## 1 Introduction  
Deep learning has been widely used due to its advanced performance and automatic feature extraction. Training deep neural networks (DNNs) requires a large amount of training data. In medical image analysis fields where privacy and security concerns exist, the proper collection of training data can be challenging. Conventional training methods address this problem by applying transfer learning [1; 2]. Transfer learning reuses source domain knowledge to solve a new task in the target domain [3]. Transfer learning can be divided into three approaches: supervised, semi-supervised, and unsupervised learning. Unsupervised and semi-supervised learning approaches assume that the target domain labels are the same as the source domain labels [4; 5]. However, in the application to the medical field, and in others as others as well, it is difficult to collect data where the source domain and target domain use the same labels. In addition, many semi-supervised and unsupervised learning methods have to train DNNs by using the source and target domains at the same time. It is difficult to upload the target domain data outside of a hospital and prepare a sufficient computer environment, especially for small- and medium-sized hospitals. This paper addresses tasks to classify diseases using proteome data for these small- and medium-sized hospitals. Therefore, we argue that the supervised transfer learning approach fits the clinical demand in this target environment. Supervised transfer learning has been widely used in the field of computer vision [6; 7; 8]. Given the labeled source/target domain data, first, many methods train a DNN using the source domain data. Then, a second DNN is constructed based on the target domain data by reusing the hidden layers of the first DNN to set the initial values for the network structure and weights. This approach has the advantages that the DNN for the source domain can be constructed prior to obtaining and preparing the target domain data and it is not necessary to retain the source domain data. However, there is a risk of poor classification performance owing to the random initial values of weights (and biases) that are not reused. This can occur when these parameters are trained on a small amount of target domain data. To avoid this problem, it is important to reuse all layers, including the output (last) layer [2]. To reuse all layers, [PERSON] et al. [2] proposed the _all-transfer deep learning_ (_ATDL_) method. ATDL trains the first DNN to solve the source domain task. It then averages the target domain data of each target domain label in the output space, which has the same dimension as the number of source domain labels. This computation is conducted in the output layer, which is thrown away by conventional methods [6; 7; 8]. In [2], this vector is called the _relation vectors_ (Section 2.2.1). Following that, the second DNN is initialized by the first DNN and optimized using the estimated relation vectors instead of the one-hot target vectors. By using this method, it is not necessary to throw away the output layer. The main difference between the ATDL and other supervised transfer learning methods is that the ATDL can use the first DNN to regularize all parameters of a second DNN. This means that the ATDL can reduce the risk of the local optimal solution caused by the random initial values of the non-transferred parameters. However, their estimation cannot consider the relation between the target domain labels. To improve the classification performance, the appropriate configuration of relation vectors must be considered in regard to this relation. This paper proposes a relation vector modification based on constrained pairwise repulsive forces. A strong pairwise repulsive force between the relation vectors is introduced to produce a large distance (Section 3.1). In addition, to mitigate the risk of divergence, we constrain these vectors to be close to the distributions computed on the target domain data in the output space (Section 3.2).