Adapted tensor decomposition and PCA based unsupervised feature extraction select more biologically reasonable differentially expressed genes than conventional methods

Abstract

Tensor decomposition- and principal component analysis-based unsupervised feature extraction were proposed almost 5 and 10 years ago, respectively; although these methods have been successfully applied to a wide range of genome analyses, including drug repositioning, biomarker identification, and disease-causing genes’ identification, some fundamental problems have been identified: the number of genes identified was too small to assume that there were no false negatives, and the histogram of P values derived was not fully coincident with the null hypothesis that principal component and singular value vectors follow the Gaussian distribution. Optimizing the standard deviation such that the histogram of P values is as much as possible coincident with the null hypothesis results in an increase in the number and biological reliability of the selected genes. Our contribution was that we improved these methods so as to be able to select biologically more reasonable differentially expressed genes than the state of art methods that must empirically assume negative binomial distributions and dispersion relation, which is required for the selecting more expressed genes than less expressed ones, which can be achieved by the proposed methods that do not have to assume these.

Tensor Decomposition and Principal Component Analysis-Based Unsupervised Feature Extraction Outperforms State-of-the-Art Methods When Applied to Histone Modification Profiles

“…In contrast to the other methods that must assume some statistical properties on histone modification distribution along the genome, the proposed method assumes only that PCs and SVVs obtained obey Gaussian distributions. Other methods can be successfully applied to gene expression [13] and DNA methylation [14] because target specific methods can be developed. However, since no assumptions about the statistical properties of histone modification can be made, other methods are not robust when applied to identification of histone modification.…”

“…To fulfill this requirement, the method of tensor de-composition (TD) and principal component analysis (PCA)- based unsupervised feature extraction (FE) with optimized standard deviation (SD) that were successfully applied to gene expression [13] and DNA methylation [14] were tested to determine if histone modification could also be identified. In contrast to two previous studies [13], [14] where PC or singular value vectors (SVVs) obey the Gaussian distribution which is assumed in the null hypothesis after SD optimization, in our method PC and SVVs follow a mixed Gaussian distribution instead. Nevertheless, empirically, SD optimization allows the correct identification of histone modification to some extent, even when compared to various state-of-the-art methods.…”

Principal component analysis- and tensor decomposition-based unsupervised feature extraction to select more suitable differentially methylated cytosines: Optimization of standard deviation versus state-of-the-art methods

“…A full explanation is provided in our previous paper (Taguchi and Turki, 2022) and our recent book (Taguchi, 2020). In brief, the purpose of the method is to select a limited number of variables associated with the classification; in this study, the classifications were clinical, medical, or biological information, e.g., healthy controls and patients.…”

“…See also Algorithm S2. A full explanation is, again, provided in our previous paper (Taguchi and Turki, 2022) and our recent book (Taguchi, 2020). As TD was only applied to EH1072 here, we assumed that the tensor represented the EH1072 dataset.…”

“…To address these problems, we applied principal component analysis (PCA)- and tensor decomposition (TD)-based unsupervised feature extraction (FE) with optimized standard deviation (SD) to identify DMCs. This approach was recently successfully applied to identify differentially expressed genes (Taguchi and Turki, 2022). We found that the proposed method can outperform modern methods, especially when applied to HTS data.…”