We have recently published a clustering method, namely CSMR, based on mixture regression in the context of high-dimensional predictors [1]. The motivation of our work was to provide a scalable method to deal with high-dimensional molecular features when there exist heterogeneous relationships between the molecular features and a disease phenotype of interest. In our original work, we simulated different data environments, including sample size |$N$|⁠, number of cluster-differentiating and cluster-specific predictors |${M}_0$|⁠, number of clusters |$K$|⁠, and noise level |$\sigma$|⁠. We evaluated CSMR on the simulation datasets, based on its accuracy of clustering using Rand index, and feature selection using true positive/negative rate, as well as the consistency of predicted and observed response values using Pearson correlation. In a real-world Cancer Cell Line Encyclopedia (CCLE) dataset [2], we evaluated CSMR based on the consistency of predicted and observed response values using cross-validation. The letter by Zhang et al. raised the concerns that the performance of CSMR drops significantly when the number of cluster-differentiating predictors |${M}_0$| increases from 5 to 20, as demonstrated by evaluation metrics including the adjusted Rand index (ARI) and the clustering internal consistency (IC), both of which are advocated by Zhang et al. to be used for evaluating clustering methods. We appreciate Zhang et al.’s interests in our method and agree that their observations of the performance drop in the large |${M}_0$| case are indeed true. We would like to mention that mixture regression models, with the presence of both low- and high-dimensional features, rely on Expectation–Maximization (EM) algorithm or its variants for a solution. However, EM algorithm often converges to the maximum likelihood estimate of the mixture parameters locally [3], and using EM algorithm to solve mixture regression problem might yield poor clustering performance if the parameters are not initialized properly, and finding a good initial value is always a challenge. In other words, EM algorithm is highly sensitive to initialization, and different initial values may lead to different solutions and hence the instability. Many works have been published on establishing the convergence and stability criterion for EM algorithm [4–7]. For example, a guarantee for the EM algorithm to converge to the unique global optimum is when the likelihood is unimodal with certain regularity conditions [4]. However, the likelihood function could be multi-modal in many cases, for which only local optimum could be guaranteed; and what’s worse, sometimes the local optimum is a poor one that is far away from any global optimum of the likelihood [7]. In all, while EM algorithm has enjoyed popular use in solving mixture model, there is still space for improved theoretical understanding.

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 Positive and unlabeled Learning from Unbalanced cases and Sparse 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.

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.

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.

Deconvolution of mouse transcriptomic data is challenged by the fact that mouse models carry various genetic and physiological perturbations, making it questionable to assume fixed cell types and cell type marker genes for different data set scenarios. We developed a Semi-Supervised Mouse data Deconvolution (SSMD) method to study the mouse tissue microenvironment. SSMD is featured by (i) a novel nonparametric method to discover data set-specific cell type signature genes; (ii) a community detection approach for fixing cell types and their marker genes; (iii) a constrained matrix decomposition method to solve cell type relative proportions that is robust to diverse experimental platforms. In summary, SSMD addressed several key challenges in the deconvolution of mouse tissue data, including: (i) varied cell types and marker genes caused by highly divergent genotypic and phenotypic conditions of mouse experiment; (ii) diverse experimental platforms of mouse transcriptomics data; (iii) small sample size and limited training data source and (iv) capable to estimate the proportion of 35 cell types in blood, inflammatory, central nervous or hematopoietic systems. In silico and experimental validation of SSMD demonstrated its high sensitivity and accuracy in identifying (sub) cell types and predicting cell proportions comparing with state-of-the-arts methods. A user-friendly R package and a web server of SSMD are released via https://github.com/xiaoyulu95/SSMD.

Boolean matrix has been used to represent digital information in many fields, including bank transaction, crime records, natural language processing, protein-protein interaction, etc. Boolean matrix factorization (BMF) aims to find an approximation of a binary matrix as the Boolean product of two low rank Boolean matrices, which could generate vast amount of information for the patterns of relationships between the features and samples. Inspired by binary matrix permutation theories and geometric segmentation, we developed a fast and efficient BMF approach, called MEBF (Median Expansion for Boolean Factorization). Overall, MEBF adopted a heuristic approach to locate binary patterns presented as submatrices that are dense in 1's. At each iteration, MEBF permutates the rows and columns such that the permutated matrix is approximately Upper Triangular-Like (UTL) with so-called Simultaneous Consecutive-ones Property (SC1P). The largest submatrix dense in 1 would lie on the upper triangular area of the permutated matrix, and its location was determined based on a geometric segmentation of a triangular. We compared MEBF with other state of the art approaches on data scenarios with different density and noise levels. MEBF demonstrated superior performances in lower reconstruction error, and higher computational efficiency, as well as more accurate density patterns than popular methods such as ASSO, PANDA and Message Passing. We demonstrated the application of MEBF on both binary and non-binary data sets, and revealed its further potential in knowledge retrieving and data denoising.

Single cell RNA-sequencing (scRNA-seq) technology enables comprehensive transcriptomic profiling of thousands of cells with distinct phenotypic and physiological states in a complex tissue. Substantial efforts have been made to characterize single cells of distinct identities from scRNA-seq data, including various cell clustering techniques. While existing approaches can handle single cells in terms of different cell (sub)types at a high resolution, identification of the functional variability within the same cell type remains unsolved. In addition, there is a lack of robust method to handle the inter-subject variation that often brings severe confounding effects for the functional clustering of single cells. In this study, we developed a novel data denoising and cell clustering approach, namely CIBS, to provide biologically explainable functional classification for scRNA-seq data. CIBS is based on a systems biology model of transcriptional regulation that assumes a multi-modality distribution of the cells' activation status, and it utilizes a Boolean matrix factorization approach on the discretized expression status to robustly derive functional modules. CIBS is empowered by a novel fast Boolean Matrix Factorization method, namely PFAST, to increase the computational feasibility on large scale scRNA-seq data. Application of CIBS on two scRNA-seq datasets collected from cancer tumor micro-environment successfully identified subgroups of cancer cells with distinct expression patterns of epithelial-mesenchymal transition and extracellular matrix marker genes, which was not revealed by the existing cell clustering analysis tools. The identified cell groups were significantly associated with the clinically confirmed lymph-node invasion and metastasis events across different patients.

Low rank representation of binary matrix is powerful in disentangling sparse individual-attribute associations, and has received wide applications. Existing binary matrix factorization (BMF) or co-clustering (CC) methods often assume i.i.d background noise. However, this assumption could be easily violated in real data, where heterogeneous row- or column-wise probability of binary entries results in disparate element-wise background distribution, and paralyzes the rationality of existing methods. We propose a binary data denoising framework, namely BIND, which optimizes the detection of true patterns by estimating the row- or column-wise mixture distribution of patterns and disparate background, and eliminating the binary attributes that are more likely from the background. BIND is supported by thoroughly derived mathematical property of the row- and column-wise mixture distributions. Our experiment on synthetic and real-world data demonstrated BIND effectively removes background noise and drastically increases the fairness and accuracy of state-of-the arts BMF and CC methods.

Boolean tensor has been broadly utilized in representing high dimensional logical data collected on spatial, temporal and/or other relational domains. Boolean Tensor Decomposition (BTD) factorizes a binary tensor into the Boolean sum of multiple rank-1 tensors, which is an NP-hard problem. Existing BTD methods have been limited by their high computational cost, in applications to large scale or higher order tensors. In this work, we presented a computationally efficient BTD algorithm, namely Geometric Expansion for all-order Tensor Factorization (GETF), that sequentially identifies the rank-1 basis components for a tensor from a geometric perspective. We conducted rigorous theoretical analysis on the validity as well as algorithemic efficiency of GETF in decomposing all-order tensor. Experiments on both synthetic and real-world data demonstrated that GETF has significantly improved performance in reconstruction accuracy, extraction of latent structures and it is an order of magnitude faster than other state-of-the-art methods.

BACKGROUND: Various statistical models have been developed to model the single cell RNA-seq expression profiles, capture its multimodality, and conduct differential gene expression test. However, for expression data generated by different experimental design and platforms, there is currently lack of capability to determine the most proper statistical model. RESULTS: We developed an R package, namely Multi-Modal Model Selection (M3S), for gene-wise selection of the most proper multi-modality statistical model and downstream analysis, useful in a single-cell or large scale bulk tissue transcriptomic data. M3S is featured with (1) gene-wise selection of the most parsimonious model among 11 most commonly utilized ones, that can best fit the expression distribution of the gene, (2) parameter estimation of a selected model, and (3) differential gene expression test based on the selected model. CONCLUSION: A comprehensive evaluation suggested that M3S can accurately capture the multimodality on simulated and real single cell data. An open source package and is available through GitHub at https://github.com/zy26/M3S.

Brain-computer interface (BCI) systems can translate the human mind into control commands, which makes it feasible to improve the life quality of physically challenged people. However, in real-life situations, it is still difficult for users to utilize robots to provide basic services with BCI systems. We aimed to propose a BCI-based system with a visual servo module to operate a service robot. We recorded single-channel steady-state visual evoked potentials (SSVEP) as input signals for the BCI system of this study. The visual stimuli for inducing SSVEP were modulated at seven different frequencies with the sampled sinusoidal method. Correspondingly, this SSVEP-based BCI system can generate seven control commands for the operation of the service robot, which can provide three fundamental services: mobility, manipulation, and delivery. The visual servo module was established to reduce the burden of users and accelerate service procedures. To evaluate the performance of this system, subjects were recruited to participate in the experiments. All the participants succeed in operating the robot to provide the basic services. According to the experimental results, this SSVEP-based BCI system that incorporates the visual servo module can be effectively used to operate service robots with reduced number of channels and increased ability to perform multiple tasks.