Covariance Matrix'
# print Sb
# alpha = 0.001
Sb = np.zeros((nc, nc))
for k in range(K):
omega = float(NE[k]) / float(nr)
xmean_m = XMEAN[k, :] - TMEAN
Sb = Sb + omega * np.outer(xmean_m, xmean_m)
# print 'Between Class Covariance Matrix'
# print Sb.dtype
# print Sb
Sw = St - Sb
# Sw = Sw + alpha * np.eye(nc)
# print 'Within Class Covariance Matrix'
# print Sw.dtype
# print Sw
Eval, Evec = klin.pencil(Sb, Sw)
return (Eval[:ldim], Evec[:, :ldim], TMEAN, XMEAN)
import klin
m = 5
data = [
[0.011, 0.012, 0.013, 0.014, 0.015],
[0.012, 0.022, 0.023, 0.024, 0.025],
[0.013, 0.023, 0.033, 0.034, 0.035],
[0.014, 0.024, 0.034, 0.044, 0.045],
[0.015, 0.025, 0.035, 0.045, 0.055],
]
A = np.array(data)
B = np.zeros((m, m))
for i in range(m):
B[i, i] = i + 1.0
print "A"
print A
print "B"
print B
Eval, Evec = klin.pencil(A, B)
print "Eval is"
print Eval
print "Evec is"
print Evec
import numpy as np
import klin
m = 5
data = [[0.011, 0.012, 0.013, 0.014,
0.015], [0.012, 0.022, 0.023, 0.024, 0.025],
[0.013, 0.023, 0.033, 0.034,
0.035], [0.014, 0.024, 0.034, 0.044, 0.045],
[0.015, 0.025, 0.035, 0.045, 0.055]]
A = np.array(data)
B = np.zeros((m, m))
for i in range(m):
B[i, i] = i + 1.0
print 'A'
print A
print 'B'
print B
Eval, Evec = klin.pencil(A, B)
print 'Eval is'
print Eval
print 'Evec is'
print Evec
def cca(X, Y):
# print '#### Canonical Correlation Analyais ####'
# print 'X\n', X
# print 'Y\n', Y
xsamples, n = X.shape
ysamples, m = Y.shape
# print 'xsamples=', xsamples, 'n=', n
# print 'ysamples=', ysamples, 'm=', m
if (xsamples != ysamples):
print 'The number of samples are inconsistent'
else:
nsamples = xsamples
XMean = sum(X) / float(nsamples)
YMean = sum(Y) / float(nsamples)
# print 'XMean', XMean
# print 'YMean', YMean
XX = X - XMean
YY = Y - YMean
SXX = np.dot(XX.T, XX) / float(nsamples-1)
SYY = np.dot(YY.T, YY) / float(nsamples-1)
SXY = np.dot(XX.T, YY) / float(nsamples-1)
SYYinv = np.linalg.inv(SYY)
SXYYYXY = np.dot(SXY,np.dot(SYYinv, SXY.T))
Eval, Evec = klin.pencil(SXYYYXY,SXX)
idx= Eval.argsort()
Eval = Eval[idx][::-1]
Evec = Evec[:,idx][:,::-1]
A = Evec
# print 'sqrt(Eval)', np.sqrt(Eval)
# print 'A\n', A
# U = np.dot(XX, A)
# print 'U\n', U
# print 'inv(Eval)', 1 / np.sqrt(Eval)
Evalinv = 1.0 / np.sqrt(Eval)
B = np.dot(np.dot(SYYinv, np.dot(SXY.T, A)), np.diag(Evalinv))
# print 'B\n', B
# V = np.dot(YY, B)
# print 'V\n', V
return (A, B, XMean, YMean)
def su3(data):
EPS = 1.0e-6
m, n = data.shape
if (m < n):
minmn = m
else:
minmn = n
total = np.sum(data)
# R = np.zeros((m,n))
R = data / float(total)
####################
P = np.dot(R, np.ones((n)))
Pinv = np.zeros((m))
for i in range(m):
if (P[i] >= EPS):
Pinv[i] = 1.0 / P[i]
Q = np.dot(np.ones((m)), R)
Qinv = np.zeros((n))
for i in range(n):
if (Q[i] >= EPS):
Qinv[i] = 1.0 / Q[i]
# print 'R\n', R
# print 'P\n', P
# print 'Q\n', Q
# Solve the eigen problem with smaller dimension
if (m <= n):
# R Qinv R^T
UU = np.dot(np.dot(R, np.diag(Qinv)), R.T)
W = np.diag(P)
Eval, Evec = klin.pencil(UU, W)
E = Eval[1:]
U = Evec[:,1:]
Einv = np.zeros(m-1)
for i in range(m-1):
if (E[i] >= EPS):
Einv[i] = 1.0 / np.sqrt(E[i])
# print 'R\n', R
# print 'Einv\n', Einv
V = np.dot(np.dot(np.dot(np.diag(Qinv), R.T), U), np.diag(Einv))
else:
# VV = R^T Pinv R
VV = np.dot(np.dot(R.T, np.diag(Pinv)), R)
W = np.diag(Q)
Eval, Evec = klin.pencil(VV, W)
E = Eval[1:]
V = Evec[:,1:]
Einv = np.zeros(n-1)
for i in range(n-1):
if (E[i] >= EPS):
Einv[i] = 1.0 / np.sqrt(E[i])
U = np.dot(np.dot(np.dot(np.diag(Pinv), R), V), np.diag(Einv))
# remove the first eigen value and eigen vector
return (E, U, V)
