## 2 Related Work
### Label Similarity Analysis MMFT (LSA-MMFT)  
Identifying non-related domains to minimize the effect of NT is highly significant in enhancing classification performance across individual target domains. Hence, the LSA-MMFT algorithm first performs source selection by iterating through domains to identify the beneficial sources utilized to perform transfer mapping. To achieve this goal, LSA-MMFT utilizes both single-to-single (STS) and multi-source transfer (MST) to evaluate the similarities across domains [11]. Consequently, to effectively detect the transferability of individual-source domains, the labels acquired using the STS classifier are compared with the labels acquired through the MST classifier. As such, LSA-MMFT iterates through domains, evaluating the label similarities across the domains, and then discards a single less-related domain in each iteration based on said label similarities.  
\[sim\big{(}y_{real},\,y_{ps}\big{)}=\sum_{i=1}^{n_{t}}A_{i} \tag{6}\]  
\[A_{i}=\begin{cases}y_{real,j}=y_{ps,i}\\ 0\text{ otherwise}\end{cases} \tag{7}\]  
The label similarity across domains is evaluated using Equation (6) and is denoted by \(sim\big{(}y_{real},\,y_{ps}\big{)}\), with \(n_{t}\) representing the number of samples in the target domain [11]. The predicted single-source domain labels are denoted by \(y_{ps}\), and the target domain labels are denoted by \(y_{real}\), while \(A_{i}\) represent the overall number of samples, as denoted by Equation (7).  
\[Accuracy=sim\big{(}y_{real},y_{ps}\big{)}\,/\,n_{t} \tag{8}\]  
A single-to-single (STS) transfer prediction rate in this instance is utilized to measure the transferability of the individual-source domain denoted by Equation (8). In this instance,the number of samples in the target domain is \(n_{t}\), while \(y_{ps}\) represents the predicted single-SD labels and \(y_{real}\) the TD labels.  
\[y_{ps}^{1}=y_{pm}^{1}=y_{real}^{1} \tag{9}\]  
\[sim\big{(}y_{real},y_{ps}\big{)}=sim\big{(}y_{real}^{1},y_{ps}^{1}\big{)}+sim \big{(}y_{real}^{2},y_{ps}^{2}\big{)}+sim\big{(}y_{real}^{3},y_{ps}^{3}\big{)} \tag{10}\]  
To evaluate the transferability of source domains based on STS, Equations (9) and (10) are both utilized, whereby a higher prediction rate is interpreted as a higher transferability, with \(y_{ps}\) depicting the predicted single-SD labels and \(y_{real}\) representing the TD labels, while the predicted multi-source labels used to determine the transferability of the SDs are denoted by \(y_{pm}\). [11].  
\[sim\big{(}y_{ps},y_{pm}\big{)}=sim\big{(}y_{ps}^{1},y_{pm}^{1}\big{)}+sim \big{(}y_{ps}^{2},y_{pm}^{2}\big{)}+sim\big{(}y_{ps}^{3},y_{pm}^{3}\big{)} \tag{11}\]  
Equations (9) and (11) are utilized to evaluate the transferability of source domains based on multi-source transfer (MST). In this case, \(sim(\ )\) is utilized to quantify the label similarity between two types of predicted TD labels, with the predicted single-SD labels being depicted by \(y_{ps}\) and \(y_{pm}\) representing the predicted multi-source labels [11].  
\[\mathcal{R}\Big{(}\mathcal{D}_{s}^{(j)},\mathcal{D}_{t}\Big{)}=sim\bigg{(}f_{ s}\Big{(}\mathcal{D}_{s}^{(j)},\mathcal{D}_{t}\Big{)},\,f_{m}\bigg{(}\bigg{\{} \mathcal{D}_{s}^{(j)}\bigg{\}}_{j=1}^{z},\mathcal{D}_{t}\bigg{)}\bigg{)} \tag{12}\]  
Furthermore, Equation (12) is utilized to compute the transferability across the source domain and target domain, with the transferability being denoted by \(\mathcal{R}\). The source domain in this instance is denoted by \(\mathcal{D}_{s}^{(j)}\), and the target domain is depicted by \(\mathcal{D}_{t}\), while \(j\) represents the number of source domains [11]. The STS transfer classifier is denoted by \(f_{s}\), while the multi-source transfer classifier is denoted by \(f_{m}\).