Naiyang Guan

NeNMF: An Optimal Gradient Method for Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) is a powerful matrix decomposition technique that approximates a nonnegative matrix by the product of two low-rank nonnegative matrix factors. It has been widely applied to signal processing, computer vision, and data mining. Traditional NMF solvers include the multiplicative update rule (MUR), the projected gradient method (PG), the projected nonnegative least squares (PNLS), and the active set method (AS). However, they suffer from one or some of the following three problems: slow convergence rate, numerical instability and nonconvergence. In this paper, we present a new efficient NeNMF solver to simultaneously overcome the aforementioned problems. It applies Nesterovs optimal gradient method to alternatively optimize one factor with another fixed. In particular, at each iteration round, the matrix factor is updated by using the PG method performed on a smartly chosen search point, where the step size is determined by the Lipschitz constant. Since NeNMF does not use the time consuming line search and converges optimally at rate in optimizing each matrix factor, it is superior to MUR and PG in terms of efficiency as well as approximation accuracy. Compared to PNLS and AS that suffer from numerical instability problem in the worst case, NeNMF overcomes this deficiency. In addition, NeNMF can be used to solve -norm, -norm and manifold regularized NMF with the optimal convergence rate. Numerical experiments on both synthetic and real-world datasets show the efficiency of NeNMF for NMF and its variants comparing to representative NMF solvers. Extensive experiments on document clustering suggest the effectiveness of NeNMF.

Manifold Regularized Discriminative Nonnegative Matrix Factorization With Fast Gradient Descent

Nonnegative matrix factorization (NMF) has become a popular data-representation method and has been widely used in image processing and pattern-recognition problems. This is because the learned bases can be interpreted as a natural parts-based representation of data and this interpretation is consistent with the psychological intuition of combining parts to form a whole. For practical classification tasks, however, NMF ignores both the local geometry of data and the discriminative information of different classes. In addition, existing research results show that the learned basis is unnecessarily parts-based because there is neither explicit nor implicit constraint to ensure the representation parts-based. In this paper, we introduce the manifold regularization and the margin maximization to NMF and obtain the manifold regularized discriminative NMF (MD-NMF) to overcome the aforementioned problems. The multiplicative update rule (MUR) can be applied to optimizing MD-NMF, but it converges slowly. In this paper, we propose a fast gradient descent (FGD) to optimize MD-NMF. FGD contains a Newton method that searches the optimal step length, and thus, FGD converges much faster than MUR. In addition, FGD includes MUR as a special case and can be applied to optimizing NMF and its variants. For a problem with 165 samples in R1600 , FGD converges in 28 s, while MUR requires 282 s. We also apply FGD in a variant of MD-NMF and experimental results confirm its efficiency. Experimental results on several face image datasets suggest the effectiveness of MD-NMF.

Online Nonnegative Matrix Factorization With Robust Stochastic Approximation

Nonnegative matrix factorization (NMF) has become a popular dimension-reduction method and has been widely applied to image processing and pattern recognition problems. However, conventional NMF learning methods require the entire dataset to reside in the memory and thus cannot be applied to large-scale or streaming datasets. In this paper, we propose an efficient online RSA-NMF algorithm (OR-NMF) that learns NMF in an incremental fashion and thus solves this problem. In particular, OR-NMF receives one sample or a chunk of samples per step and updates the bases via robust stochastic approximation. Benefitting from the smartly chosen learning rate and averaging technique, OR-NMF converges at the rate of in each update of the bases. Furthermore, we prove that OR-NMF almost surely converges to a local optimal solution by using the quasi-martingale. By using a buffering strategy, we keep both the time and space complexities of one step of the OR-NMF constant and make OR-NMF suitable for large-scale or streaming datasets. Preliminary experimental results on real-world datasets show that OR-NMF outperforms the existing online NMF (ONMF) algorithms in terms of efficiency. Experimental results of face recognition and image annotation on public datasets confirm the effectiveness of OR-NMF compared with the existing ONMF algorithms.

Non-Negative Patch Alignment Framework

In this paper, we present a non-negative patch alignment framework (NPAF) to unify popular non-negative matrix factorization (NMF) related dimension reduction algorithms. It offers a new viewpoint to better understand the common property of different NMF algorithms. Although multiplicative update rule (MUR) can solve NPAF and is easy to implement, it converges slowly. Thus, we propose a fast gradient descent (FGD) to overcome the aforementioned problem. FGD uses the Newton method to search the optimal step size, and thus converges faster than MUR. Experiments on synthetic and real-world datasets confirm the efficiency of FGD compared with MUR for optimizing NPAF. Based on NPAF, we develop non-negative discriminative locality alignment (NDLA). Experiments on face image and handwritten datasets suggest the effectiveness of NDLA in classification tasks and its robustness to image occlusions, compared with representative NMF-related dimension reduction algorithms.

Discriminant Projective Non-Negative Matrix Factorization

Projective non-negative matrix factorization (PNMF) projects high-dimensional non-negative examples X onto a lower-dimensional subspace spanned by a non-negative basis W and considers WT X as their coefficients, i.e., X≈WWT X. Since PNMF learns the natural parts-based representation Wof X, it has been widely used in many fields such as pattern recognition and computer vision. However, PNMF does not perform well in classification tasks because it completely ignores the label information of the dataset. This paper proposes a Discriminant PNMF method (DPNMF) to overcome this deficiency. In particular, DPNMF exploits Fishers criterion to PNMF for utilizing the label information. Similar to PNMF, DPNMF learns a single non-negative basis matrix and needs less computational burden than NMF. In contrast to PNMF, DPNMF maximizes the distance between centers of any two classes of examples meanwhile minimizes the distance between any two examples of the same class in the lower-dimensional subspace and thus has more discriminant power. We develop a multiplicative update rule to solve DPNMF and prove its convergence. Experimental results on four popular face image datasets confirm its effectiveness comparing with the representative NMF and PNMF algorithms.

Sparse Representation Based Discriminative Canonical Correlation Analysis for Face Recognition

Canonical correlation analysis (CCA) has been widely used in pattern recognition and machine learning. However, both CCA and its extensions sometimes cannot give satisfactory results. In this paper, we propose a new CCA-type method termed sparse representation based discriminative CCA (SPDCCA) by incorporating sparse representation and discriminative information simultaneously into traditional CCA. In particular, SPDCCA not only preserves the sparse reconstruction relationship within data based on sparse representation, but also preserves the maximum-margin based discriminative information, and thus it further enhances the classification performance. Experimental results on Yale, Extended Yale B, and ORL datasets show that SPDCCA outperforms both CCA and its extensions including KCCA, LPCCA and LDCCA in face recognition.

Graph Based Semi-supervised Non-negative Matrix Factorization for Document Clustering

Non-negative matrix factorization (NMF) approximates a non-negative matrix by the product of two low-rank matrices and achieves good performance in clustering. Recently, semi-supervised NMF (SS-NMF) further improves the performance by incorporating part of the labels of few samples into NMF. In this paper, we proposed a novel graph based SS-NMF (GSS-NMF). For each sample, GSS-NMF minimizes its distances to the same labeled samples and maximizes the distances against different labeled samples to incorporate the discriminative information. Since both labeled and unlabeled samples are embedded in the same reduced dimensional space, the discriminative information from the labeled samples is successfully transferred to the unlabeled samples, and thus it greatly improves the clustering performance. Since the traditional multiplicative update rule converges slowly, we applied the well-known projected gradient method to optimizing GSS-NMF and the proposed algorithm can be applied to optimizing other manifold regularized NMF efficiently. Experimental results on two popular document datasets, i.e., Reuters21578 and TDT-2, show that GSS-NMF outperforms the representative SS-NMF algorithms.

Semi-Supervised Projective Non-Negative Matrix Factorization for Cancer Classification

Advances in DNA microarray technologies have made gene expression profiles a significant candidate in identifying different types of cancers. Traditional learning-based cancer identification methods utilize labeled samples to train a classifier, but they are inconvenient for practical application because labels are quite expensive in the clinical cancer research community. This paper proposes a semi-supervised projective non-negative matrix factorization method (Semi-PNMF) to learn an effective classifier from both labeled and unlabeled samples, thus boosting subsequent cancer classification performance. In particular, Semi-PNMF jointly learns a non-negative subspace from concatenated labeled and unlabeled samples and indicates classes by the positions of the maximum entries of their coefficients. Because Semi-PNMF incorporates statistical information from the large volume of unlabeled samples in the learned subspace, it can learn more representative subspaces and boost classification performance. We developed a multiplicative update rule (MUR) to optimize Semi-PNMF and proved its convergence. The experimental results of cancer classification for two multiclass cancer gene expression profile datasets show that Semi-PNMF outperforms the representative methods.

Cogena, a novel tool for co-expressed gene-set enrichment analysis, applied to drug repositioning and drug mode of action discovery

BackgroundDrug repositioning, finding new indications for existing drugs, has gained much recent attention as a potentially efficient and economical strategy for accelerating new therapies into the clinic. Although improvement in the sensitivity of computational drug repositioning methods has identified numerous credible repositioning opportunities, few have been progressed. Arguably the “black box” nature of drug action in a new indication is one of the main blocks to progression, highlighting the need for methods that inform on the broader target mechanism in the disease context.ResultsWe demonstrate that the analysis of co-expressed genes may be a critical first step towards illumination of both disease pathology and mode of drug action. We achieve this using a novel framework, co-expressed gene-set enrichment analysis (cogena) for co-expression analysis of gene expression signatures and gene set enrichment analysis of co-expressed genes. The cogena framework enables simultaneous, pathway driven, disease and drug repositioning analysis. Cogena can be used to illuminate coordinated changes within disease transcriptomes and identify drugs acting mechanistically within this framework. We illustrate this using a psoriatic skin transcriptome, as an exemplar, and recover two widely used Psoriasis drugs (Methotrexate and Ciclosporin) with distinct modes of action. Cogena out-performs the results of Connectivity Map and NFFinder webservers in similar disease transcriptome analyses. Furthermore, we investigated the literature support for the other top-ranked compounds to treat psoriasis and showed how the outputs of cogena analysis can contribute new insight to support the progression of drugs into the clinic. We have made cogena freely available within Bioconductor or https://github.com/zhilongjia/cogena.ConclusionsIn conclusion, by targeting co-expressed genes within disease transcriptomes, cogena offers novel biological insight, which can be effectively harnessed for drug discovery and repositioning, allowing the grouping and prioritisation of drug repositioning candidates on the basis of putative mode of action.

Transductive nonnegative matrix factorization for semi-supervised high-performance speech separation

Regarding the non-negativity property of the magnitude spectrogram of speech signals, nonnegative matrix factorization (NMF) has obtained promising performance for speech separation by independently learning a dictionary on the speech signals of each known speaker. However, traditional NM-F fails to represent the mixture signals accurately because the dictionaries for speakers are learned in the absence of mixture signals. In this paper, we propose a new transductive NMF algorithm (TNMF) to jointly learn a dictionary on both speech signals of each speaker and the mixture signals to be separated. Since TNMF learns a more descriptive dictionary by encoding the mixture signals than that learned by NMF, it significantly boosts the separation performance. Experiments results on a popular TIMIT dataset show that the proposed TNMF-based methods outperform traditional NMF-based methods for separating the monophonic mixtures of speech signals of known speakers.