A Semi-Supervised Transfer Learning with Dynamic Associate Domain Adaptation for Human Activity Recognition Using WiFi Signals

. 2021 Dec 19;21(24):8475. doi: 10.3390/s21248475

Algorithm 2: The dynamic associate domain adaptation phase.

Input:
The source domain label data $D_{s} = {{\tilde{H}}_{i}^{s}, y_{i}^{s}}_{i = 1 \dots n_{s}}$ , the target domain label data $D_{t} = {{\tilde{H}}_{i}^{t}, y_{i}^{t}}_{i = 1 \dots n}$ and the target domain unlabelled data $D_{t} = {{\tilde{H}}_{i}^{t}}_{i = n + 1 \dots n_{t}}$ .
Output:
Similarity loss $L_{s i m}$ .

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Mapped the data to same space by $ϕ$ .

$S_{i} = ϕ ({{\tilde{H}}_{i}^{s}}_{i = 1 \dots n_{s}})$ , $U_{j} = ϕ ({{\tilde{H}}_{i}^{t}}_{i = 1 \dots n})$ , $L_{k} = ϕ ({{\tilde{H}}_{i}^{t}}_{i = n + 1 \dots n_{t}})$

Calculate similarity matrix $F_{i j}$ and $G_{i k}$ by dot product.

$F_{i j} = S_{i} \times U_{j}$ , $G_{i k} = S_{i} \times L_{k}$

Calculate conversion probability matrix of the similarity matrix $F_{i j}$ and $G_{i k}$ by softmax function SM.

$P_{i j}^{S U} = P (U_{j} | S_{i}) = S M_{c o l u m n s} {(F)}_{i j} = \frac{e x p (F_{i j})}{Σ_{j^{'}} e x p (F_{i j^{'}})}$

$P_{j i}^{U S} = P (S_{i} | U_{j}) = S M_{r o w s} {(F)}_{i j} = \frac{e x p (F_{i j})}{Σ_{i^{'}} e x p (F_{i^{'} j})}$

$P_{i k}^{S L} = P (L_{k} | S_{i}) = S M_{c o l u m n s} {(G)}_{i k} = \frac{e x p (F_{i k})}{Σ_{k^{'}} e x p (F_{i k^{'}})}$

$P_{k i}^{L S} = P (L_{k} | U_{j}) = S M_{r o w s} {(G)}_{i k} = \frac{e x p (F_{i k})}{Σ_{i^{'}} e x p (F_{i^{'} k})}$

- - - - - - - - - - - - - - - - - - - - - - - Step 2 - - - - - - - - - - - - - - - - - - - - - -

Calculate $L_{S U S}$ by conversion probability, $P^{S U S}$ is the round-trip probability and the label distribution $Y_{i j}$ .

$P^{S U S} = {(P^{S U} P^{U S})}_{i j} = Σ_{n} P_{i n}^{S U} P_{n i}^{U S}$

$Y_{i j} {= {}_{0 e l s e}^{\frac{1}{S_{i}} c l a s s (S_{i}) = c l a s s (S_{j})}$

$L_{S U S} = Q (Y_{i j}, P^{S U S})$ Calculate $L_{L S}$ by conversion probability, $P^{L S}$ is the conversion probability and the label distribution $J_{i K}$ .

$J_{i k} {= {}_{0 e l s e}^{\frac{1}{L_{k}} c l a s s (L_{k}) = c l a s s (S_{i})}$

$L_{L S} = H (J_{i j}, P^{L S})$

- - - - - - - - - - - - - - - - - - - - - - - Step 3 - - - - - - - - - - - - - - - - - - - - - -

Combine $L_{S U S}$ and $L_{L S}$ as divergence loss $L_{d i v}$ .

$L_{d i v} = m a x [L_{S U S}, L_{L S}]$

Calculate synchronize loss $L_{s y n}$ .

$L_{s y n} = H (P_{j}^{U S}, P_{j}^{S U})$ $P_{j}^{S U} = Σ_{j^{'}} P_{i j^{'}}^{S U}$

$P_{j}^{U S} = Σ_{j^{'}} {P_{i j^{'}}^{U S}}^{T}$

$L_{s y n} = Q (P_{j}^{U S}, P_{j}^{S U})$

Combine $L_{d i v}$ and $L_{s y n}$ as $L_{s i m}$ .

$L_{s i m} = β L_{d i v} + (β - 1) L_{s y n}$