Assessing Methods for Evaluating the Number of Components in Non-Negative Matrix Factorization

Functional transcriptional signatures for tumor-type-agnostic phenotype prediction

Cancer transcriptional patterns exhibit both shared and unique features across diverse cancer types, but whether these patterns are sufficient to characterize the full breadth of tumor phenotype heterogeneity remains an open question. We hypothesized that cancer transcriptional diversity mirrors patterns in normal tissues optimized for distinct functional tasks. Starting with normal tissue transcriptomic profiles, we use non-negative matrix factorization to derive six distinct transcriptomic phenotypes, called archetypes, which combine to describe both normal tissue patterns and variations across a broad spectrum of malignancies. We show that differential enrichment of these signatures correlates with key tumor characteristics, including overall patient survival and drug sensitivity, independent of clinically actionable DNA alterations. Additionally, we show that in HR+/HER2- breast cancers, metastatic tumors adopt transcriptomic signatures consistent with the invaded tissue. Broadly, our findings suggest that cancer often arrogates normal tissue transcriptomic characteristics as a component of both malignant progression and drug response. This quantitative framework provides a strategy for connecting the diversity of cancer phenotypes and could potentially help manage individual patients.

Inferring therapeutic vulnerability within tumors through integration of pan-cancer cell line and single-cell transcriptomic profiles

Single-cell RNA sequencing greatly advanced our understanding of intratumoral heterogeneity through identifying tumor subpopulations with distinct biologies. However, translating biological differences into treatment strategies is challenging, as we still lack tools to facilitate efficient drug discovery that tackles heterogeneous tumors. One key component of such approaches tackles accurate prediction of drug response at the single-cell level to offer therapeutic options to specific cell subpopulations. Here, we present a transparent computational framework (nicknamed scIDUC) to predict therapeutic efficacies on an individual-cell basis by integrating single-cell transcriptomic profiles with large, data-rich pan-cancer cell line screening datasets. Our method achieves high accuracy, with predicted sensitivities easily able to separate cells into their true cellular drug resistance status as measured by effect size (Cohen's d > 1.0). More importantly, we examine our method's utility with three distinct prospective tests covering different diseases (rhabdomyosarcoma, pancreatic ductal adenocarcinoma, and castration-resistant prostate cancer), and in each our predicted results are accurate and mirrored biological expectations. In the first two, we identified drugs for cell subpopulations that are resistant to standard-of-care (SOC) therapies due to intrinsic resistance or effects of tumor microenvironments. Our results showed high consistency with experimental findings from the original studies. In the third test, we generated SOC therapy resistant cell lines, used scIDUC to identify efficacious drugs for the resistant line, and validated the predictions with in-vitro experiments. Together, scIDUC quickly translates scRNA-seq data into drug response for individual cells, displaying the potential as a first-line tool for nuanced and heterogeneity-aware drug discovery.

Clustering single-cell multimodal omics data with jrSiCKLSNMF

Introduction: The development of multimodal single-cell omics methods has enabled the collection of data across different omics modalities from the same set of single cells. Each omics modality provides unique information about cell type and function, so the ability to integrate data from different modalities can provide deeper insights into cellular functions. Often, single-cell omics data can prove challenging to model because of high dimensionality, sparsity, and technical noise. Methods: We propose a novel multimodal data analysis method called joint graph-regularized Single-Cell Kullback-Leibler Sparse Non-negative Matrix Factorization (jrSiCKLSNMF, pronounced "junior sickles NMF") that extracts latent factors shared across omics modalities within the same set of single cells. Results: We compare our clustering algorithm to several existing methods on four sets of data simulated from third party software. We also apply our algorithm to a real set of cell line data. Discussion: We show overwhelmingly better clustering performance than several existing methods on the simulated data. On a real multimodal omics dataset, we also find our method to produce scientifically accurate clustering results.

Decision of the Optimal Rank of a Nonnegative Matrix Factorization Model for Gene Expression Data Sets Utilizing the Unit Invariant Knee Method: Development and Evaluation of the Elbow Method for Rank Selection

BACKGROUND

There is a great need to develop a computational approach to analyze and exploit the information contained in gene expression data. The recent utilization of nonnegative matrix factorization (NMF) in computational biology has demonstrated the capability to derive essential details from a high amount of data in particular gene expression microarrays. A common problem in NMF is finding the proper number rank (r) of factors of the degraded demonstration, but no agreement exists on which technique is most appropriate to utilize for this purpose. Thus, various techniques have been suggested to select the optimal value of rank factorization (r).

OBJECTIVE

In this work, a new metric for rank selection is proposed based on the elbow method, which was methodically compared against the cophenetic metric.

METHODS

To decide the optimum number rank (r), this study focused on the unit invariant knee (UIK) method of the NMF on gene expression data sets. Since the UIK method requires an extremum distance estimator that is eventually employed for inflection and identification of a knee point, the proposed method finds the first inflection point of the curvature of the residual sum of squares of the proposed algorithms using the UIK method on gene expression data sets as a target matrix.

RESULTS

Computation was conducted for the UIK task using gene expression data of acute lymphoblastic leukemia and acute myeloid leukemia samples. Consequently, the distinct results of NMF were subjected to comparison on different algorithms. The proposed UIK method is easy to perform, fast, free of a priori rank value input, and does not require initial parameters that significantly influence the model's functionality.

CONCLUSIONS

This study demonstrates that the elbow method provides a credible prediction for both gene expression data and for precisely estimating simulated mutational processes data with known dimensions. The proposed UIK method is faster than conventional methods, including metrics utilizing the consensus matrix as a criterion for rank selection, while achieving significantly better computational efficiency without visual inspection on the curvatives. Finally, the suggested rank tuning method based on the elbow method for gene expression data is arguably theoretically superior to the cophenetic measure.

Adaptive Kernel Graph Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) is an efficient method for feature learning in the field of machine learning and data mining. To investigate the nonlinear characteristics of datasets, kernel-method-based NMF (KNMF) and its graph-regularized extensions have received much attention from various researchers due to their promising performance. However, the graph similarity matrix of the existing methods is often predefined in the original space of data and kept unchanged during the matrix-factorization procedure, which leads to non-optimal graphs. To address these problems, we propose a kernel-graph-learning-based, nonlinear, nonnegative matrix-factorization method in this paper, termed adaptive kernel graph nonnegative matrix factorization (AKGNMF). In order to automatically capture the manifold structure of the data on the nonlinear feature space, AKGNMF learned an adaptive similarity graph. We formulated a unified objective function, in which global similarity graph learning is optimized jointly with the matrix decomposition process. A local graph Laplacian is further imposed on the learned feature subspace representation. The proposed method relies on both the factorization that respects geometric structure and the mapped high-dimensional subspace feature representations. In addition, an efficient iterative solution was derived to update all variables in the resultant objective problem in turn. Experiments on the synthetic dataset visually demonstrate the ability of AKGNMF to separate the nonlinear dataset with high clustering accuracy. Experiments on real-world datasets verified the effectiveness of AKGNMF in three aspects, including clustering performance, parameter sensitivity and convergence. Comprehensive experimental findings indicate that, compared with various classic methods and the state-of-the-art methods, the proposed AKGNMF algorithm demonstrated effectiveness and superiority.

MSDA-NMF: A Multilayer Complex System Model Integrating Deep Autoencoder and NMF

In essence, the network is a way of encoding the information of the underlying social management system. Ubiquitous social management systems rarely exist alone and have dynamic complexity. For complex social management systems, it is difficult to extract and represent multi-angle features of data only by using non-negative matrix factorization. Existing deep NMF models integrating multi-layer information struggle to explain the results obtained after mid-layer NMF. In this paper, NMF is introduced into the multi-layer NMF structure, and the feature representation of the input data is realized by using the complex hierarchical structure. By adding regularization constraints for each layer, the essential features of the data are obtained by characterizing the feature transformation layer-by-layer. Furthermore, the deep autoencoder and NMF are fused to construct the multi-layer NMF model MSDA-NMF that integrates the deep autoencoder. Through multiple data sets such as HEP-TH, OAG and HEP-TH, Pol blog, Orkut and Livejournal, compared with 8 popular NMF models, the Micro index of the better model increased by 1.83, NMI value increased by 12%, and link prediction performance improved by 13%. Furthermore, the robustness of the proposed model is verified.