## Results  
### Gene Selections  
HOSVD was applied to tensors \(x_{ijks}\) of HEC-1-A and mESC (Figures 2 and 3). Independent of target species,  
* \(u_{1j}\), which is attributed to measurements, represents constant values for histone modifications, m6A, and nascent RNA; it likely exhibits transcription activated by m6A through histone modification. * \(u_{2k}\) (and \(u_{3k}\) for mESC), which are both attributed to the distinction between METTL3 KO and control, exhibit the distinction between them; they are more likely related to mA6 mediated effects. * \(u_{1s}\), which is attributed to two biological replicates, represents constant values between two replicates; it likely exhibits features independent of replicates. In general, singular value vectors exhibit the patterns of representative genes. The fact that \(u_{1j}\)s take constant values means that the amounts of histone modification, m6A, and nascent RNA simultaneously vary over some sets of genes, because otherwise such a singular value vector cannot appear. The fact that \(u_{3k}\)s take opposite signs between \(k=1\) and \(k=2\) means that there are some sets of genes whose amounts of histone modification, m6A, and nascent RNA are distinct between control and METTL3 KO, because otherwise such a singular value vector cannot appear. The fact that \(u_{1s}\)s take constant values means that the amounts of histone modification, m6A, and nascent RNA will be independent of biological replicates, because otherwise such a singular value vector cannot appear. Next, we needed to identify which \(G\)s had larger absolute values, given \(\ell_{1}=1,\ell_{2}=2\) (and also 3 for mouse), and \(\ell_{3}=1\). \(G\) represents the weight by which the combination of \(u_{\ell_{1}j}u_{\ell_{2}k}u_{\ell_{3}s}u_{\ell_{4}i}\) contributes to \(x_{ijk}\)s (Equation (1)), because \(u_{\ell_{1}j},u_{\ell_{2}k},u_{\ell_{3}s}\), and \(u_{\ell_{4}j}\) are unit vectors. Since we have already identified which \(u_{\ell_{1}j},u_{\ell_{2}k}\), and \(u_{\ell_{3}s}\) are associated with the properties of interest, by identifying which \(G(\ell_{1}\ell_{2}\ell_{3}\ell_{4})\) has the largest absolute value given \(\ell_{1},\ell_{2}\), and \(\ell_{3}\), we can know which \(u_{\ell_{4}j}\) is most associated with the properties of interest. Independent of target species, \(U_{5i}\) has the absolutely largest \(G(1,2,1,\ell_{4})\) (Table 3). Although one might wonder why \(\ell_{4}=7\) was not employed in spite of that \(|G(1,3,1,7)|>|G(1,3,1,5)|\), \(\ell_{4}=5\) was selected because of larger \(\sum_{\ell_{2}=2}^{3}G(1,\ell_{2},1,\ell_{4})^{2}\). Following this, \(p\)-values were attributed to \(i\)th gene (Ensembl gene ID) using Equation (2). After correcting \(P_{i}\) using BH criterion [18], 740 human and 667 mouse genes with Ensembl gene ID were selected, respectively (full list is available as Supplementary Materials). After converting  
Figure 3: Singular value vectors obtained by applying HOSVD to mESC, \(x_{ijk}\)s. U11: \(u_{1j}\), U22: \(u_{2k}\), U23: \(u_{3k}\), U31: \(u_{1s}\). Ensembl gene IDs into gene symbols using gene ID conversion tools implemented in DAVID [20], we investigated the intersection between these two sets of genes. Figure 4 shows the Venn diagram between gene symbols selected using TD-based unsupervised FE. [PERSON]'s exact test shows that the overlap is highly significant (Table 4). \begin{table}
\begin{tabular}{c c c c} \hline \hline  & & \multicolumn{2}{c}{**Human**} \\ \cline{3-4}  & & **Not Selected** & **Selected** \\ \hline \multirow{2}{*}{mouse} & not selected & 15704 & 496 \\  & selected & 499 & 63 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Confusion matrix of gene symbols selected by TD-based unsupervised FE between HAC-1-A (human) and mESC (mouse). Odds ratio is 4.00, \(P=1.91\times 10^{-17}\). Since only common gene symbols between mice and humans were considered to generate the confusion matrix, the total number of genes considered was less than the total numbers of mouse and human genes respectively.