PCA via joint graph Laplacian and sparse constraint: Identification of differentially expressed genes and sample clustering on gene expression data

Accurate identification of single-cell types via correntropy-based Sparse PCA combining hypergraph and fusion similarity

The advent of single-cell RNA sequencing (scRNA-seq) technology enables researchers to gain deep insights into cellular heterogeneity. However, the high dimensionality and noise of scRNA-seq data pose significant challenges to clustering. Therefore, we propose a new single-cell type identification method, called CHLSPCA, to address these challenges. In this model, we innovatively combine correntropy with PCA to address the noise and outliers inherent in scRNA-seq data. Meanwhile, we integrate the hypergraph into the model to extract more valuable information from the local structure of the original data. Subsequently, to capture crucial similarity information not considered by the PCA model, we employ the Gaussian kernel function and the Euclidean metric to mine the similarity information between cells, and incorporate this information into the model as the similarity constraint. Furthermore, the principal components (PCs) of PCA are very dense. A new sparse constraint is introduced into the model to gain sparse PCs. Finally, based on the principal direction matrix learned from CHLSPCA, we conduct extensive downstream analyses on real scRNA-seq datasets. The experimental results show that CHLSPCA performs better than many popular clustering methods and is expected to promote the understanding of cellular heterogeneity in scRNA-seq data analysis and support biomedical research.

PLPCA: Persistent Laplacian-Enhanced PCA for Microarray Data Analysis

Over the years, Principal Component Analysis (PCA) has served as the baseline approach for dimensionality reduction in gene expression data analysis. Its primary objective is to identify a subset of disease-causing genes from a vast pool of thousands of genes. However, PCA possesses inherent limitations that hinder its interpretability, introduce class ambiguity, and fail to capture complex geometric structures in the data. Although these limitations have been partially addressed in the literature by incorporating various regularizers, such as graph Laplacian regularization, existing PCA based methods still face challenges related to multiscale analysis and capturing higher-order interactions in the data. To address these challenges, we propose a novel approach called Persistent Laplacian-enhanced Principal Component Analysis (PLPCA). PLPCA amalgamates the advantages of earlier regularized PCA methods with persistent spectral graph theory, specifically persistent Laplacians derived from algebraic topology. In contrast to graph Laplacians, persistent Laplacians enable multiscale analysis through filtration and can incorporate higher-order simplicial complexes to capture higher-order interactions in the data. We evaluate and validate the performance of PLPCA using ten benchmark microarray data sets that exhibit a wide range of dimensions and data imbalance ratios. Our extensive studies over these data sets demonstrate that PLPCA provides up to 12% improvement to the current state-of-the-art PCA models on five evaluation metrics for classification tasks after dimensionality reduction.

A Tensor-Based Online RPCA Model for Compressive Background Subtraction

Background subtraction of videos has been a fundamental research topic in computer vision in the past decades. To alleviate the computation burden and enhance the efficiency, background subtraction from online compressive measurements has recently attracted much attention. However, current methods still have limitations. First, they are all based on matrix modeling, which breaks the spatial structure within video frames. Second, they generally ignore the complex disturbance within the background, which reduces the efficiency of the low-rank assumption. To alleviate this issue, we propose a tensor-based online compressive video reconstruction and background subtraction method, abbreviated as NIOTenRPCA, by explicitly modeling the background disturbance in different frames as nonidentical but correlated noise. By virtue of such sophisticated modeling, the proposed method can well adapt to complex video scenes and, thus, perform more robustly. Extensive experiments on a series of real-world video datasets have demonstrated the effectiveness of the proposed method compared with the existing state of the arts. The code of our method is released on the website: https://github.com/crystalzina/NIOTenRPCA.

Enhancing Characteristic Gene Selection and Tumor Classification by the Robust Laplacian Supervised Discriminative Sparse PCA

Characteristic gene selection and tumor classification of gene expression data play major roles in genomic research. Due to the characteristics of a small sample size and high dimensionality of gene expression data, it is a common practice to perform dimensionality reduction prior to the use of machine learning-based methods to analyze the expression data. In this context, classical principal component analysis (PCA) and its improved versions have been widely used. Recently, methods based on supervised discriminative sparse PCA have been developed to improve the performance of data dimensionality reduction. However, such methods still have limitations: most of them have not taken into consideration the improvement of robustness to outliers and noise, label information, sparsity, as well as capturing intrinsic geometrical structures in one objective function. To address this drawback, in this study, we propose a novel PCA-based method, known as the robust Laplacian supervised discriminative sparse PCA, termed RLSDSPCA, which enforces the L2,1 norm on the error function and incorporates the graph Laplacian into supervised discriminative sparse PCA. To evaluate the efficacy of the proposed RLSDSPCA, we applied it to the problems of characteristic gene selection and tumor classification problems using gene expression data. The results demonstrate that the proposed RLSDSPCA method, when used in combination with other related methods, can effectively identify new pathogenic genes associated with diseases. In addition, RLSDSPCA has also achieved the best performance compared with the state-of-the-art methods on tumor classification in terms of major performance metrics. The codes and data sets used in the study are freely available at http://csbio.njust.edu.cn/bioinf/rlsdspca/.

Identifying biomarkers for breast cancer by gene regulatory network rewiring

Background

Mining gene regulatory network (GRN) is an important avenue for addressing cancer mechanism. Mutations in cancer genome perturb GRN and cause a rewiring in an orchestrated network. Hence, the exploration of gene regulatory network rewiring is significant to discover potential biomarkers and indicators for discriminating cancer phenotypes.

Results

Here, we propose a new bioinformatics method of identifying biomarkers based on network rewiring in different states. It firstly reconstructs GRN in different phenotypic conditions from gene expression data with a priori background network. We employ the algorithm based on path consistency algorithm and conditional mutual information to delete false-positive regulatory interactions between independent nodes/genes or not closely related gene pairs. And then a differential gene regulatory network (D-GRN) is constructed from the rewiring parts in the two phenotype-specific GRNs. Community detection technique is then applied for D-GRN to detect functional modules. Finally, we apply logistic regression classifier with recursive feature elimination to select biomarker genes in each module individually. The extracted feature genes result in a gene set of biomarkers with impressing ability to distinguish normal samples from controls. We verify the identified biomarkers in external independent validation datasets. For a proof-of-concept study, we apply the framework to identify diagnostic biomarkers of breast cancer. The identified biomarkers obtain a maximum AUC of 0.985 in the internal sample classification experiments. And these biomarkers achieve a maximum AUC of 0.989 in the external validations.

Conclusion

In conclusion, network rewiring reveals significant differences between different phenotypes, which indicating cancer dysfunctional mechanisms. With the development of sequencing technology, the amount and quality of gene expression data become available. Condition-specific gene regulatory networks that are close to the real regulations in different states will be established. Revealing the network rewiring will greatly benefit the discovery of biomarkers or signatures for phenotypes. D-GRN is a general method to meet this demand of deciphering the high-throughput data for biomarker discovery. It is also easy to be extended for identifying biomarkers of other complex diseases beyond breast cancer.