The Diagonalized Newton Algorithm for Nonnegative Matrix Factorization

Non-negative matrix factorization (NMF) has become a popular machine learning approach to many problems in text mining, speech and image processing, bio-informatics and seismic data analysis to name a few. In NMF, a matrix of non-negative data is approximated by the low-rank product of two matrices with non-negative entries. In this paper, the approximation quality is measured by the Kullback-Leibler divergence between the data and its low-rank reconstruction. The existence of the simple multiplicative update (MU) algorithm for computing the matrix factors has contributed to the success of NMF. Despite the availability of algorithms showing faster convergence, MU remains popular due to its simplicity. In this paper, a diagonalized Newton algorithm (DNA) is proposed showing faster convergence while the implementation remains simple and suitable for high-rank problems. The DNA algorithm is applied to various publicly available data sets, showing a substantial speed-up on modern hardware.Comment: 8 pages + references; International Conference on Learning Representations, 201

A multilevel approach for nonnegative matrix factorization

Nonnegative Matrix Factorization (NMF) is the problem of approximating a nonnegative matrix with the product of two low-rank nonnegative matrices and has been shown to be particularly useful in many applications, e.g., in text mining, image processing, computational biology, etc. In this paper, we explain how algorithms for NMF can be embedded into the framework of multi- level methods in order to accelerate their convergence. This technique can be applied in situations where data admit a good approximate representation in a lower dimensional space through linear transformations preserving nonnegativity. A simple multilevel strategy is described and is experi- mentally shown to speed up significantly three popular NMF algorithms (alternating nonnegative least squares, multiplicative updates and hierarchical alternating least squares) on several standard image datasets.nonnegative matrix factorization, algorithms, multigrid and multilevel methods, image processing

RNA-protein binding motifs mining with a new hybrid deep learning based cross-domain knowledge integration approach

BACKGROUND: RNAs play key roles in cells through the interactions with proteins known as the RNA-binding proteins (RBP) and their binding motifs enable crucial understanding of the post-transcriptional regulation of RNAs. How the RBPs correctly recognize the target RNAs and why they bind specific positions is still far from clear. Machine learning-based algorithms are widely acknowledged to be capable of speeding up this process. Although many automatic tools have been developed to predict the RNA-protein binding sites from the rapidly growing multi-resource data, e.g. sequence, structure, their domain specific features and formats have posed significant computational challenges. One of current difficulties is that the cross-source shared common knowledge is at a higher abstraction level beyond the observed data, resulting in a low efficiency of direct integration of observed data across domains. The other difficulty is how to interpret the prediction results. Existing approaches tend to terminate after outputting the potential discrete binding sites on the sequences, but how to assemble them into the meaningful binding motifs is a topic worth of further investigation. RESULTS: In viewing of these challenges, we propose a deep learning-based framework (iDeep) by using a novel hybrid convolutional neural network and deep belief network to predict the RBP interaction sites and motifs on RNAs. This new protocol is featured by transforming the original observed data into a high-level abstraction feature space using multiple layers of learning blocks, where the shared representations across different domains are integrated. To validate our iDeep method, we performed experiments on 31 large-scale CLIP-seq datasets, and our results show that by integrating multiple sources of data, the average AUC can be improved by 8% compared to the best single-source-based predictor; and through cross-domain knowledge integration at an abstraction level, it outperforms the state-of-the-art predictors by 6%. Besides the overall enhanced prediction performance, the convolutional neural network module embedded in iDeep is also able to automatically capture the interpretable binding motifs for RBPs. Large-scale experiments demonstrate that these mined binding motifs agree well with the experimentally verified results, suggesting iDeep is a promising approach in the real-world applications. CONCLUSION: The iDeep framework not only can achieve promising performance than the state-of-the-art predictors, but also easily capture interpretable binding motifs. iDeep is available at http://www.csbio.sjtu.edu.cn/bioinf/iDeep ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12859-017-1561-8) contains supplementary material, which is available to authorized users

A novel update rule of HALS algorithm for nonnegative matrix factorization and Zangwill’s global convergence

Nonnegative Matrix Factorization (NMF) has attracted a great deal of attention as an effective technique for dimensionality reduction of large-scale nonnegative data. Given a nonnegative matrix, NMF aims to obtain two low-rank nonnegative factor matrices by solving a constrained optimization problem. The Hierarchical Alternating Least Squares (HALS) algorithm is a well-known and widely-used iterative method for solving such optimization problems. However, the original update rule used in the HALS algorithm is not well defined. In this paper, we propose a novel well-defined update rule of the HALS algorithm, and prove its global convergence in the sense of Zangwill. Unlike conventional globally-convergent update rules, the proposed one allows variables to take the value of zero and hence can obtain sparse factor matrices. We also present two stopping conditions that guarantee the finite termination of the HALS algorithm. The practical usefulness of the proposed update rule is shown through experiments using real-world datasets