## 4 Discussion  
The analysis of the mutational signatures of tumor patients has expanded the existing understanding of the tumor genome and provided new insights into tumor initiation and progression. However, identifying the biological processes and functions underlying somatic mutagenesis remains challenging. This study searched for mutational signatures associated with immune cell infiltration in patients with tumors using non-negative CCA and verified that the approach would be useful to uncover their functional roles in survival and immunological contexts. To my knowledge, this study is the first work to systematically investigate the functional roles of the mutational signatures. Although some variables (mutational signatures) may represent negative effects on the immune cell infiltration, the non-negative constraints of the coefficients help to interpret the influences of the variables using the magnitude of the coefficient values, similar to NMF which has commonly been used in many biological data analyses [46; 47; 48]. The composition of mutational signatures in each tumor sample was estimated using deconstructSigs. Although the COSMIC mutational signature version 3 was constructed recently, deconstructSigs did not support version 3. Moreover, single base substitution (SBS) signatures were partitioned into 60 signatures, which is an excessive amount of variables compared to the number of samples, and it would lead to making the interpretation difficult. Mutational signature version 2 was therefore used in this experiment. The estimation of cell subtype composition based on the bulk gene expression profiles can facilitate advanced analysis of heterogeneous tumor samples and has the potential to provide crucial insights into functional genomics research. Despite the innovative value of tumor genome analysis, the estimation results of these approaches are not reliable. Recently, [PERSON] et al. conducted a systematic evaluation of computational methods used to assess the abundance of cell subtypes from bulk transcriptome data [49]. They showed that EPIC was one of the most reliable methods; thus, I chose EPIC to estimate the cellular composition. As mentioned above, the relationships between the mutational signatures and immunity were studied in LUSC [11; 12], which showed that the APOBECC signature was associated with the immune response. Furthermore, recently, the relationship between APOBECC mutagenesis and the immune response in breast cancer has been reported [50], and some studies have shown an association between APOBECC mutagenesis and immunity in HNSC [51; 52]. In my experimental results, the APOBECC signatures were also observed as the highest coefficients in BRCA, HNSC, as well as LUSC. Moreover, the identified mutational signatures were distinct from the abundance of mutational signatures in each tumor type, Thus, these results verified that the CCA-based approach was valid for the identification of immunity-related mutational signatures. A limitation of this study was that it did not use molecular features or clinical information such as tumor grade, histology, and lymph node involvement. For instance, breast tumors were subdivided into luminal A, luminal B, basal-like, Her2-enriched, etc. By subgrouping the samples based on oncological features or molecular properties, subsequent analysis might obtain informative functional characteristics of the mutational signatures. Instead, this study carried out survival analysis using the correlated genes with the mutational signatures identified by non-negative CCA. Survival analysis is a useful data-driven method for clinical trials. In our experiment, in most of tumor types, the \(p\)-values were lower than or close to 0.05, as shown in Figure 4. Although three tumor types, HNSC, LUAD, and OV, showed relatively high \(p\)-values (>0.1), relative differences between the two groups were observed in the Kaplan-Meier plots.