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SPDNet_utils.py
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SPDNet_utils.py
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##################################################################################################
# This code originally comes from: https://github.com/YirongMao/SPDNet/blob/master/spd_net_util.py by YirongMao.
# We use rec_mat_v2(), log_mat_v2() and update_para_riemann() in this project.
# Author：Yirong Mao, Ce Ju, Dashan Gao
# Date : July 29, 2020
# Paper : Ce Ju et al., Federated Transfer Learning for EEG Signal Classification, IEEE EMBS 2020.
# Description: Source domain includes all good subjects, target domain is the bad subject.
##################################################################################################
import torch
from torch.autograd import Function
import numpy as np
class RecFunction(Function):
def forward(self, input):
Us = torch.zeros_like(input)
Ss = torch.zeros((input.shape[0], input.shape[1])).double()
max_Ss = torch.zeros_like(input)
max_Ids = torch.zeros_like(input)
for i in range(input.shape[0]):
U, S, V = torch.svd(input[i, :, :])
eps = 0.0001
max_S = torch.clamp(S, min=eps)
max_Id = torch.ge(S, eps).float()
Ss[i, :] = S
Us[i, :, :] = U
max_Ss[i, :, :] = torch.diag(max_S)
max_Ids[i, :, :] = torch.diag(max_Id)
result = torch.matmul(Us, torch.matmul(max_Ss, torch.transpose(Us, 1, 2)))
self.Us = Us
self.Ss = Ss
self.max_Ss = max_Ss
self.max_Ids = max_Ids
self.save_for_backward(input)
return result
def backward(self, grad_output):
Ks = torch.zeros_like(grad_output)
dLdC = grad_output
dLdC = 0.5 * (dLdC + torch.transpose(dLdC, 1, 2)) # checked
Ut = torch.transpose(self.Us, 1, 2)
dLdV = 2 * torch.matmul(torch.matmul(dLdC, self.Us), self.max_Ss)
dLdS_1 = torch.matmul(torch.matmul(Ut, dLdC), self.Us)
dLdS = torch.matmul(self.max_Ids, dLdS_1) # checked
diag_dLdS = torch.zeros_like(grad_output)
for i in range(grad_output.shape[0]):
diagS = self.Ss[i, :]
diagS = diagS.contiguous()
vs_1 = diagS.view([diagS.shape[0], 1])
vs_2 = diagS.view([1, diagS.shape[0]])
K = 1.0 / (vs_1 - vs_2)
K[K >= float("Inf")] = 0.0
Ks[i, :, :] = K
diag_dLdS[i, :, :] = torch.diag(torch.diag(dLdS[i, :, :]))
tmp = torch.transpose(Ks, 1, 2) * torch.matmul(Ut, dLdV)
tmp = 0.5 * (tmp + torch.transpose(tmp, 1, 2)) + diag_dLdS
grad = torch.matmul(self.Us, torch.matmul(tmp, Ut)) # checked
return grad
class LogFunction(Function):
def forward(self, input):
Us = torch.zeros_like(input)
Ss = torch.zeros((input.shape[0], input.shape[1])).double()
logSs = torch.zeros_like(input)
invSs = torch.zeros_like(input)
for i in range(input.shape[0]):
U, S, V = torch.svd(input[i, :, :])
Ss[i, :] = S
Us[i, :, :] = U
logSs[i, :, :] = torch.diag(torch.log(S))
invSs[i, :, :] = torch.diag(1.0 / S)
result = torch.matmul(Us, torch.matmul(logSs, torch.transpose(Us, 1, 2)))
self.Us = Us
self.Ss = Ss
self.logSs = logSs
self.invSs = invSs
self.save_for_backward(input)
return result
def backward(self, grad_output):
grad_output = grad_output.double()
Ks = torch.zeros_like(grad_output)
dLdC = grad_output
dLdC = 0.5 * (dLdC + torch.transpose(dLdC, 1, 2)) # checked
Ut = torch.transpose(self.Us, 1, 2)
dLdV = 2 * torch.matmul(dLdC, torch.matmul(self.Us, self.logSs)) # [d, ind]
dLdS_1 = torch.matmul(torch.matmul(Ut, dLdC), self.Us) # [ind, ind]
dLdS = torch.matmul(self.invSs, dLdS_1)
diag_dLdS = torch.zeros_like(grad_output)
for i in range(grad_output.shape[0]):
diagS = self.Ss[i, :]
diagS = diagS.contiguous()
vs_1 = diagS.view([diagS.shape[0], 1])
vs_2 = diagS.view([1, diagS.shape[0]])
K = 1.0 / (vs_1 - vs_2)
# K.masked_fill(mask_diag, 0.0)
K[K >= float("Inf")] = 0.0
Ks[i, :, :] = K
diag_dLdS[i, :, :] = torch.diag(torch.diag(dLdS[i, :, :]))
tmp = torch.transpose(Ks, 1, 2) * torch.matmul(Ut, dLdV)
tmp = 0.5 * (tmp + torch.transpose(tmp, 1, 2)) + diag_dLdS
grad = torch.matmul(self.Us, torch.matmul(tmp, Ut)) # checked
return grad
def rec_mat(input):
return RecFunction()(input)
def log_mat(input):
return LogFunction()(input)
def update_para_riemann(X, U, t):
Up = cal_riemann_grad(X, U)
new_X = cal_retraction(X, Up, t)
return new_X
def cal_riemann_grad(X, U):
"""
Calculate Riemann gradient.
:param X: the parameter
:param U: the eculidean gradient
:return: the riemann gradient
"""
# XtU = X'*U;
XtU = np.matmul(np.transpose(X), U)
# symXtU = 0.5 * (XtU + XtU');
symXtU = 0.5 * (XtU + np.transpose(XtU))
# Up = U - X * symXtU;
Up = U - np.matmul(X, symXtU)
return Up
def cal_retraction(X, rU, t):
"""
Calculate the retraction value
:param X: the parameter
:param rU: the riemann gradient
:param t: the learning rate
:return: the retraction:
"""
# Y = X + t * U;
# [Q, R] = qr(Y, 0);
# Y = Q * diag(sign(diag(R)));
Y = X - t * rU
Q, R = np.linalg.qr(Y, mode='reduced')
sR = np.diag(np.sign(np.diag(R)))
Y = np.matmul(Q, sR)
return Y