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Determination of latent dimensionality in international trade flow

MACHINE LEARNING-SCIENCE AND TECHNOLOGY 2020年第4期1卷

作者： Truong, Duc P. Erik, Skau Valtchinov, Vladimir I. Alexandrov, Boian S. Southern Methodist Univ Dept Math Dallas TX USA Los Alamos Natl Lab Comp Computat & Stat Sci Div Los Alamos NM USA Brigham & Womens Hosp Dept Radiol 75 Francis St Boston MA 02115 USA Brigham & Womens Hosp Ctr Evidence Based Imaging 75 Francis St Boston MA 02115 USA Harvard Med Sch Dept Biomed Informat Boston MA 02115 USA Los Alamos Natl Lab Div Theoret Los Alamos NM 87545 USA

Currently, high-dimensional data is ubiquitous in data science, which necessitates the development of techniques to decompose and interpret such multidimensional (aka tensor) datasets. Finding a low dimensional representation of the data, that is, its inherent structure, is one of the approaches that can serve to understand the dynamics of low dimensional latent features hidden in the data. Moreover, decomposition methods with non-negative constraints are shown to extract more insightful factors. nonnegative RESCAL is one such technique, particularly well suited to analyze self-relational data, such as dynamic networks found in international trade flows. Particularly, non-negative RESCAL computes a low dimensional tensor representation by finding the latent space containing multiple modalities. Furthermore, estimating the dimensionality of this latent space is crucial for extracting meaningful latent features. Here, to determine the dimensionality of the latent space with non-negative RESCAL, we propose a latent dimension determination method which is based on clustering of the solutions of multiple realizations of non-negative RESCAL decompositions. We demonstrate the performance of our model selection method on synthetic data. We then apply our method to decompose a network of international trade flows data from International Monetary Fund and shows that with a correct latent dimension determination, the resulting features are able to capture relevant empirical facts from economic literature.

关键词： latent dimension determination non-negative tensor factorization international trade network

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MULTI-DOMAIN FEATURE EXTRACTION FOR SMALL EVENT-RELATED POTENTIALS THROUGH nonnegative MULTI-WAY ARRAY DECOMPOSITION FROM LOW DENSE ARRAY EEG

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INTERNATIONAL JOURNAL OF NEURAL SYSTEMS 2013年第2期23卷 135006-1-1350006-18页

作者： Cong, Fengyu Phan, Anh-Huy Astikainen, Piia Zhao, Qibin Wu, Qiang Hietanen, Jari K. Ristaniemi, Tapani Cichocki, Andrzej Univ Jyvaskyla Dept Math Informat Technol SF-40351 Jyvaskyla Finland RIKEN Brain Sci Inst Lab Adv Brain Signal Proc Tokyo Japan Univ Jyvaskyla Dept Psychol SF-40351 Jyvaskyla Finland Shandong Univ Sch Informat Sci & Engn Jinan Shandong Peoples R China Univ Tampere Sch Social Sci & Humanities Human Informat Proc Lab FIN-33101 Tampere Finland Polish Acad Sci Syst Res Inst PL-01447 Warsaw Poland

non-negative Canonical Polyadic decomposition (NCPD) and non-negative Tucker decomposition (NTD) were compared for extracting the multi-domain feature of visual mismatch negativity (vMMN), a small event-related potential (ERP), for the cognitive research. Since signal-to-noise ratio in vMMN is low, NTD outperformed NCPD. Moreover, we proposed an approach to select the multi-domain feature of an ERP among all extracted features and discussed determination of numbers of extracted components in NCPD and NTD regarding the ERP context.

关键词： EEG event-related potential visual mismatch negativity multi-domain feature non-negative canonical polyadic decomposition non-negative tucker decomposition non-negative tensor factorization

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Segmented convex-hull algorithms for near-separable NMF and NTF

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NEUROCOMPUTING 2019年 331卷 150-164页

作者： Zdunek, Rafal Sadowski, Tomasz Wroclaw Univ Sci & Technol Dept Elect Wybrzeze Wyspianskiego 27 PL-50370 Wroclaw Poland

Many computational problems in machine learning can be represented with near-separable matrix factorization models. In a geometric approach, linear separability means that the entire set of data points can be modeled as a conical combination of a few data points, referred to as the extreme rays that express meaningful features. In this study, we propose segmented convex-hull algorithms for estimating the extreme rays of the simplicial cone generated by observations in the near-separable and inconsistent non-negative matrix factorization (NMF) and non-negative tensor factorization (NTF) models. The segmentation is based on the concept of hierarchical convex-hull NMF. The proposed algorithms are used to solve near-separable noisy blind source separation problems and classification problems. For the former, the experimental results demonstrate that they significantly outperform the state-of-the-art geometry-based NMF algorithms and the basic hierarchical alternating least squares NTF, if observations are noisy with signal-to-noise ratio lower than 100 dB. For the latter, the classification results also provide strong evidence for the effectiveness of the proposed approach with respect to existing geometry-based NMF algorithms. (C) 2018 Elsevier B.V. All rights reserved.

关键词： non-negative matrix factorization non-negative tensor factorization Convex-hull Near-separable non-negative factorizations Spectral unmixing Classification

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A Method for Automatic Construction of Ontological Knowledge Bases. III. Automatic Generation of Taxonomy as the Basis for Ontology(*)

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CYBERNETICS AND SYSTEMS ANALYSIS 2016年第3期52卷 365-370页

作者： Marchenko, O. O. Taras Shevchenko Natl Univ Kyiv Kiev Ukraine

A method is developed for the automatic generation of ontological knowledge bases. An algorithm is created for the extraction of explicit semantic relationships between concepts of an ontology on the basis of their semantic-syntactic valence vectors. Vectors of semantic-syntactic valences of words were also used as context vectors in an algorithm for formal concept analysis, which made it possible to develop a method for the automatic generation of high-quality taxonomies. As a result, a basic algorithm for the automatic generation of ontological knowledge bases was developed on the basis of the tensor semantic-syntactic model of natural language.

关键词： automatic knowledge extraction corpus linguistics ontology non-negative tensor factorization

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MetaFac: Community Discovery via Relational Hypergraph factorization 09

MetaFac: Community Discovery via Relational Hypergraph Facto...

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15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

作者： Lin, Yu-Ru Sun, Jimeng Castro, Paul Konuru, Ravi Sundaram, Hari Kelliher, Aisling Arizona State Univ Arts Media & Engn Program Tempe AZ 85281 USA

ISBN: (纸本)9781605584959

This paper aims at discovering community structure in rich media social networks. through analysis of time-varying, multi-relational data. Community structure represents the latent social context of user actions. It has important applications in information tasks such as search and recommendation. Social media has several unique challenges. (a) In social media, the context of user actions is constantly changing and co-evolving;hence the social context contains time-evolving multi-dimensional relations. (b) The social context is determined by the available system features and is unique in each social media website. In this paper we propose MetaFac (MetaGraph factorization), a framework that extracts community structures from various social contexts and interactions. Our work has three key contributions: (1) metagraph, a novel relational hypergraph representation for modeling multi-relational and multi-dimensional social data, (2) an efficient factorization method for community extraction oil a given metagraph;(3) an on-line method to handle time-varying relations through incremental metagraph factorization. Extensive experiments on real-world social data collected from the Digg social media website suggest that our technique is scalable and is able to extract meaningful communities based on the social media contexts. We illustrate the usefulness of our framework through prediction tasks. We outperform baseline methods (including aspect model and tensor analysis) by an order or magnitude.

关键词： MetaFac metagraph factorization relational hypergraph non-negative tensor factorization community discovery dynamic social network analysis

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COMMON FATE MODEL FOR UNISON SOURCE SEPARATION 41

COMMON FATE MODEL FOR UNISON SOURCE SEPARATION

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41st IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Stoter, Fabian-Robert Liutkus, Antoine Badeau, Roland Edler, Bernd Magron, Paul Int Audio Labs Erlangen Erlangen Germany Inria Speech Proc Team Villers Les Nancy France Telecom ParisTech CNRS LTCI Inst Mines Telecom Paris France

ISBN: (纸本)9781479999880

In this paper we present a novel source separation method aiming to overcome the difficulty of modelling non-stationary signals. The method can be applied to mixtures of musical instruments with frequency and/or amplitude modulation, e.g. typically caused by vibrato. It is based on a signal representation that divides the complex spectrogram into a grid of patches of arbitrary size. These complex patches are then processed by a two-dimensional discrete Fourier transform, forming a tensor representation which reveals spectral and temporal modulation textures. Our representation can be seen as an alternative to modulation transforms computed on magnitude spectrograms. An adapted factorization model allows to decompose different time-varying harmonic sources based on their particular common modulation profile: hence the name Common Fate Model. The method is evaluated on musical instrument mixtures playing the same fundamental frequency (unison), showing improvement over other state-of-the-art methods.

关键词： Sound source separation Common Fate Model non-negative tensor factorization

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User-Guided Clustering in Heterogeneous Information Networks via Motif-Based Comprehensive Transcription

User-Guided Clustering in Heterogeneous Information Networks...

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European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML PKDD)

作者： Shi, Yu He, Xinwei Zhang, Naijing Yang, Carl Han, Jiawei Univ Illinois Urbana IL 61801 USA

ISBN: (纸本)9783030461508;9783030461492

Heterogeneous information networks (HINs) with rich semantics are ubiquitous in real-world applications. For a given HIN, many reasonable clustering results with distinct semantic meaning can simultaneously exist. User-guided clustering is hence of great practical value for HINs where users provide labels to a small portion of nodes. To cater to a broad spectrum of user guidance evidenced by different expected clustering results, carefully exploiting the signals residing in the data is potentially useful. Meanwhile, as one type of complex networks, HINs often encapsulate higher-order interactions that reflect the interlocked nature among nodes and edges. Network motifs, sometimes referred to as meta-graphs, have been used as tools to capture such higher-order interactions and reveal the many different semantics. We therefore approach the problem of user-guided clustering in HINs with network motifs. In this process, we identify the utility and importance of directly modeling higher-order interactions without collapsing them to pairwise interactions. To achieve this, we comprehensively transcribe the higher-order interaction signals to a series of tensors via motifs and propose the MoCHIN model based on joint non-negative tensor factorization. This approach applies to arbitrarily many, arbitrary forms of HIN motifs. An inference algorithm with speed-up methods is also proposed to tackle the challenge that tensor size grows exponentially as the number of nodes in a motif increases. We validate the effectiveness of the proposed method on two real-world datasets and three tasks, and MoCHIN outperforms all baselines in three evaluation tasks under three different metrics. Additional experiments demonstrated the utility of motifs and the benefit of directly modeling higher-order information especially when user guidance is limited. (The code and the data are available at https://***/NoSegfault/MoCHIN.)

关键词： Heterogeneous information networks User-guided clustering Higher-order interactions Network motifs non-negative tensor factorization

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Spectral Matching Functions and Ellipse Mappings in Search for More Uniform Chromaticity and Color Spaces

Spectral Matching Functions and Ellipse Mappings in Search f...

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12th International Conference on Advanced Concepts for Intelligent Vision Systems

作者： Pahjehfouladgaran, Maryam Kaarna, Arto Lappeenranta Univ Technol Dept Informat Technol Machine Vis & Pattern Recognit Lab FI-53851 Lappeenranta Finland

ISBN: (纸本)9783642176876

In this study, modifying the CIE xyz color matching functions was considered to achieve a more uniform chromaticity space. New color matching functions resulting both from the non-negative tensor factorization and from the optimization were combined with two ellipse mapping approaches. In both approaches the original MacAdam ellipses were mapped to the new space. The first mapping approach depended on the dominant wavelengths and the second one on the spectral information for the five points on the locus of each ellipse. Equal semiaxis lengths (a constant radius) and equal areas for the mapped MacAdam ellipses were the characteristics for the uniformity of the new chromaticity space. The new color matching functions were modelled with the non-uniform rational B-splines and the optimization modified the independent parameters, namely the control points, for NURBS. The cost function was based on the size and shape of the mapped MacAdam ellipses. NURBS were also utilized as a smoothing operator when the color matching functions were directly output from the optimization task. The results indicate that modified color matching functions yield in more uniform chromaticity space. There still remains uncertainty about the ellipse mapping approaches and formulation on the cost function in the optimization tasks.

关键词： Uniform Chromaticity Space Color Matching Functions MacAdam Ellipses non-uniform Rational B-splines non-negative tensor factorization Smoothing

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Incorporation of Localization Information for Sound Source Separation in Spherical Harmonic Domain 23

Incorporation of Localization Information for Sound Source S...

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23rd IEEE International Workshop on Multimedia Signal Processing (IEEE MMSP)

作者： Guzik, Mateusz Fras, Mieszko Kowalczyk, Konrad AGH Univ Sci & Technol Inst Elect Krakow Poland

ISBN: (纸本)9781665432870

This paper concerns the problem of convolutive sound source separation from mutlichannel recordings made with a spherical microphone array. In particular, we formulate two state-of-the-art separation techniques based on Expectation Maximization (EM) and nonnegative tensor factorization (NTF) in the spherical harmonic domain (SHD). Furthermore, we adjust and incorporate the Gaussian Localization Prior (GLP) to the proposed algorithms, which yields two variants of the derived methods. For the source signal reconstruction, a Minimum Variance Distortionless Response (MVDR) beamformer with a single-channel Wiener post-filter is employed. The performance comparison is based on experimental evaluation using microphone signals simulated with the image-source method in several scenarios, including diverse geometrical setup, different number of sources and various types of source signals, namely the recordings of speech utterances and musical instruments. The experimental results for the first-order ambisonic signals show that the proposed methods enable high-quality sound source separation in the spherical harmonic domain. In particular, we show that incorporation of the Gaussian Localization Prior to the proposed algorithms leads to a substantial improvement in separation performance.

关键词： source separation convolutive mixtures non-negative tensor factorization spherical harmonic decomposition expectation maximization

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Performance Assessment of Adaptive Controller for Switched Systems based on tensor Approach 27

Performance Assessment of Adaptive Controller for Switched S...

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27th Chinese Control and Decision Conference (CCDC)

作者： Jiang, Deng-Yin Hu, Li-Sheng Shanghai Jiao Tong Univ Dept Automat Shanghai 200240 Peoples R China

ISBN: (纸本)9781479970162

This paper mainly concentrates on the robust multiple model adaptive controller performance assessment for switched systems via using the tensor approach. The multiple model adaptive control scheme is employed for the switched control systems performance assessment. The non-negative tensor factorization model is proposed to analyze the tensor data, which stems from uniqueness of low-rank decomposition of higher-order tensor. The data-driven algorithms based on tensor space approach are derived for the calculation of performance measures by applying non-negative tensor factorization. It is shown that the controller performance can he obtained by the data processing method of non negative tensor factorization. Under some sufficient conditions, such as a strong finite time switching, or a finite number of the dynamical subprocess, the closed-loop subprocess controller performance can be improved obviously for multivariate switched systems. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed tensor approach by comparing the adaptive switching controller with other adaptive schemes or the single controller.

关键词： Multiple model adaptive control Robust adaptive controller performance assessment tensor Switched systems non-negative tensor factorization

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