Robust orthogonal nonnegative matrix tri-factorization for data representation

Difference of Convex Functions Programming With Machine-Learning Prior for the Imaging Problem in Electrical Capacitance Tomography

The electrical capacitance tomography technology has potential benefits for the process industry by providing visualization of material distributions. One of the main technical gaps and impediments that must be overcome is the low-quality tomogram. To address this problem, this study introduces the data-guided prior and combines it with the electrical measurement mechanism and the sparsity prior to produce a new difference of convex functions programming problem that turns the image reconstruction problem into an optimization problem. The data-guided prior is learned from a provided dataset and captures the details of imaging targets since it is a specific image. A new numerical scheme that allows a complex optimization problem to be split into a few less difficult subproblems is developed to solve the challenging difference of convex functions programming problem. A new dimensionality reduction method is developed and combined with the relevance vector machine to generate a new learning engine for the forecast of the data-guided prior. The new imaging method fuses multisource information and unifies data-guided and measurement physics modeling paradigms. Performance evaluation results have validated that the new method successfully works on a series of test tasks with higher reconstruction quality and lower noise sensitivity than the popular imaging methods.

Robust capped norm dual hyper-graph regularized non-negative matrix tri-factorization

Non-negative matrix factorization (NMF) has been widely used in machine learning and data mining fields. As an extension of NMF, non-negative matrix tri-factorization (NMTF) provides more degrees of freedom than NMF. However, standard NMTF algorithm utilizes Frobenius norm to calculate residual error, which can be dramatically affected by noise and outliers. Moreover, the hidden geometric information in feature manifold and sample manifold is rarely learned. Hence, a novel robust capped norm dual hyper-graph regularized non-negative matrix tri-factorization (RCHNMTF) is proposed. First, a robust capped norm is adopted to handle extreme outliers. Second, dual hyper-graph regularization is considered to exploit intrinsic geometric information in feature manifold and sample manifold. Third, orthogonality constraints are added to learn unique data presentation and improve clustering performance. The experiments on seven datasets testify the robustness and superiority of RCHNMTF.

NMTF-DTI: A Nonnegative Matrix Tri-factorization Approach With Multiple Kernel Fusion for Drug-Target Interaction Prediction

Prediction of drug-target interactions (DTIs) plays a significant role in drug development and drug discovery. Although this task requires a large investment in terms of time and cost, especially when it is performed experimentally, the results are not necessarily significant. Computational DTI prediction is a shortcut to reduce the risks of experimental methods. In this study, we propose an effective approach of nonnegative matrix tri-factorization, referred to as NMTF-DTI, to predict the interaction scores between drugs and targets. NMTF-DTI utilizes multiple kernels (similarity measures) for drugs and targets and Laplacian regularization to boost the prediction performance. The performance of NMTF-DTI is evaluated via cross-validation and is compared with existing DTI prediction methods in terms of the area under the receiver operating characteristic (ROC) curve (AUC) and the area under the precision and recall curve (AUPR). We evaluate our method on four gold standard datasets, comparing to other state-of-the-art methods. Cross-validation and a separate, manually created dataset are used to set parameters. The results show that NMTF-DTI outperforms other competing methods. Moreover, the results of a case study also confirm the superiority of NMTF-DTI.

Multiple Graph Adaptive Regularized Semi-Supervised Nonnegative Matrix Factorization with Sparse Constraint for Data Representation

Multiple graph and semi-supervision techniques have been successfully introduced into the nonnegative matrix factorization (NMF) model for taking full advantage of the manifold structure and priori information of data to capture excellent low-dimensional data representation. However, the existing methods do not consider the sparse constraint, which can enhance the local learning ability and improve the performance in practical applications. To overcome this limitation, a novel NMF-based data representation method, namely, the multiple graph adaptive regularized semi-supervised nonnegative matrix factorization with sparse constraint (MSNMFSC) is developed in this paper for obtaining the sparse and discriminative data representation and increasing the quality of decomposition of NMF. Particularly, based on the standard NMF, the proposed MSNMFSC method combines the multiple graph adaptive regularization, the limited supervised information and the sparse constraint together to learn the more discriminative parts-based data representation. Moreover, the convergence analysis of MSNMFSC is studied. Experiments are conducted on several practical image datasets in clustering tasks, and the clustering results have shown that MSNMFSC achieves better performance than several most related NMF-based methods.

JSNMF enables effective and accurate integrative analysis of single-cell multiomics data

The single-cell multiomics technologies provide an unprecedented opportunity to study the cellular heterogeneity from different layers of transcriptional regulation. However, the datasets generated from these technologies tend to have high levels of noise, making data analysis challenging. Here, we propose jointly semi-orthogonal nonnegative matrix factorization (JSNMF), which is a versatile toolkit for the integrative analysis of transcriptomic and epigenomic data profiled from the same cell. JSNMF enables data visualization and clustering of the cells and also facilitates downstream analysis, including the characterization of markers and functional pathway enrichment analysis. The core of JSNMF is an unsupervised method based on JSNMF, where it assumes different latent variables for the two molecular modalities, and integrates the information of transcriptomic and epigenomic data with consensus graph fusion, which better tackles the distinct characteristics and levels of noise across different molecular modalities in single-cell multiomics data. We applied JSNMF to single-cell multiomics datasets from different tissues and different technologies. The results demonstrate the superior performance of JSNMF in clustering and data visualization of the cells. JSNMF also allows joint analysis of multiple single-cell multiomics experiments and single-cell multiomics data with more than two modalities profiled on the same cell. JSNMF also provides rich biological insight on the markers, cell-type-specific region-gene associations and the functions of the identified cell subpopulation.

A Block Coordinate Descent-Based Projected Gradient Algorithm for Orthogonal Non-Negative Matrix Factorization

This article uses the projected gradient method (PG) for a non-negative matrix factorization problem (NMF), where one or both matrix factors must have orthonormal columns or rows. We penalize the orthonormality constraints and apply the PG method via a block coordinate descent approach. This means that at a certain time one matrix factor is fixed and the other is updated by moving along the steepest descent direction computed from the penalized objective function and projecting onto the space of non-negative matrices. Our method is tested on two sets of synthetic data for various values of penalty parameters. The performance is compared to the well-known multiplicative update (MU) method from Ding (2006), and with a modified global convergent variant of the MU algorithm recently proposed by Mirzal (2014). We provide extensive numerical results coupled with appropriate visualizations, which demonstrate that our method is very competitive and usually outperforms the other two methods.