Brain Decoding of Multiple Subjects for Estimating Visual Information Based on a Probabilistic Generative Model

. 2022 Aug 17;22(16):6148. doi: 10.3390/s22166148

Algorithm 1: PGM for shared features

c_{n}

1:
Initialize:
2:
$P_{i}$ , $ρ_{i}$ , $Σ_{c}$ , $μ_{i}$ , J, N, $M A X L O O P$ , $A_{i}$ , $ρ_{i}^{{new}^{2}}$ , ${Σ_{c}}^{new}$
3:
for $i = 1 \dots J$ do
4:
for $n = 1 \dots N$ do
5:
$μ_{i} \leftarrow μ_{i} + b_{i, n}$
6:
end for
7:
$μ_{i} \leftarrow \frac{1}{N} μ_{i}$
8:
end for
9:
$l \leftarrow 1$
10:
while $M A X L O O P \geq l$ do // EM algorithm for updating parameters
11:
${Var}_{c | b} [c] \leftarrow Σ_{c} - {Σ_{c}}^{⊤} P^{⊤} {(P Σ_{c} P^{⊤} + Ψ)}^{- 1} P Σ_{c}$ // Start expectation step
12:
for $n = 1 \dots N$ do
13:
$E_{c | b} [c_{n}] \leftarrow {(P Σ_{c})}^{⊤} {(P Σ_{c} P^{⊤} + Ψ)}^{- 1} (b_{n} - μ)$
14:
$E_{c | b} [c_{n} c_{n}^{⊤}] \leftarrow {Var}_{c | b} [c] + E_{c | b} [c_{n}] E_{c | b} {[c_{n}]}^{⊤}$
15:
end for // End expectation step
16:
for $i = 1 \dots J$ do // Start maximization step
17:
for $n = 1 \dots N$ do
18:
$A_{i} \leftarrow A_{i} + (b_{i, n} - μ_{i}) E_{c | b} {[c_{n}]}^{⊤}$
19:
end for
20:
$A_{i} \leftarrow \frac{1}{2} A_{i}$
21:
$P_{i}^{new} \leftarrow A_{i} {(A_{i}^{⊤} A_{i})}^{- 1 / 2}$
22:
for $n = 1 \dots N$ do
23:
$ρ_{i}^{{new}^{2}} \leftarrow ρ_{i}^{{new}^{2}} + | | b_{i, n} - μ_{i} {| |}^{2} - 2 {(b_{i, n} - μ_{i})}^{⊤} P_{i}^{new} E_{c | b} [c_{n}] + t r (E_{c | b} [c_{n} c_{n}^{⊤}])$
24:
end for
25:
$ρ_{i}^{{new}^{2}} \leftarrow \frac{1}{N d_{i}} ρ_{i}^{{new}^{2}}$
26:
end for
27:
for $n = 1 \dots N$ do
28:
${Σ_{c}}^{new} \leftarrow {Σ_{c}}^{new} + E_{c | b} [c_{n} c_{n}^{⊤}]$
29:
end for
30:
${Σ_{c}}^{new} \leftarrow \frac{1}{N} {Σ_{c}}^{new}$
31:
$P_{i}$ , $ρ_{i}^{2}$ , $Σ_{c}$ ← $P_{i}^{new}$ , $ρ_{i}^{{new}^{2}}$ , ${Σ_{c}}^{new}$ // End maximization step
32:
Initialize:
33:
$A_{i}$ , $ρ_{i}^{{new}^{2}}$ , ${Σ_{c}}^{new}$
34:
$l \leftarrow l + 1$
35:
end while