## 2 Materials and Methods  
Patient serum. Serum samples were collected from 20 patients at Nihon University Hospital in accordance with the regulations of the ethics committee, and written informed consent was obtained from each patient before inclusion in the study. The patient group included both males and females, and the distribution of ages was 35 to 79 years of age. Sixty microliters of serum were used in the experiments. Removal of major proteins contained in serum. An Aurum Serum Protein Mini Kit (Bio-Rad, Tokyo, Japan) was used to remove the albumin and IgG contained in large amounts in serum. A Seppro(r) IgGY14 protein kit (Sigma-Aldrich, Tokyo, Japan) was used to remove 14 other proteins that are contained in large amounts. 2D-PAGE. For accurate quantification necessary for high-precision analyses, the amount of protein in each sample was determined using a 2-D Quant Kit (GE Healthcare Japan, Tokyo, Japan). Removal of impurities and desalination of the samples were carried out using a 2-D Clean-Up Kit (GE Healthcare). Treated samples were dissolved in Destreak rehydration solution (GE Healthcare) and applied for swelling of Immobiline dry strips (GE Healthcare). Isoelectric focusing  
Figure 1: Outline of our proposed method. (**A**): Training the deep neural network (DNN) using the source domain data, **(B)**: estimating the relation vectors of each target domain label, **(C)**: tuning all parameters using pairs of target domain data and relation vectors. as the first dimension was carried out using the swelled strips on a Multiphor II system (GE Healthcare). Second dimension separation was carried out on a discontinuous SDS gel system as first described by [PERSON] [16] using a NuPAGE 4-12% Bis-Tris Z00m Gel (Thermo Fisher Scientific, Tokyo, Japan). The resulting gels were stained with a fluorescent dye, SYPRO Ruby Protein Gel Stain (Thermo Fisher Scientific). Fluorescent images were acquired from the stained gels using a Typhoon FLA 9500 apparatus with Ettan DIGE imager software (GE Healthcare), and the images were analyzed using Image Master 2D Platinum 7.0 software (GE Healthcare). Conventional Transfer Learning for DNN and Our Proposed Approach. To estimate relation vectors, we consider the distance between hyperplane and the relation vectors. The last step of our method converges the target domain data around the corresponding relation vectors. Namely, the above distance strongly relates to the margin between the hyperplane and the target domain data. Figure 2 shows the relationship between the relation vectors and the hyperplane. We assume that a large margin provides high classification performance similar to that of a support vector machine. However, if we maximize the margin without any constraints, the relation vectors obviously diverge, and the final fine-tuning process fails. From these considerations, we estimate relation vectors as follows:  
\[\gamma_{l}=m_{l}+\epsilon_{l}\]  
where \(\gamma_{l}\) represents relation vectors, and \(m_{l}\) represents the average vector. This is computed by the vectors and achieved by feeding the target domain data having the \(l\)-th target domain label (sepsis or not) to the source DNN. \(\epsilon_{l}\) represent a vector which increases a distance between relation vectors. We call this vector as a repulsive force vector. To maximize the margin while preventing divergence, we add constraints to the repulsive force vector. In this article, the length of this vector is set so that the Mahalanobis distance with \(m_{l}\) is 1.0, and the direction is set so that the distance between other relation vectors is maximized. By using this setting, without the risk of divergence, our method can provide a large margin compared to \(\epsilon_{l}=0\) which is the simplest approach of relation vectors estimation [17] shown in Figure 2. Table 1 lists the confusion matrix when \(\epsilon_{l}=0\) Compared to Table 2, using our method we can improve the classification performance. Figure 2: Relationship between relation vectors and hyperplane.