def cost_and_grad(W):
W = vec_to_mat(W, N, KK[-2])
W_m = []
disper = []
Y = [np.zeros((N, R, k)) for k in K]
for p in range(P):
W_m.append(W[:, :, KK[p - 1]:KK[p]])
for k in range(K[p]):
Y[p][:, :, k] = dot(W_m[p][:, :, k], X[p][:, :, k])
disper = [
np.array([dot(Y[p][n, :, :].T, Y[p][n, :, :]) for n in range(N)])
for p in range(P)
]
A = [
np.array([
dot(pinv(disper[p][n, :, :]), Y[p][n, :, :].T)
for n in range(N)
]) for p in range(P)
]
YdY = np.zeros((N, R))
for n in range(N):
#YdY[n,:] = np.sum(sum([Y[p][n,:,:].T * A[p][n,:,:] for p in range(P)]), 0)
for p in range(P):
YdY[n, :] = YdY[n, :] + np.sum(Y[p][n, :, :].T * A[p][n, :, :],
0)
YdY = np.sqrt(YdY)
cost = np.sum(YdY) * (np.sqrt(R - 1) / R)
for p in range(P):
for k in range(K[p]):
cost = cost - log(abs(det(W_m[p][:, :, k])))
for n in range(N):
cost = cost + log(det(disper[p][n, :, :])) * (1.0 / 2.0)
if verbose:
print cost
gradient = [np.zeros((N, N, K[p])) for p in range(P)]
for p in range(P):
for n in range(N):
B = A[p][n, :, :] * (((np.sqrt(R - 1) / R)) /
(YdY[n, :] + sys.float_info.epsilon))
C = np.identity(K[p]) - dot(B, Y[p][n, :, :])
val = B + dot(C, A[p][n, :, :])
for k in range(K[p]):
gradient[p][n, :, k] = np.dot(val[k, :], X[p][:, :, k].T)
for k in range(K[p]):
gradient[p][:, :, k] = (gradient[p][:, :, k] -
pinv(W_m[p][:, :, k]).T)
gradient = np.array(mat_to_vec(gradient))
return cost, gradient
def dIVA_L(X, W_init=[], verbose=False) :
cost_and_grad = set_para(X, verbose)
N,R = X[0].shape[0], X[0].shape[1]
K = [x.shape[2] for x in X]
P = len(K)
KK = [sum(K[0:p+1]) for p in range(P)]
KK.append(0)
if W_init == [] :
W_init = [np.random.rand(N,N,K[p]) for p in range(P)]
W_init = mat_to_vec(W_init)
W,d,i = fmin_l_bfgs_b(cost_and_grad, x0=W_init)
if verbose :
print "Optimization Finished"
W = vec_to_mat(W,N,KK[-2])
W_m = []
for p in range(P) :
W_m.append(W[:,:,KK[p-1]:KK[p]])
return W_m, d, i
def dIVA_L(X, W_init=[], verbose=False):
cost_and_grad = set_para(X, verbose)
N, R = X[0].shape[0], X[0].shape[1]
K = [x.shape[2] for x in X]
P = len(K)
KK = [sum(K[0:p + 1]) for p in range(P)]
KK.append(0)
if W_init == []:
W_init = [np.random.rand(N, N, K[p]) for p in range(P)]
W_init = mat_to_vec(W_init)
W, d, i = fmin_l_bfgs_b(cost_and_grad, x0=W_init)
if verbose:
print "Optimization Finished"
W = vec_to_mat(W, N, KK[-2])
W_m = []
for p in range(P):
W_m.append(W[:, :, KK[p - 1]:KK[p]])
return W_m, d, i
def cost_and_grad(W) :
W = vec_to_mat(W,N,KK[-2])
W_m = []
disper = []
Y = [np.zeros((N,R,k)) for k in K]
for p in range(P) :
W_m.append(W[:,:,KK[p-1]:KK[p]])
for k in range(K[p]) :
Y[p][:,:,k] = dot(W_m[p][:,:,k], X[p][:,:,k])
disper = [np.array([dot(Y[p][n,:,:].T, Y[p][n,:,:]) for n in range(N)]) for p in range(P)]
A = [np.array([dot(pinv(disper[p][n,:,:]), Y[p][n,:,:].T) for n in range(N)]) for p in range(P)]
YdY = np.zeros((N,R))
for n in range(N) :
#YdY[n,:] = np.sum(sum([Y[p][n,:,:].T * A[p][n,:,:] for p in range(P)]), 0)
for p in range(P) :
YdY[n,:] = YdY[n,:] + np.sum(Y[p][n,:,:].T * A[p][n,:,:], 0)
YdY = np.sqrt(YdY)
cost = np.sum(YdY) * (np.sqrt(R-1)/R)
for p in range(P) :
for k in range(K[p]) :
cost = cost - log(abs(det(W_m[p][:,:,k])))
for n in range(N) :
cost = cost + log(det(disper[p][n,:,:])) * (1.0/2.0)
if verbose :
print cost
gradient = [np.zeros((N,N,K[p])) for p in range(P)]
for p in range(P) :
for n in range(N) :
B = A[p][n,:,:] * (((np.sqrt(R-1)/R)) / (YdY[n,:] + sys.float_info.epsilon) )
C = np.identity(K[p]) - dot(B, Y[p][n,:,:])
val = B + dot(C, A[p][n,:,:])
for k in range(K[p]) :
gradient[p][n,:,k] = np.dot(val[k,:], X[p][:,:,k].T)
for k in range(K[p]) :
gradient[p][:,:,k] = (gradient[p][:,:,k] - pinv(W_m[p][:,:,k]).T)
gradient = np.array(mat_to_vec( gradient ))
return cost, gradient