Hybrid clustering based on content and connection structure using joint nonnegative matrix factorization

Du, Rundong; Drake, Barry; Park, Haesun

doi:10.1007/s10898-017-0578-x

Cited by 18 publications

(5 citation statements)

References 31 publications

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“…By transforming to a similarity graph cut problem, many graph clustering algorithms have been proposed, such as spectral clustering (von Luxburg 2007), SymNMF (Kuang, Park, and Ding 2012) and modularity maximization (Newman 2006). For the hybrid clustering method, (Cai et al 2011) proposes an NMF with graph regularization and (Du, Drake, and Park 2017) proposes a joint NMF and SymNMF clustering framework .…”

Section: Related Workmentioning

confidence: 99%

Tensor Decomposition for Multilayer Networks Clustering

Chen

Zheng

et al. 2019

AAAI

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Clustering on multilayer networks has been shown to be a promising approach to enhance the accuracy. Various multilayer networks clustering algorithms assume all networks derive from a latent clustering structure, and jointly learn the compatible and complementary information from different networks to excavate one shared underlying structure. However, such an assumption is in conflict with many emerging real-life applications due to the existence of noisy/irrelevant networks. To address this issue, we propose Centroid-based Multilayer Network Clustering (CMNC), a novel approach which can divide irrelevant relationships into different network groups and uncover the cluster structure in each group simultaneously. The multilayer networks is represented within a unified tensor framework for simultaneously capturing multiple types of relationships between a set of entities. By imposing the rank-(Lr,Lr,1) block term decomposition with nonnegativity, we are able to have well interpretations on the multiple clustering results based on graph cut theory. Numerically, we transform this tensor decomposition problem to an unconstrained optimization, thus can solve it efficiently under the nonlinear least squares (NLS) framework. Extensive experimental results on synthetic and real-world datasets show the effectiveness and robustness of our method against noise and irrelevant data.

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Section: Related Workmentioning

confidence: 99%

Tensor Decomposition for Multilayer Networks Clustering

Chen

Zheng

et al. 2019

AAAI

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“…Such joint-clustering methods based on matrix low-rank approximation have been used in other contexts, such as document clustering (Du et al ., 2019) and. Additionally, promising NMF models have been developed for cell type identification for data ranging from just scRNA-Seq data to encompassing multiple modalities (Duren et al ., 2018; Jin et al ., 2020; Kotliar et al ., 2019; Shao and Höfer, 2017; Welch et al ., 2019).…”

Section: Introductionmentioning

confidence: 99%

Hybrid Clustering of single-cell gene expression and cell spatial information via integrated NMF and k-means

Park

Zhang

2020

Preprint

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Recent advances in single cell transcriptomics have allowed us to examine the identify of each single cell, thus have led to discovery of new cell types and provide a high resolution map of cell type composition in tissues. Technologies which can measure another type of data of a single cell in addition to the gene-expression data provide a more comprehensive picture of a cell, and meanwhile pose challenges for data integration tasks. We consider the spatial location of cells, which is an important feature of cells, combined with the cells’ gene-expression profiles, to determine the cell type identity. We aim to jointly classify cells based on their locations relative to other cells in the system as well as their gene expression profiles. We have developed scHybridNMF (single-cell Hybrid Nonnegative Matrix Factorization), which performs cell type identification by incorporating single cell gene expression data with cell location data. We combined two classical methods, nonnegative matrix factorization with a k-means clustering scheme, to respectively represent high-dimensional gene expression data and low-dimensional location data together. Our method incorporates a novel cell location term to the gene expression clustering. We show that scHybridNMF can make use of the location data to improve cell type clustering. In particular, we show that under multiple scenarios, including that when the number of genes profiled is low, and when the location data is noisy, scHybridNMF outperforms the standalone algorithms NMF and k-means, and an existing method HMRF which also uses cell location and gene-expression data for cell type identification.

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“…Nonnegative matrix factorization (NMF) is the problem of approximating a input nonnegative matrix X as the product of two nonnegative matrices: Given X ∈ R m×n ≥0 and an integer r, find W ∈ R m×r ≥0 and H ∈ R r×n ≥0 such that X ≈ W H. NMF allows to reconstruct data using a purely additive model: each column of X is a nonnegative linear combination of the columns of W . For this reason, it is widely employed in research fields like image processing and computer vision [8,20], data mining and document clustering [6], hyperspectral image analysis [18,24], signal processing [31] and computational biology [19]; see also [5,9] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Improved SVD-based Initialization for Nonnegative Matrix Factorization using Low-Rank Correction

Syed,

Qazi,

Gillis

2018

Preprint

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Due to the iterative nature of most nonnegative matrix factorization (NMF) algorithms, initialization is a key aspect as it significantly influences both the convergence and the final solution obtained. Many initialization schemes have been proposed for NMF, among which one of the most popular class of methods are based on the singular value decomposition (SVD). However, these SVD-based initializations do not satisfy a rather natural condition, namely that the error should decrease as the rank of factorization increases. In this paper, we propose a novel SVD-based NMF initialization to specifically address this shortcoming by taking into account the SVD factors that were discarded to obtain a nonnegative initialization. This method, referred to as nonnegative SVD with low-rank correction (NNSVD-LRC), allows us to significantly reduce the initial error at a negligible additional computational cost using the low-rank structure of the discarded SVD factors. NNSVD-LRC has two other advantages compared to previous SVD-based initializations:(1) it provably generates sparse initial factors, and (2) it is faster as it only requires to compute a truncated SVD of rank r/2+1 where r is the factorization rank of the sought NMF decomposition (as opposed to a rank-r truncated SVD for other methods). We show on several standard dense and sparse data sets that our new method competes favorably with state-of-the-art SVD-based initializations for NMF.

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Hybrid clustering based on content and connection structure using joint nonnegative matrix factorization

Cited by 18 publications

References 31 publications

Tensor Decomposition for Multilayer Networks Clustering

Tensor Decomposition for Multilayer Networks Clustering

Hybrid Clustering of single-cell gene expression and cell spatial information via integrated NMF and k-means

Improved SVD-based Initialization for Nonnegative Matrix Factorization using Low-Rank Correction

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