## 1 Introduction  
The causes of somatic mutations in patients with tumors are only partially known. For example, exogenous mutagens are introduced by tobacco smoking or ultraviolet exposure, and endogenous mutagens are introduced by spontaneous methylcytosine examination in the 5'-CG dinucleotide context, resulting in C-to-T mutations [1, 2]. Furthermore, DNA repair deficiency occurs through homologous recombination deficiency or DNA mismatch repair deficiency, and enzymatic DNA editing is caused by the functional activity of the APOBECE protein family induced by cytidine deaminase enzymes [3, 4]. However, the complete identification of many mutational processes is very difficult. To address these difficulties, mutation signatures representing specific patterns have been developed from a large catalog of mutations generated by several types of cancer genome sequencing [1, 5, 6]. Mutational signatures are distinctive combinations of somatic alteration resulting from a specific cause raised generally in the cancer genome. Single nucleotide variants (SNVs) are generally classified into six mutational spectra (C:G \(>\) A:T, C:G \(>\) G:C, C:G \(>\) T:A \(>\) A:T, T:A \(>\) C:G, T:A \(>\) G:C); in the trinucleotide context,96 combinations of SNVs are possible. Tumor samples with 96 variables are then decomposed using a non-negative matrix factorization (NMF) method, and new matrices are generated using mutational signatures [7]. Mutational signatures have helped understand the mutational processes and causes of tumors; many cancer researchers have also used mutational signatures for their analyses [8; 9; 10]. Recent studies have revealed that the apolipoprotein B mRNA editing enzyme, catalytic polypeptide-like (APOBEC) mutational signature is potentially associated with immune responses in non-small cell lung cancer [11; 12]. Two members of the APOBEC family, APOBECC3A and APOBECC3B, are known to contribute to mutations in cancers by generating C > T and C > G mutations in TCN trinucleotides [13; 14]. The authors characterized the APOBECC mutational signatures related to the response to immune checkpoint blockade therapy. These studies were mostly conducted on non-small cell lung cancer and demonstrated the potential of APOBECC signatures. However, the functional characteristics of most mutational signatures remain unknown. Moreover, until now, to my knowledge, there have been no systematic analyses to examine the connections between the mutational signatures and the immune cell infiltration. Here, this study investigated the immunological effects of mutational signatures. Firstly, the mutational signatures and the immune cell infiltration were inferred from somatic mutation and gene expression profiles in each tumor sample, respectively. Then, the relationships between the mutational signatures and the immune cell infiltration were examined based on canonical correlation analysis (CCA). CCA is a useful approach to determining the correlation between two multivariate datasets [15]. Both datasets are projected into lower-dimensional spaces, where their correlation is maximal. Generally, CCA is considered as a dimensionality reduction method [16; 17], however, it has been applied for various purposes, including classification and clustering [18; 19; 20]. CCA has also been employed to solve many biological problems, mainly using the integrative analysis of multi-omics datasets [21; 22; 23]. As shown in some previous works using CCA, the estimated coefficients of the variables by the CCA can reveal the importance of the variables for another input dataset of the CCA. Thus, this study applied the CCA to infer the functional roles of each mutational signature. However, traditional CCA is sensitive to outliers and noise. In addition, the occurrence of negative values of the coefficients hinders the intuitive interpretation of the results [24].