Search for: All records

Matrix low rank approximation is an effective method to reduce or eliminate the statistical redundancy of its components. Compared with the traditional global low rank methods such as singular value decomposition (SVD), local low rank approximation methods are more advantageous to uncover interpretable data structures when clear duality exists between the rows and columns of the matrix. Local low rank approximation is equivalent to low rank submatrix detection. Unfortunately,existing local low rank approximation methods can detect only submatrices of specific mean structure, which may miss a substantial amount of true and interesting patterns. In this work, we develop a novel matrix computational framework called RPSP (Random Probing based submatrix Propagation) that provides an effective solution for the general matrix local low rank representation problem. RPSP detects local low rank patterns that grow from small submatrices of low rank property, which are determined by a random projection approach. RPSP is supported by theories of random projection. Experiments on synthetic data demonstrate that RPSP outperforms all state-of-the-art methods, with the capacity to robustly and correctly identify the low rank matrices when the pattern has a similar mean as the background, background noise is heteroscedastic and multiple patterns present in the data. On real-world datasets, RPSP also demonstrates its effectiveness in identifying interpretable local low rank matrices. 

Metastatic cancer accounts for over 90% of all cancer deaths, and evaluations of metastasis potential are vital for minimizing the metastasis-associated mortality and achieving optimal clinical decision-making. Computational assessment of metastasis potential based on large-scale transcriptomic cancer data is challenging because metastasis events are not always clinically detectable. The under-diagnosis of metastasis events results in biased classification labels, and classification tools using biased labels may lead to inaccurate estimations of metastasis potential. This issue is further complicated by the unknown metastasis prevalence at the population level, the small number of confirmed metastasis cases, and the high dimensionality of the candidate molecular features. Our proposed algorithm, called P ositive and unlabeled L earning from U nbalanced cases and S parse structures ( PLUS ), is the first to use a positive and unlabeled learning framework to account for the under-detection of metastasis events in building a classifier. PLUS is specifically tailored for studying metastasis that deals with the unbalanced instance allocation as well as unknown metastasis prevalence, which are not considered by other methods. PLUS achieves superior performance on synthetic datasets compared with other state-of-the-art methods. Application of PLUS to The Cancer Genome Atlas Pan-Cancer gene expression data generated metastasis potential predictions that show good agreement with the clinical follow-up data, in addition to predictive genes that have been validated by independent single-cell RNA-sequencing datasets. 

Abstract Identifying relationships between genetic variations and their clinical presentations has been challenged by the heterogeneous causes of a disease. It is imperative to unveil the relationship between the high-dimensional genetic manifestations and the clinical presentations, while taking into account the possible heterogeneity of the study subjects.We proposed a novel supervised clustering algorithm using penalized mixture regression model, called component-wise sparse mixture regression (CSMR), to deal with the challenges in studying the heterogeneous relationships between high-dimensional genetic features and a phenotype. The algorithm was adapted from the classification expectation maximization algorithm, which offers a novel supervised solution to the clustering problem, with substantial improvement on both the computational efficiency and biological interpretability. Experimental evaluation on simulated benchmark datasets demonstrated that the CSMR can accurately identify the subspaces on which subset of features are explanatory to the response variables, and it outperformed the baseline methods. Application of CSMR on a drug sensitivity dataset again demonstrated the superior performance of CSMR over the others, where CSMR is powerful in recapitulating the distinct subgroups hidden in the pool of cell lines with regards to their coping mechanisms to different drugs. CSMR represents a big data analysis tool with the potential to resolve the complexity of translating the clinical representations of the disease to the real causes underpinning it. We believe that it will bring new understanding to the molecular basis of a disease and could be of special relevance in the growing field of personalized medicine. 

In this paper, we propose a Spatial Robust Mixture Regression model to investigate the relationship between a response variable and a set of explanatory variables over the spatial domain, assuming that the relationships may exhibit complex spatially dynamic patterns that cannot be captured by constant regression coefficients. Our method integrates the robust finite mixture Gaussian regression model with spatial constraints, to simultaneously handle the spatial non-stationarity, local homogeneity, and outlier contaminations. Compared with existing spatial regression models, our proposed model assumes the existence a few distinct regression models that are estimated based on observations that exhibit similar response-predictor relationships. As such, the proposed model not only accounts for non-stationarity in the spatial trend, but also clusters observations into a few distinct and homogenous groups. This provides an advantage on interpretation with a few stationary sub-processes identified that capture the predominant relationships between response and predictor variables. Moreover, the proposed method incorporates robust procedures to handle contaminations from both regression outliers and spatial outliers. By doing so, we robustly segment the spatial domain into distinct local regions with similar regression coefficients, and sporadic locations that are purely outliers. Rigorous statistical hypothesis testing procedure has been designed to test the significance of such segmentation. Experimental results on many synthetic and real-world datasets demonstrate the robustness, accuracy, and effectiveness of our proposed method, compared with other robust finite mixture regression, spatial regression and spatial segmentation methods. 

The metabolic heterogeneity and metabolic interplay between cells are known as significant contributors to disease treatment resistance. However, with the lack of a mature high-throughput single-cell metabolomics technology, we are yet to establish systematic understanding of the intra-tissue metabolic heterogeneity and cooperative mechanisms. To mitigate this knowledge gap, we developed a novel computational method, namely, single-cell flux estimation analysis (scFEA), to infer the cell-wise fluxome from single-cell RNA-sequencing (scRNA-seq) data. scFEA is empowered by a systematically reconstructed human metabolic map as a factor graph, a novel probabilistic model to leverage the flux balance constraints on scRNA-seq data, and a novel graph neural network–based optimization solver. The intricate information cascade from transcriptome to metabolome was captured using multilayer neural networks to capitulate the nonlinear dependency between enzymatic gene expressions and reaction rates. We experimentally validated scFEA by generating an scRNA-seq data set with matched metabolomics data on cells of perturbed oxygen and genetic conditions. Application of scFEA on this data set showed the consistency between predicted flux and the observed variation of metabolite abundance in the matched metabolomics data. We also applied scFEA on five publicly available scRNA-seq and spatial transcriptomics data sets and identified context- and cell group–specific metabolic variations. The cell-wise fluxome predicted by scFEA empowers a series of downstream analyses including identification of metabolic modules or cell groups that share common metabolic variations, sensitivity evaluation of enzymes with regards to their impact on the whole metabolic flux, and inference of cell–tissue and cell–cell metabolic communications.