## 4 Experimental Results
### Simulation Experiments  
To accurately grasp our novel method's ability, it is important to start with a small scale environment [19]. In this article, our method was applied to two simulation experiments with respect to changing the size of the target domain data: (1) using CIFAR (Canadian Institute For Advanced Research)-10 database [20] as the source domain and images of an automobile and pedestrian crossings from ImageNet database [21] as the target domain and (2) using SVHN (Street View House Numbers) database [22] as the source domain and MNIST (Modified National Institute of Standards and Technology database) database [23] as the target domain. Task (1) is an example where the source and target domain data comprise color images, while Task (2) is an example of multiclass classification. For Task (2), since the labels of MNIST and SVHN have the same meaning, [PERSON] et al. 's method [14] was also used for comparison. This method, which is also a supervised transfer learning method, can only function when the source and target domain data have the same label. For Task (1), the number of hidden layers was set to \(H=3\); the numbers of dimensions of the \(h\)-th hidden layer were set to \(D_{h}=1000\)\((h=1,2,3)\), \(D_{y}^{s}=10\), \(D_{y}^{t}=2\); the size of the source domain data was set to \(N^{s}\) = 50,000. For target test data, 750 images of automobiles and 750 of pedestrian crossings were used. For Task (2), parameters were set to \(H=3\), \(D_{y}^{s}=10\), \(D_{y}^{t}=10\), \(D_{h}=100\), and \(N^{s}=73\),257, and the SVHN images were converted to gray-scale. For the target test data, 10,000 images from MNIST were used. The target domain data dimensions of Tasks (1) and (2) were both set to match the dimensions of the source domain data. In addition, these architectures were experimentally determined beforehand. Table 1 show the classification accuracies for different sizes of \(N^{t}\). As shown in these tables, our method outperformed other methods when \(N^{t}=400\), 800, and 1200 for Task (1) and \(N^{t}=1000\) and 5000 for Task (2). A comparison of \(\setminus\)Tuning and [2] shows that the minimization of Equation (3) and \(\mathbf{r}_{l}^{*}\) are necessary for improving the classification performance. The effectiveness of \(\mathbf{r}_{l}^{*}\) was also indicated by a comparison with [14]. These tables also show that strong regularization by reusing all layers does not necessarily improve the performance when the size of the target domain data is large (\(N^{t}=1500\) for Task (1) and \(N^{t}=10\),000 for Task (2)). These results indicate that reusing all layers with appropriate relation vectors is effective when \(N^{t}\) is small. To investigate the influence of our method, the distance was evaluated as follows:  
\[d=\frac{1}{N_{l,l^{\prime}}}\sum_{l,l^{\prime}}\|\mathbf{r}_{l}^{*}-\mathbf{r}_{l^{ \prime}}^{*}\|^{2} \tag{8}\]  
where \(N_{l,l^{\prime}}\) is the number of pairwise combinations. We also evaluated the variables of \(\mathbf{r}_{l}^{*}\). Similar to \(\mathbf{m}_{l}\), the \(k\)-th variable \(r_{l}^{*}(k)\) is expected to indicate the strength of the relation between the \(k\)-th source domain label and the \(l\)-th target domain label. If \(\mathbf{r}_{l}^{*}\) exhibits this characteristic, it will be possible to identify the instances where labels of the source domain are similar to those of the target domain. Figure 3A shows the relation vectors of Task (1), and Figure 3B shows the comparison of \(d\) with a conventional ATDL. As shown in these figures, the highest relation of \"Automobile\" of ImageNet is \"Automobile\" and \"Truck\" of CIFAR-10, while \"Pedestrian Crossings\" is not substantially related to CIFAR-10 (Figure 3A). In addition, by using our method, \(d\) became larger than the conventional ATDL (Figure 3B).