Multi-Source Co-adaptation for EEG-Based Emotion Recognition by Mining Correlation Information

. 2021 May 13;15:677106. doi: 10.3389/fnins.2021.677106

Algorithm 1. Multiple sources adaptation learning by utilizing correlation knowledge.
Input: Source datasets ${X_{i}^{s}}_{i = 1}^{S}$ , ${L_{i}}_{i = 1}^{S}$ , target dataset X^t, and parameters α, β, and λ, the maximal iteration number ℓ. Output: Converged projection matrices ${W_{i}}_{i = 1}^{S}$ , and matrices ${F_{i}}_{i = 1}^{S}$ and W₀. Initialization: Set itr = 0, and initialize ${W_{i}^{i t r}}_{i = 0}^{S}$ randomly. Let $W^{i t r} = [W_{1}^{i t r}, \dots, W_{S}^{i t r}]$ ; 1: for i = 1 to S do { Compute matrix $M_{i}^{i t r}$ and $M_{i (l)}^{i t r}$ , and $K_{i}^{i t r}$ and $K_{i (l)}^{i t r}$ with empirical kernel mapping, thus computing $C_{i}^{i t r} = \sum_{l = 0}^{c} C_{i (l)}^{i t r}$ by $C_{i (0)}^{i t r} = K_{i}^{i t r} M_{i}^{i t r} K_{i}^{i t r}$ and $C_{i (l)}^{i t r} = K_{i (l)}^{i t r} M_{i (l)}^{i t r} K_{i (l)}^{i t r}$ , l = 1, …, c; Compute $η_{i}^{i t r}$ by Eq. 28, and then construct matrix η^itr and $η_{0}^{i t r} = [η_{1}^{i t r} I_{r}; \dots; η_{S}^{i t r} I_{r}]$ ; Compute $F_{i}^{i t r} = K_{i}^{T} W_{i}^{i t r}$ ; } 2: repeat { Compute $W_{0}^{i t r}$ by (12); Compute the diagonal matrix U^itr by (15); Compute the matrix Ω^itr by (16); set i = 1; repeat { Compute $G_{i}^{i t r}$ with respect to $W_{i}^{i t r}$ ; Compute $Z_{i}^{i t r}$ with respect to $K_{i}^{T} W_{i}^{i t r} - F_{i}^{i t r}$ ; Compute $g_{i}^{i t r} = t r ({(K_{i}^{T} W_{i}^{i t r} - F_{i}^{i t r})}^{T} Z_{i} (K_{i}^{T} W_{i}^{i t r} - F_{i}^{i t r})) [c p s b r e a k] + t r ({(W_{i}^{i t r})}^{T} C_{i}^{i t r} W_{i}^{i t r})$ ; Compute $ϑ_{i}^{i t r}$ according to Eq. 24, and then construct ϑ^itr; Compute the matrix $E_{i}^{i t r}$ by Eq. 17, and then $N_{i}^{i t r}$ by Eq. 19; Compute $F_{i}^{i t r}$ according to Eq. 20; Compute $W_{i}^{i t r}$ according to Eq. 14; i = i + 1; } until i > S Update $W_{i}^{i t r + 1} = W_{i}^{i t r}$ s.t.i = 1,..,S; Update $F_{i}^{i t r + 1} = F_{i}^{i t r}$ according to (20) s.t.i = 1,..,S; Update $ϑ_{i}^{i t r + 1}$ according to (24) s.t.i = 1,..,S; Update $η_{i}^{i t r + 1}$ according to (27) s.t.i = 1,..,S; Update $W_{0}^{i t r + 1}$ according to (12); Let itr = itr + 1; }until itr > ℓ or ς < 10⁻⁵ 3: return ${W_{a}}_{a = 0}^{S}$ and ${F_{i}}_{i = 1}^{S}$ .

Algorithm 1. Multiple sources adaptation learning by utilizing correlation knowledge.

Input: Source datasets

{X_{i}^{s}}_{i = 1}^{S}

{L_{i}}_{i = 1}^{S}

, target dataset X^t, and parameters α, β, and λ, the maximal iteration number ℓ.
Output: Converged projection matrices

{W_{i}}_{i = 1}^{S}

, and matrices

{F_{i}}_{i = 1}^{S}

and W₀.
Initialization: Set itr = 0, and initialize

{W_{i}^{i t r}}_{i = 0}^{S}

randomly. Let

W^{i t r} = [W_{1}^{i t r}, \dots, W_{S}^{i t r}]

;
1: for i = 1 to S do
{
Compute matrix

M_{i}^{i t r}

and

M_{i (l)}^{i t r}

, and

K_{i}^{i t r}

and

K_{i (l)}^{i t r}

with empirical kernel mapping, thus computing

C_{i}^{i t r} = \sum_{l = 0}^{c} C_{i (l)}^{i t r}

C_{i (0)}^{i t r} = K_{i}^{i t r} M_{i}^{i t r} K_{i}^{i t r}

and

C_{i (l)}^{i t r} = K_{i (l)}^{i t r} M_{i (l)}^{i t r} K_{i (l)}^{i t r}

, l = 1, …, c;
Compute

η_{i}^{i t r}

by Eq. 28, and then construct matrix η^itr and

η_{0}^{i t r} = [η_{1}^{i t r} I_{r}; \dots; η_{S}^{i t r} I_{r}]

;
Compute

F_{i}^{i t r} = K_{i}^{T} W_{i}^{i t r}

;
}
2: repeat
{
Compute

W_{0}^{i t r}

by (12);
Compute the diagonal matrix U^itr by (15);
Compute the matrix Ω^itr by (16); set i = 1;
repeat
{
Compute

G_{i}^{i t r}

with respect to

W_{i}^{i t r}

;
Compute

Z_{i}^{i t r}

with respect to

K_{i}^{T} W_{i}^{i t r} - F_{i}^{i t r}

;
Compute

g_{i}^{i t r} = t r ({(K_{i}^{T} W_{i}^{i t r} - F_{i}^{i t r})}^{T} Z_{i} (K_{i}^{T} W_{i}^{i t r} - F_{i}^{i t r})) [c p s b r e a k] + t r ({(W_{i}^{i t r})}^{T} C_{i}^{i t r} W_{i}^{i t r})

;
Compute

ϑ_{i}^{i t r}

according to Eq. 24, and then construct ϑ^itr;
Compute the matrix

E_{i}^{i t r}

by Eq. 17, and then

N_{i}^{i t r}

by Eq. 19;
Compute

F_{i}^{i t r}

according to Eq. 20;
Compute

W_{i}^{i t r}

according to Eq. 14;
i = i + 1;
} until i > S
Update

W_{i}^{i t r + 1} = W_{i}^{i t r}

s.t.i = 1,..,S;
Update

F_{i}^{i t r + 1} = F_{i}^{i t r}

according to (20) s.t.i = 1,..,S;
Update

ϑ_{i}^{i t r + 1}

according to (24) s.t.i = 1,..,S;
Update

η_{i}^{i t r + 1}

according to (27) s.t.i = 1,..,S;
Update

W_{0}^{i t r + 1}

according to (12);
Let itr = itr + 1;
}until itr > ℓ or ς < 10⁻⁵
3: return

{W_{a}}_{a = 0}^{S}

and

{F_{i}}_{i = 1}^{S}