Adaptive total-variation for non-negative matrix factorization on manifold

Identification of the methotrexate resistance-related diagnostic markers in osteosarcoma via adaptive total variation netNMF and multi-omics datasets

Osteosarcoma is one of the most common malignant bone tumors with high chemoresistance and poor prognosis, exhibiting abnormal gene regulation and epigenetic events. Methotrexate (MTX) is often used as a primary agent in neoadjuvant chemotherapy for osteosarcoma; However, the high dosage of methotrexate and strong drug resistance limit its therapeutic efficacy and application prospects. Studies have shown that abnormal expression and dysfunction of some coding or non-coding RNAs (e.g., DNA methylation and microRNA) affect key features of osteosarcoma progression, such as proliferation, migration, invasion, and drug resistance. Comprehensive multi-omics analysis is critical to understand its chemoresistant and pathogenic mechanisms. Currently, the network analysis-based non-negative matrix factorization (netNMF) method is widely used for multi-omics data fusion analysis. However, the effects of data noise and inflexible settings of regularization parameters affect its performance, while integrating and processing different types of genetic data is also a challenge. In this study, we introduced a novel adaptive total variation netNMF (ATV-netNMF) method to identify feature modules and characteristic genes by integrating methylation and gene expression data, which can adaptively choose an anisotropic smoothing scheme to denoise or preserve feature details based on the gradient information of the data by introducing an adaptive total variation constraint in netNMF. By comparing with other similar methods, the results showed that the proposed method could extract multi-omics fusion features more effectively. Furthermore, by combining the mRNA and miRNA data of methotrexate (MTX) resistance with the extracted feature genes, four genes, Carboxypeptidase E (CPE), LIM, SH3 protein 1 (LASP1), Pyruvate Dehydrogenase Kinase 1 (PDK1) and Serine beta-lactamase-like protein (LACTB) were finally identified. The results showed that the gene signature could reliably predict the prognostic status and immune status of osteosarcoma patients.

Automatic Epileptic Seizure Detection Using Graph-Regularized Non-Negative Matrix Factorization and Kernel-Based Robust Probabilistic Collaborative Representation

Automatic seizure detection system can serve as a meaningful clinical tool for the treatment and analysis of epilepsy using electroencephalogram (EEG) and has obtained rapid development. An automatic detection of epileptic seizure method based on kernel-based robust probabilistic collaborative representation (ProCRC) combined with graph-regularized non-negative matrix factorization (GNMF) is proposed in this work. The raw EEG signals are pre-processed through the wavelet transform to obtain time-frequency distribution of EEG signals as preliminary feature information and GNMF is further employed for dimension reduction, retaining and enhancing the productive feature information of EEG signals. Then, the test sample is represented using robust ProCRC that can decide whether the testing sample belongs to each class (seizure or non-seizure) by jointly maximizing the likelihood. In addition, the kernel trick is applied to improve the separability of non-linear high dimensional EEG signals in robust ProCRC. Finally, post-processing techniques are introduced to generate more accurate and reliable results. The average epoch-based sensitivity of 96.48%, event-based sensitivity of 93.65% and specificity of 98.55% are acquired in this method, which is evaluated on the public Freiburg EEG database.

Spatially Coherent Clustering Based on Orthogonal Nonnegative Matrix Factorization

Classical approaches in cluster analysis are typically based on a feature space analysis. However, many applications lead to datasets with additional spatial information and a ground truth with spatially coherent classes, which will not necessarily be reconstructed well by standard clustering methods. Motivated by applications in hyperspectral imaging, we introduce in this work clustering models based on Orthogonal Nonnegative Matrix Factorization (ONMF), which include an additional Total Variation (TV) regularization procedure on the cluster membership matrix to enforce the needed spatial coherence in the clusters. We propose several approaches with different optimization techniques, where the TV regularization is either performed as a subsequent post-processing step or included into the clustering algorithm. Finally, we provide a numerical evaluation of 12 different TV regularized ONMF methods on a hyperspectral dataset obtained from a matrix-assisted laser desorption/ionization imaging measurement, which leads to significantly better clustering results compared to classical clustering models.

Adaptive Total-Variation Regularized Low-Rank Representation for Analyzing Single-Cell RNA-seq Data

High-throughput sequencing of single-cell gene expression reveals a complex mechanism of individual cell's heterogeneity in a population. An important purpose for analyzing single-cell RNA sequencing (scRNA-seq) data is to identify cell subtypes and functions by cell clustering. To deal with high levels of noise and cellular heterogeneity, we introduced a new single cell data analysis model called Adaptive Total-Variation Regularized Low-Rank Representation (ATV-LRR). In scRNA-seq data, ATV-LRR can reconstruct the low-rank subspace structure to learn the similarity of cells. The low-rank representation can not only segment multiple linear subspaces, but also extract important information. Moreover, adaptive total variation also can remove cell noise and preserve cell feature details by learning the gradient information of the data. At the same time, to analyze scRNA-seq data with unknown prior information, we introduced the maximum eigenvalue method into the ATV-LRR model to automatically identify cell populations. The final clustering results show that the ATV-LRR model can detect cell types more effectively and stably.