The document proposes using tensor decomposition on matrix products of multi-view data to perform unsupervised feature extraction. It applies this method to synthetic data containing embedded correlated variables and multi-omics data involving mRNA and miRNA. For the synthetic data, the method recovers the original orthogonal vectors after identifying correlations. For the multi-omics data, a few inter-correlated miRNAs and mRNAs are identified as statistically significant among many features.
12. SummarySummary
・ As a feature selection in multi view data, after applying
tensor decomposition to a tensor generated by product of
matrices, I propose to select features associated with BH
corrected Pvalues <0.01 computed by χ2
dist assumed for
a mode.
・ As for synthetic data set, apparently uncorrelated
variables embedded into noised are decomposed to original
orthogonal vectors after identifying correlated variables.
・As for muli omics data set, a few (a few %) intercorrelated
and biologically reasonable miRNAs and mRNAs are
identified among huge number of mRNAs and miRNAs