BEM: Mining Coregulation Patterns in Transcriptomics via Boolean Matrix Factorization

Binary matrix factorization via collaborative neurodynamic optimization

Binary matrix factorization is an important tool for dimension reduction for high-dimensional datasets with binary attributes and has been successfully applied in numerous areas. This paper presents a collaborative neurodynamic optimization approach to binary matrix factorization based on the original combinatorial optimization problem formulation and quadratic unconstrained binary optimization problem reformulations. The proposed approach employs multiple discrete Hopfield networks operating concurrently in search of local optima. In addition, a particle swarm optimization rule is used to reinitialize neuronal states iteratively to escape from local minima toward better ones. Experimental results on eight benchmark datasets are elaborated to demonstrate the superior performance of the proposed approach against six baseline algorithms in terms of factorization error. Additionally, the viability of the proposed approach is demonstrated for pattern discovery on three datasets.

Robust integrative biclustering for multi-view data

In many biomedical research, multiple views of data (e.g. genomics, proteomics) are available, and a particular interest might be the detection of sample subgroups characterized by specific groups of variables. Biclustering methods are well-suited for this problem as they assume that specific groups of variables might be relevant only to specific groups of samples. Many biclustering methods exist for detecting row-column clusters in a view but few methods exist for data from multiple views. The few existing algorithms are heavily dependent on regularization parameters for getting row-column clusters, and they impose unnecessary burden on users thus limiting their use in practice. We extend an existing biclustering method based on sparse singular value decomposition for single-view data to data from multiple views. Our method, integrative sparse singular value decomposition (iSSVD), incorporates stability selection to control Type I error rates, estimates the probability of samples and variables to belong to a bicluster, finds stable biclusters, and results in interpretable row-column associations. Simulations and real data analyses show that integrative sparse singular value decomposition outperforms several other single- and multi-view biclustering methods and is able to detect meaningful biclusters. iSSVD is a user-friendly, computationally efficient algorithm that will be useful in many disease subtyping applications.

Bias Aware Probabilistic Boolean Matrix Factorization

Boolean matrix factorization (BMF) is a combinatorial problem arising from a wide range of applications including recommendation system, collaborative filtering, and dimensionality reduction. Currently, the noise model of existing BMF methods is often assumed to be homoscedastic; however, in real world data scenarios, the deviations of observed data from their true values are almost surely diverse due to stochastic noises, making each data point not equally suitable for fitting a model. In this case, it is not ideal to treat all data points as equally distributed. Motivated by such observations, we introduce a probabilistic BMF model that recognizes the object- and feature-wise bias distribution respectively, called bias aware BMF (BABF). To the best of our knowledge, BABF is the first approach for Boolean decomposition with consideration of the feature-wise and object-wise bias in binary data. We conducted experiments on datasets with different levels of background noise, bias level, and sizes of the signal patterns, to test the effectiveness of our method in various scenarios. We demonstrated that our model outperforms the state-of-the-art factorization methods in both accuracy and efficiency in recovering the original datasets, and the inferred bias level is highly significantly correlated with true existing bias in both simulated and real world datasets.

Binary matrix factorization on special purpose hardware

Many fundamental problems in data mining can be reduced to one or more NP-hard combinatorial optimization problems. Recent advances in novel technologies such as quantum and quantum-inspired hardware promise a substantial speedup for solving these problems compared to when using general purpose computers but often require the problem to be modeled in a special form, such as an Ising or quadratic unconstrained binary optimization (QUBO) model, in order to take advantage of these devices. In this work, we focus on the important binary matrix factorization (BMF) problem which has many applications in data mining. We propose two QUBO formulations for BMF. We show how clustering constraints can easily be incorporated into these formulations. The special purpose hardware we consider is limited in the number of variables it can handle which presents a challenge when factorizing large matrices. We propose a sampling based approach to overcome this challenge, allowing us to factorize large rectangular matrices. In addition to these methods, we also propose a simple baseline algorithm which outperforms our more sophisticated methods in a few situations. We run experiments on the Fujitsu Digital Annealer, a quantum-inspired complementary metal-oxide-semiconductor (CMOS) annealer, on both synthetic and real data, including gene expression data. These experiments show that our approach is able to produce more accurate BMFs than competing methods.

ORN: Inferring patient-specific dysregulation status of pathway modules in cancer with OR-gate Network

Pathway level understanding of cancer plays a key role in precision oncology. However, the current amount of high-throughput data cannot support the elucidation of full pathway topology. In this study, instead of directly learning the pathway network, we adapted the probabilistic OR gate to model the modular structure of pathways and regulon. The resulting model, OR-gate Network (ORN), can simultaneously infer pathway modules of somatic alterations, patient-specific pathway dysregulation status, and downstream regulon. In a trained ORN, the differentially expressed genes (DEGs) in each tumour can be explained by somatic mutations perturbing a pathway module. Furthermore, the ORN handles one of the most important properties of pathway perturbation in tumours, the mutual exclusivity. We have applied the ORN to lower-grade glioma (LGG) samples and liver hepatocellular carcinoma (LIHC) samples in TCGA and breast cancer samples from METABRIC. Both datasets have shown abnormal pathway activities related to immune response and cell cycles. In LGG samples, ORN identified pathway modules closely related to glioma development and revealed two pathways closely related to patient survival. We had similar results with LIHC samples. Additional results from the METABRIC datasets showed that ORN could characterize critical mechanisms of cancer and connect them to less studied somatic mutations (e.g., BAP1, MIR604, MICAL3, and telomere activities), which may generate novel hypothesis for targeted therapy.