Hessian regularization based symmetric nonnegative matrix factorization for clustering gene expression and microbiome data

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.

A Two-Phase Algorithm for Robust Symmetric Non-Negative Matrix Factorization

As a special class of non-negative matrix factorization, symmetric non-negative matrix factorization (SymNMF) has been widely used in the machine learning field to mine the hidden non-linear structure of data. Due to the non-negative constraint and non-convexity of SymNMF, the efficiency of existing methods is generally unsatisfactory. To tackle this issue, we propose a two-phase algorithm to solve the SymNMF problem efficiently. In the first phase, we drop the non-negative constraint of SymNMF and propose a new model with penalty terms, in order to control the negative component of the factor. Unlike previous methods, the factor sequence in this phase is not required to be non-negative, allowing fast unconstrained optimization algorithms, such as the conjugate gradient method, to be used. In the second phase, we revisit the SymNMF problem, taking the non-negative part of the solution in the first phase as the initial point. To achieve faster convergence, we propose an interpolation projected gradient (IPG) method for SymNMF, which is much more efficient than the classical projected gradient method. Our two-phase algorithm is easy to implement, with convergence guaranteed for both phases. Numerical experiments show that our algorithm performs better than others on synthetic data and unsupervised clustering tasks.

Microbiome Data Analysis by Symmetric Non-negative Matrix Factorization With Local and Global Regularization

A network is an efficient tool to organize complicated data. The Laplacian graph has attracted more and more attention for its good properties and has been applied to many tasks including clustering, feature selection, and so on. Recently, studies have indicated that though the Laplacian graph can capture the global information of data, it lacks the power to capture fine-grained structure inherent in network. In contrast, a Vicus matrix can make full use of local topological information from the data. Given this consideration, in this paper we simultaneously introduce Laplacian and Vicus graphs into a symmetric non-negative matrix factorization framework (LVSNMF) to seek and exploit the global and local structure patterns that inherent in the original data. Extensive experiments are conducted on three real datasets (cancer, cell populations, and microbiome data). The experimental results show the proposed LVSNMF algorithm significantly outperforms other competing algorithms, suggesting its potential in biological data analysis.

A hybrid multi-objective whale optimization algorithm for analyzing microarray data based on Apache Spark

A microarray is a revolutionary tool that generates vast volumes of data that describe the expression profiles of genes under investigation that can be qualified as Big Data. Hadoop and Spark are efficient frameworks, developed to store and analyze Big Data. Analyzing microarray data helps researchers to identify correlated genes. Clustering has been successfully applied to analyze microarray data by grouping genes with similar expression profiles into clusters. The complex nature of microarray data obligated clustering methods to employ multiple evaluation functions to ensure obtaining solutions with high quality. This transformed the clustering problem into a Multi-Objective Problem (MOP). A new and efficient hybrid Multi-Objective Whale Optimization Algorithm with Tabu Search (MOWOATS) was proposed to solve MOPs. In this article, MOWOATS is proposed to analyze massive microarray datasets. Three evaluation functions have been developed to ensure an effective assessment of solutions. MOWOATS has been adapted to run in parallel using Spark over Hadoop computing clusters. The quality of the generated solutions was evaluated based on different indices, such as Silhouette and Davies-Bouldin indices. The obtained clusters were very similar to the original classes. Regarding the scalability, the running time was inversely proportional to the number of computing nodes.

MHSNMF: multi-view hessian regularization based symmetric nonnegative matrix factorization for microbiome data analysis

BACKGROUND

With the rapid development of high-throughput technique, multiple heterogeneous omics data have been accumulated vastly (e.g., genomics, proteomics and metabolomics data). Integrating information from multiple sources or views is challenging to obtain a profound insight into the complicated relations among micro-organisms, nutrients and host environment. In this paper we propose a multi-view Hessian regularization based symmetric nonnegative matrix factorization algorithm (MHSNMF) for clustering heterogeneous microbiome data. Compared with many existing approaches, the advantages of MHSNMF lie in: (1) MHSNMF combines multiple Hessian regularization to leverage the high-order information from the same cohort of instances with multiple representations; (2) MHSNMF utilities the advantages of SNMF and naturally handles the complex relationship among microbiome samples; (3) uses the consensus matrix obtained by MHSNMF, we also design a novel approach to predict the classification of new microbiome samples.

RESULTS

We conduct extensive experiments on two real-word datasets (Three-source dataset and Human Microbiome Plan dataset), the experimental results show that the proposed MHSNMF algorithm outperforms other baseline and state-of-the-art methods. Compared with other methods, MHSNMF achieves the best performance (accuracy: 95.28%, normalized mutual information: 91.79%) on microbiome data. It suggests the potential application of MHSNMF in microbiome data analysis.

CONCLUSIONS

Results show that the proposed MHSNMF algorithm can effectively combine the phylogenetic, transporter, and metabolic profiles into a unified paradigm to analyze the relationships among different microbiome samples. Furthermore, the proposed prediction method based on MHSNMF has been shown to be effective in judging the types of new microbiome samples.

An Accelerated Symmetric Nonnegative Matrix Factorization Algorithm Using Extrapolation

Symmetric nonnegative matrix factorization (SNMF) approximates a symmetric nonnegative matrix by the product of a nonnegative low-rank matrix and its transpose. SNMF has been successfully used in many real-world applications such as clustering. In this paper, we propose an accelerated variant of the multiplicative update (MU) algorithm of He et al. designed to solve the SNMF problem. The accelerated algorithm is derived by using the extrapolation scheme of Nesterov and a restart strategy. The extrapolation scheme plays a leading role in accelerating the MU algorithm of He et al. and the restart strategy ensures that the objective function of SNMF is monotonically decreasing. We apply the accelerated algorithm to clustering problems and symmetric nonnegative tensor factorization (SNTF). The experiment results on both synthetic and real-world data show that it is more than four times faster than the MU algorithm of He et al. and performs favorably compared to recent state-of-the-art algorithms.

Clustering and Integrating of Heterogeneous Microbiome Data by Joint Symmetric Nonnegative Matrix Factorization with Laplacian Regularization

Many datasets that exists in the real world are often comprised of different representations or views which provide complementary information to each other. To integrate information from multiple views, data integration approaches such as nonnegative matrix factorization (NMF) have been developed to combine multiple heterogeneous data simultaneously to obtain a comprehensive representation. In this paper, we proposed a novel variant of symmetric nonnegative matrix factorization (SNMF), called Laplacian regularization based joint symmetric nonnegative matrix factorization (LJ-SNMF) for clustering multi-view data. We conduct extensive experiments on several realistic datasets including Human Microbiome Project data. The experimental results show that the proposed method outperforms other variants of NMF, which suggests the potential application of LJ-SNMF in clustering multi-view datasets. Additionally, we also demonstrate the capability of LJ-SNMF in community finding.

Integrative Analysis for Identifying Co-Modules of Microbe-Disease Data by Matrix Tri-Factorization With Phylogenetic Information

Microbe-disease association relationship mining is drawing more and more attention due to its potential in capturing disease-related microbes. Hence, it is essential to develop new tools or algorithms to study the complex pathogenic mechanism of microbe-related diseases. However, previous research studies mainly focused on the paradigm of “one disease, one microbe,” rarely investigated the cooperation and associations between microbes, diseases or microbe-disease co-modules from system level. In this study, we propose a novel two-level module identifying algorithm (MDNMF) based on nonnegative matrix tri-factorization which integrates two similarity matrices (disease and microbe similarity matrices) and one microbe-disease association matrix into the objective of MDNMF. MDNMF can identify the modules from different levels and reveal the connections between these modules. In order to improve the efficiency and effectiveness of MDNMF, we also introduce human symptoms-disease network and microbial phylogenetic distance into this model. Furthermore, we applied it to HMDAD dataset and compared it with two NMF-based methods to demonstrate its effectiveness. The experimental results show that MDNMF can obtain better performance in terms of enrichment index (EI) and the number of significantly enriched taxon sets. This demonstrates the potential of MDNMF in capturing microbial modules that have significantly biological function implications.

A Robust Distributed Big Data Clustering-based on Adaptive Density Partitioning using Apache Spark

Unsupervised machine learning and knowledge discovery from large-scale datasets have recently attracted a lot of research interest. The present paper proposes a distributed big data clustering approach-based on adaptive density estimation. The proposed method is developed-based on Apache Spark framework and tested on some of the prevalent datasets. In the first step of this algorithm, the input data is divided into partitions using a Bayesian type of Locality Sensitive Hashing (LSH). Partitioning makes the processing fully parallel and much simpler by avoiding unneeded calculations. Each of the proposed algorithm steps is completely independent of the others and no serial bottleneck exists all over the clustering procedure. Locality preservation also filters out the outliers and enhances the robustness of the proposed approach. Density is defined on the basis of Ordered Weighted Averaging (OWA) distance which makes clusters more homogenous. According to the density of each node, the local density peaks will be detected adaptively. By merging the local peaks, final cluster centers will be obtained and other data points will be a member of the cluster with the nearest center. The proposed method has been implemented and compared with similar recently published researches. Cluster validity indexes achieved from the proposed method shows its superiorities in precision and noise robustness in comparison with recent researches. Comparison with similar approaches also shows superiorities of the proposed method in scalability, high performance, and low computation cost. The proposed method is a general clustering approach and it has been used in gene expression clustering as a sample of its application.

Data Analysis for Gut Microbiota and Health

In recent years, data mining and analysis of high-throughput sequencing of microbiomes and metagenomic data enable researchers to discover biological knowledge by characterizing the composition and variation of species across environmental samples and to accumulate a huge amount of data, making it feasible to infer the complex principle of species interactions. The interactions of microbes in a microbial community play an important role in microbial ecological system. Data mining provides diverse approachs to identify the correlations between disease and microbes and how microbial species coexist and interact in a host-associated or natural environment. This is not only important to advance basic microbiology science and other related fields but also important to understand the impacts of microbial communities on human health and diseases.