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

Deliverable D1.1 State of the art and requirements analysis for hypervideo

This deliverable presents a state-of-art and requirements analysis report for hypervideo authored as part of the WP1 of the LinkedTV project. Initially, we present some use-case (viewers) scenarios in the LinkedTV project and through the analysis of the distinctive needs and demands of each scenario we point out the technical requirements from a user-side perspective. Subsequently we study methods for the automatic and semi-automatic decomposition of the audiovisual content in order to effectively support the annotation process. Considering that the multimedia content comprises of different types of information, i.e., visual, textual and audio, we report various methods for the analysis of these three different streams. Finally we present various annotation tools which could integrate the developed analysis results so as to effectively support users (video producers) in the semi-automatic linking of hypervideo content, and based on them we report on the initial progress in building the LinkedTV annotation tool. For each one of the different classes of techniques being discussed in the deliverable we present the evaluation results from the application of one such method of the literature to a dataset well-suited to the needs of the LinkedTV project, and we indicate the future technical requirements that should be addressed in order to achieve higher levels of performance (e.g., in terms of accuracy and time-efficiency), as necessary

Multilevel Weighted Support Vector Machine for Classification on Healthcare Data with Missing Values

This work is motivated by the needs of predictive analytics on healthcare data as represented by Electronic Medical Records. Such data is invariably problematic: noisy, with missing entries, with imbalance in classes of interests, leading to serious bias in predictive modeling. Since standard data mining methods often produce poor performance measures, we argue for development of specialized techniques of data-preprocessing and classification. In this paper, we propose a new method to simultaneously classify large datasets and reduce the effects of missing values. It is based on a multilevel framework of the cost-sensitive SVM and the expected maximization imputation method for missing values, which relies on iterated regression analyses. We compare classification results of multilevel SVM-based algorithms on public benchmark datasets with imbalanced classes and missing values as well as real data in health applications, and show that our multilevel SVM-based method produces fast, and more accurate and robust classification results.Comment: arXiv admin note: substantial text overlap with arXiv:1503.0625

Scene Image Classification and Retrieval

Scene image classification and retrieval not only have a great impact on scene image management, but also they can offer immeasurable assistance to other computer vision problems, such as image completion, human activity analysis, object recognition etc. Intuitively scene identification is correlated to recognition of objects or image regions, which prompts the notion to apply local features to scene categorization applications. Even though the adoption of local features in these tasks has yielded promising results, a global perception on scene images is also well-conditioned in cognitive science studies. Since the global description of a scene imposes less computational burden, it is favoured by some scholars despite its less discriminative capacity. Recent studies on global scene descriptors have even yielded classification performance that rivals results obtained by local approaches. The primary objective of this work is to tackle two of the limitations of existing global scene features: representation ineffectiveness and computational complexity. The thesis proposes two global scene features that seek to represent finer scene structures and reduce the dimensionality of feature vectors. Experimental results show that the proposed scene features exceed the performance of existing methods. The thesis is roughly divided into two parts. The first three chapters give an overview on the topic of scene image classification and retrieval methods, with a special attention to the most effective global scene features. In chapter 4, a novel scene descriptor, called ARP-GIST, is proposed and evaluated against the existing methods to show its ability to detect finer scene structures. In chapter 5, a low-dimensional scene feature, GIST-LBP, is proposed. In conjunction with a block ranking approach, the GIST-LBP feature is tested on a standard scene dataset to demonstrate its state-of-the-art performance

Algorithmic advances in learning from large dimensional matrices and scientific data

University of Minnesota Ph.D. dissertation.May 2018. Major: Computer Science. Advisor: Yousef Saad. 1 computer file (PDF); xi, 196 pages.This thesis is devoted to answering a range of questions in machine learning and data analysis related to large dimensional matrices and scientific data. Two key research objectives connect the different parts of the thesis: (a) development of fast, efficient, and scalable algorithms for machine learning which handle large matrices and high dimensional data; and (b) design of learning algorithms for scientific data applications. The work combines ideas from multiple, often non-traditional, fields leading to new algorithms, new theory, and new insights in different applications. The first of the three parts of this thesis explores numerical linear algebra tools to develop efficient algorithms for machine learning with reduced computation cost and improved scalability. Here, we first develop inexpensive algorithms combining various ideas from linear algebra and approximation theory for matrix spectrum related problems such as numerical rank estimation, matrix function trace estimation including log-determinants, Schatten norms, and other spectral sums. We also propose a new method which simultaneously estimates the dimension of the dominant subspace of covariance matrices and obtains an approximation to the subspace. Next, we consider matrix approximation problems such as low rank approximation, column subset selection, and graph sparsification. We present a new approach based on multilevel coarsening to compute these approximations for large sparse matrices and graphs. Lastly, on the linear algebra front, we devise a novel algorithm based on rank shrinkage for the dictionary learning problem, learning a small set of dictionary columns which best represent the given data. The second part of this thesis focuses on exploring novel non-traditional applications of information theory and codes, particularly in solving problems related to machine learning and high dimensional data analysis. Here, we first propose new matrix sketching methods using codes for obtaining low rank approximations of matrices and solving least squares regression problems. Next, we demonstrate that codewords from certain coding scheme perform exceptionally well for the group testing problem. Lastly, we present a novel machine learning application for coding theory, that of solving large scale multilabel classification problems. We propose a new algorithm for multilabel classification which is based on group testing and codes. The algorithm has a simple inexpensive prediction method, and the error correction capabilities of codes are exploited for the first time to correct prediction errors. The third part of the thesis focuses on devising robust and stable learning algorithms, which yield results that are interpretable from specific scientific application viewpoint. We present Union of Intersections (UoI), a flexible, modular, and scalable framework for statistical-machine learning problems. We then adapt this framework to develop new algorithms for matrix decomposition problems such as nonnegative matrix factorization (NMF) and CUR decomposition. We apply these new methods to data from Neuroscience applications in order to obtain insights into the functionality of the brain. Finally, we consider the application of material informatics, learning from materials data. Here, we deploy regression techniques on materials data to predict physical properties of materials

Graph coarsening: From scientific computing to machine learning

The general method of graph coarsening or graph reduction has been a remarkably useful and ubiquitous tool in scientific computing and it is now just starting to have a similar impact in machine learning. The goal of this paper is to take a broad look into coarsening techniques that have been successfully deployed in scientific computing and see how similar principles are finding their way in more recent applications related to machine learning. In scientific computing, coarsening plays a central role in algebraic multigrid methods as well as the related class of multilevel incomplete LU factorizations. In machine learning, graph coarsening goes under various names, e.g., graph downsampling or graph reduction. Its goal in most cases is to replace some original graph by one which has fewer nodes, but whose structure and characteristics are similar to those of the original graph. As will be seen, a common strategy in these methods is to rely on spectral properties to define the coarse graph

Multilevel Methods for Sparsification and Linear Arrangement Problems on Networks

The computation of network properties such as diameter, centrality indices, and paths on networks may become a major bottleneck in the analysis of network if the network is large. Scalable approximation algorithms, heuristics and structure preserving network sparsification methods play an important role in modern network analysis. In the first part of this thesis, we develop a robust network sparsification method that enables filtering of either, so called, long- and short-range edges or both. Edges are first ranked by their algebraic distances and then sampled. Furthermore, we also combine this method with a multilevel framework to provide a multilevel sparsification framework that can control the sparsification process at different coarse-grained resolutions. Experimental results demonstrate an effectiveness of the proposed methods without significant loss in a quality of computed network properties. In the second part of the thesis, we introduce asymmetric coarsening schemes for multilevel algorithms developed for linear arrangement problems. Effectiveness of the set of coarse variables, and the corresponding interpolation matrix is the central problem in any multigrid algorithm. We are pushing the boundaries of fast maximum weighted matching algorithms for coarsening schemes on graphs by introducing novel ideas for asymmetric coupling between coarse and fine variables of the problem