## 2 Related Works
### Previous Work
#### 2.4.2 The Previous Method
3 IF Method Option == RR:
4 Partial Task Input: \(X_{i}^{k}\)
5 Partial Task Output: \(Y_{i}\) // prepared in the previous Preparation step
6 ELIF Method Option == DR:
7 Partial Task Input: \(XD_{i}^{k}\gets d_{DA}^{k}\Big{(}\epsilon_{DA}^{k}\left(X_{i}^{k};\theta_{e }^{k}\right);\theta_{d}^{k}\Big{)}\)
8 Partial Task Output: \(Y_{i}\) // prepared in the previous Preparation step
9 SIM Partial Training
10 IF Method Option == RR:
11 Train the Partial Task with objective function as \(\underset{\omega^{k}}{\operatorname*{argmin}}\underset{i}{\sum}\,L\left(f^{k} \left(\omega^{k};X_{i}^{k}\right),Y_{i}\right)\)
12 Get Feature Data \(F_{i}^{k}\gets\epsilon_{FE}^{k}\left(X_{i}^{k};\theta^{k}\right)\)
13 ELIF Method Option == DR:
14 rain the Partial Task with objective function as \(\underset{\omega^{k}}{\operatorname*{argmin}}\underset{i}{\sum}\,L\left(f^{k} \left(\omega^{k};XD_{i}^{k}\right),Y_{i}\right)\)
15 IF Feature Option == DR(R):
16 Get Feature Data \(F_{i}^{k}\gets\epsilon_{FE}^{k}\left(X_{i}^{k};\theta^{k}\right)\)
17 ELIF Feature Option == DR(D):
18 Get Feature Data \(F_{i}^{k}\gets\epsilon_{FE}^{k}\left(XD_{i}^{k};\theta^{k}\right)\)
19 Host Party
20 Merging Task Training
21 IF Guest Parties use Method Option as DR with Feature Option as DR(D):
22 IF Feature Option == DR(D)-Test(R):
23\(Y_{i}\gets f^{0}\big{(}\epsilon_{FE}^{1}\big{(}X_{i}^{1};\theta^{1}\big{)},\ldots,\epsilon_{FE}^{K}\big{(}X_{i}^{K};\theta^{k}\big{)};\omega^{0}\big{)}\)
```

**Algorithm 2**SIM Partial Training of TT-VFDL-SIM for Classification

## 3 The Proposed Method (TT-VFDL-ST)

The newly proposed TT-VFDL-ST could improve the limitation of our previous method [7] maintaining our design approach suggested in [7]. TT-VFDL-ST trains the multivariate aimed task distributedly by pre-training on each univariate model split from the aimed task then fine-tuning each task-driven feature to the multivariate model in the host party. Also, TT-VFDL-ST improves the limitation of our previous method [7] by adopting a self-transfer partial training mechanism, which is also newly proposed in this paper, for training each univariate model. Self-transfer partial training mechanism is a single and consistent training mechanism for each univariate model that could effectively introduce two feature spaces similar to each other based on transfer learning. Through this, the proposed method could improve the limitation of our previous method [7], which was difficult to apply to real-world-integrated IoT service construction scenarios because it was not derived as a single consistent mechanism. In this section, we introduce strategies to design TT-VFLD-ST and its algorithms. ### The Design Approach of TT-VFDL-ST

The aimed task model of TT-VFDL-ST has a generalized structure for the deep learning model used for multivariate analysis of time-series data from multiple sources distributed through each party. The possible structures for the target task model are shown in Figure 2. Each guest party stores inputs distributedly and the host party holds raw time-series data for regression output or label data for classification output. Parsing the structure of the aimed task model, univariate models (partial task models) on guest parties and a multivariate model (merging task model) on the host party are obtained. Each partial task model consists of each single input split out from the aimed task. Then, the aimed task is distributedly trained by utilizing a transfer learning mechanism. Therefore, each univariate model and the multivariate model are used for each pre-training and fine-tuning of the aimed task. In scenarios to construct integrated IoT services, each distributed input is related and dependent on each other [41]. Therefore, it is reasonable that each univariate model of each guest party is used in pre-training for the aimed task. For the same reason [41], it could be assumed that features trained from each univariate model of guest parties are more suitable to the aimed task than features to reproduce each input.