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Many-to-Many Voice Conversion based on Bottleneck Features with Variational Autoencoder for Non-parallel Training data

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Many-to-Many Voice Conversion based on Bottleneck Features w...

Asia-Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA)

作者： Yanping Li Kong Aik Lee Yougen Yuan Haizhou Li Zhen Yang College of Telecommunication & Information Engineering Nanjing University of Posts and Telecommunications China Data Science Research Laboratories NEC Corporation Japan Northwestern Polytechnical University Xi'an China Department of Electronic and Computer-Engineering National University of Singapore Singapore

ISBN: (纸本)9781728102436;9789881476852

This paper proposes a novel approach to many-to-many (M2M) voice conversion for non-parallel training data. In the proposed approach, we first obtain bottleneck features (BNFs) as speaker representations from a deep neural network (DNN). Then, a variational autoencoder (VAE) implements the mapping function (i.e., a reconstruction process) using both the latent semantic information and the speaker representations. Furthermore, we propose an adaptive scheme by intervening the training process of the DNN, which can enrich the target speaker's personality feature space in the case of limited training data. Our approach has three advantages: 1) neither parallel training data nor explicit frame alignment process is required; 2) consolidates multiple pair-wise systems into a single M2M model (many-source speakers to many-target speakers); 3) expands M2M conversion task from closed set to open set when the training data of target speaker is very limited. The objective and subjective evaluations show that our proposed approach outperforms the baseline system.

关键词： Training data Training Machine-to-machine communications Feature extraction Speaker recognition Decoding Error analysis

Robust Sparse Approximations for Stochastic Dynamical Systems

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IFAC-PapersOnLine 2017年第1期50卷 14010-14015页

作者： Quinn, Christopher J. Pinar, Ali Gao, Jing Su, Lu School of Industrial Engineering Purdue University West LafayetteIN United States Data Sciences & Cyber Anal. Dept. Sandia National Laboratories LivermoreCA United States Dept. of Computer Science and Engineering University at Buffalo BuffaloNY United States

Inferring the exact topology of the interactions in a large, stochastic dynamical system from time-series data can often be prohibitive computationally and statistically without strong side information. One alternative is to seek approximations of the system topology that nonetheless describe the data well. In recent works, algorithms were proposed to identify sparse approximations which are optimal in terms of Kullback-Leibler divergence. Those algorithms relied on point estimates of statistics from the data. In this work, we investigate the more practical setting where point estimates are not reliable. We propose an algorithm to identify sparse, connected approximations that are robust to estimation error. © 2017

关键词： Approximation algorithms Dynamical systems Identification (control systems) Nonlinear systems Stochastic systems Time series Topology Errors in variables Model reduction Nonparametric methods Robust estimation Time series modeling

Adverse Drug Reaction Post Classification with Imbalanced Classification Techniques

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Adverse Drug Reaction Post Classification with Imbalanced Cl...

International Conference on Technologies and Applications of Artificial Intelligence (TAAI)

作者： Chen-Kai Wang Hong-Jie Dai Feng-Duo Wang Emily Chia-Yu Su Big Data Laboratories Chunghwa Telecom Laboratories Taoyuan Taiwan R.O.C. Department of Computer Science and Information Engineering National Taitung University Taitung Taiwan R.O.C. Graduate Institute of Biomedical Informatics Taipei Medical University Taipei Taiwan R.O.C.

Nowadays, social media is often being used by users to create public messages related to their health. With the increasing number of social media usage, a trend has been observed of users creating posts related to adverse drug reactions (ADR). Mining social media data for these information can be used for pharmacological post-marketing surveillance and monitoring. However, the development of automatic ADR detection systems remains challenging because the corpora compiled from real world social media were usually highly imbalanced resulting in barriers to develop classifiers with reliable performance. In this work, we implemented a variety of imbalanced techniques and compared their performance on two large imbalanced data sets released for the purpose of detecting ADR posts. Comparing with state-of-the-art approaches developed for the two dataset, based on much less features, the developed classifiers with implemented imbalanced classification techniques achieved comparable or even better F-scores.

关键词： Social network services Task analysis Training Feature extraction Drugs Classification algorithms Support vector machines

Exposure-associated DNA methylation among people exposed to multiple industrial pollutants

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Clinical epigenetics 2024年第1期16卷 111页

作者： Chi-Hsin Sally Chen Tzu-Hsuen Yuan Tzu-Pin Lu Hsin-Ying Lee Yi-Hsuen Chen Liang-Chuan Lai Mong-Hsun Tsai Eric Y Chuang Chang-Chuan Chan Institute of Environmental and Occupational Health Sciences College of Public Health National Taiwan University Taipei Taiwan. Department of Health and Welfare College of City Management University of Taipei Taipei Taiwan. Institute of Epidemiology and Preventive Medicine College of Public Health National Taiwan University Taipei Taiwan. Institute of Health Data Analytics and Statistics College of Public Health National Taiwan University Taipei Taiwan. Graduate Institute of Physiology College of Medicine National Taiwan University Taipei Taiwan. Institute of Biotechnology College of Bio-Resources and Agriculture National Taiwan University Taipei Taiwan. Department of Electrical Engineering College of Electrical Engineering and Computer Science National Taiwan University Taipei Taiwan. chuangey@ntu.edu.tw. Biomedical Technology and Device Research Laboratories Industrial Technology Research Institute Hsinchu Taiwan. chuangey@ntu.edu.tw. Research and Development Center for Medical Devices National Taiwan University Taipei Taiwan. chuangey@ntu.edu.tw. Graduate Institute of Biomedical Electronics and Bioinformatics National Taiwan University Taipei Taiwan. chuangey@ntu.edu.tw. Institute of Environmental and Occupational Health Sciences College of Public Health National Taiwan University Taipei Taiwan. ccchan@ntu.edu.tw.

BACKGROUND:Current research on the epigenetic repercussions of exposure to a combination of pollutants is limited. This study aims to discern DNA methylation probes associated with exposure to multiple pollutants, serving as early effect markers, and single-nucleotide polymorphisms (SNPs) as surrogate indicators for population susceptibility. The investigation involved the analysis of urine exposure biomarkers for 11 heavy metals (vanadium, arsenic, mercury, cadmium, chromium, nickel, lead, manganese, copper, strontium, thallium), polycyclic aromatic hydrocarbon (PAHs) (1-hydroxypyrene), genome-wide DNA methylation sequencing, and SNPs array on all study participants. The data were integrated with metabolomics information and analyzed both at a community level based on proximity to home addresses relative to the complex and at an individual level based on exposure biomarker concentrations. RESULTS:On a community level, 67 exposure-related CpG probes were identified, while 70 CpG probes were associated with urine arsenic concentration, 2 with mercury, and 46 with vanadium on an individual level. These probes were annotated to genes implicated in cancers and chronic kidney disease. Weighted quantile sum regression analysis revealed that vanadium, mercury, and 1-hydroxypyrene contributed the most to cg08238319 hypomethylation. cg08238319 is annotated to the aryl hydrocarbon receptor repressor (AHRR) gene, and AHRR hypomethylation was correlated with an elevated risk of lung cancer. AHRR was further linked to deregulations in phenylalanine metabolism, alanine, aspartate, and glutamate metabolism, along with heightened oxidative stress. Additionally, three SNPs (rs11085020, rs199442, and rs10947050) corresponding to exposure-related CpG probes exhibited significant interaction effects with multiple heavy metals and PAHs exposure, and have been implicated in cancer progression and respiratory diseases. CONCLUSION:Our findings underscore the pivotal role of AHRR methylatio

关键词： DNA methylation Gene-environment interaction Heavy metals PAHs Petrochemical industry SNPs

Harmonized-Multinational qEEG norms (HarMNqEEG)

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NEUROIMAGE 2022年 256卷 119190-119190页

作者： Li, Min Wang, Ying Lopez-Naranjo, Carlos Hu, Shiang Reyes, Ronaldo Cesar Garcia Paz-Linares, Deirel Areces-Gonzalez, Ariosky Hamid, Aini Ismafairus Abd Evans, Alan C. Savostyanov, Alexander N. Calzada-Reyes, Ana Villringer, Arno Tobon-Quintero, Carlos A. Garcia-Agustin, Daysi Yao, Dezhong Dong, Li Aubert-Vazquez, Eduardo Reza, Faruque Razzaq, Fuleah Abdul Omar, Hazim Abdullah, Jafri Malin Galler, Janina R. Ochoa-Gomez, John F. Prichep, Leslie S. Galan-Garcia, Lidice Morales-Chacon, Lilia Valdes-Sosa, Mitchell J. Trondle, Marius Zulkifly, Mohd Faizal Mohd Rahman, Muhammad Riddha Bin Abdul Milakhina, Natalya S. Langer, Nicolas Rudych, Pavel Koenig, Thomas Virues-Alba, Trinidad A. Lei, Xu Bringas-Vega, Maria L. Bosch-Bayard, Jorge F. Valdes-Sosa, Pedro Antonio [a]The Clinical Hospital of Chengdu Brain Science Institute MOE Key Lab for Neuroinformation School of Life Science and Technology University of Electronic Science and Technology of China Chengdu China [b]Cuban Center for Neurocience La Habana Cuba [c]McGill Centre for Integrative Neuroscience Ludmer Centre for Neuroinformatics and Mental Health Montreal Neurological Institute Canada [d]Department of Neurosciences School of Medical Sciences Universiti Sains Malaysia Universiti Sains Malaysia Health Campus Kota Bharu Kelantan 16150 Malaysia [e]Brain and Behaviour Cluster School of Medical Sciences Universiti Sains Malaysia Health Campus Kota Bharu Kelantan 16150 Malaysia [f]Hospital Universiti Sains Malaysia Universiti Sains Malaysia Health Campus Kota Bharu Kelantan 16150 Malaysia [g]Humanitarian Institute Novosibirsk State University Novosibirsk 630090 Russia [h]Laboratory of Psychophysiology of Individual Differences Federal State Budgetary Scientific Institution Scientific Research Institute of Neurosciences and Medicine Novosibirsk 630117 Russia [i]Laboratory of Psychological Genetics at the Institute of Cytology and Genetics Siberian Branch of the Russian Academy of Sciences Novosibirsk 630090 Russia [j]University of Pinar del Río “Hermanos Saiz Montes de Oca” Pinar del Río Cuba [k]Department of Neurology Max Planck Institute for Human Cognitive and Brain Sciences Leipzig Germany [l]Department of Cognitive Neurology University Hospital Leipzig Leipzig Germany [m]Center for Stroke Research Charité-Universitätsmedizin Berlin Berlin Germany [n]Grupo Neuropsicología y Conducta - GRUNECO Faculty of Medicine Universidad de Antioquia Colombia [o]Research Department Institución Prestadora de Servicios de Salud IPS Universitaria Colombia [p]The Cuban center aging longevity and health Havana Cuba [q]Research Unit of NeuroInformation Chinese Academy of Medical Sciences Chengdu 2019RU035 China [r]School of Electrical Engineering Zhengzhou University Zhengzhou 4500

This paper extends frequency domain quantitative electroencephalography (qEEG) methods pursuing higher sensitivity to detect Brain Developmental Disorders. Prior qEEG work lacked integration of cross-spectral information omitting important functional connectivity descriptors. Lack of geographical diversity precluded accounting for site-specific variance, increasing qEEG nuisance variance. We ameliorate these weaknesses. (i) Create lifespan Riemannian multinational qEEG norms for cross-spectral tensors. These norms result from the HarMNqEEG project fostered by the Global Brain Consortium. We calculate the norms with data from 9 countries, 12 devices, and 14 studies, including 1564 subjects. Instead of raw data, only anonymized metadata and EEG cross spectral tensors were shared. After visual and automatic quality control, developmental equations for the mean and standard deviation of qEEG traditional and Riemannian DPs were calculated using additive mixed-effects models. We demonstrate qEEG "batch effects " and provide methods to calculate harmonized z-scores. (ii) We also show that harmonized Riemannian norms produce z-scores with increased diagnostic accuracy predicting brain dysfunction produced by malnutrition in the first year of life and detecting COVID induced brain dysfunction. (iii) We offer open code and data to calculate different individual z-scores from the HarMNqEEG dataset. These results contribute to developing bias-free, low-cost neuroimaging technologies applicable in various health settings.

关键词： Quantitative EEG EEG cross-spectrum Riemannian geometry Batch effects Z-score Harmonization Malnutrition Covid induced brain dysfunction Developmental Brain Chart

2022 Roadmap on Neuromorphic Computing and Engineering

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arXiv 2021年

作者： Christensen, Dennis Valbjørn Dittmann, Regina Linares-Barranco, Bernabé Sebastian, Abu Le Gallo, Manuel Redaelli, Andrea Slesazeck, Stefan Mikolajick, Thomas Spiga, Sabina Menzel, Stephan Valov, Ilia Milano, Gianluca Ricciardi, Carlo Liang, Shi-Jun Miao, Feng Lanza, Mario Quill, Tyler J. Keene, Scott T. Salleo, Alberto Grollier, Julie Marković, Danijela Mizrahi, Alice Yao, Peng Yang, J. Joshua Indiveri, Giacomo Strachan, John Paul Datta, Suman Vianello, Elisa Valentian, Alexandre Feldmann, Johannes Li, Xuan Pernice, Wolfram H.P. Bhaskaran, Harish Furber, Steve Neftci, Emre Scherr, Franz Maass, Wolfgang Ramaswamy, Srikanth Tapson, Jonathan Panda, Priyadarshini Kim, Youngeun Tanaka, Gouhei Thorpe, Simon Bartolozzi, Chiara Cleland, Thomas A. Posch, Christoph Liu, Shih-Chii Panuccio, Gabriella Mahmud, Mufti Mazumder, Arnab Neelim Hosseini, Morteza Mohsenin, Tinoosh Donati, Elisa Tolu, Silvia Galeazzi, Roberto Christensen, Martin Ejsing Holm, Sune Ielmini, Daniele Pryds, N. Department of Energy Conversion and Storage Technical University of Denmark Kgs. LyngbyDK-2800 Denmark Peter Gruenberg Institute 7 Forschungszentrum Juelich GmbH Juelich52425 Germany JARA-FIT RWTH Aachen University Aachen52056 Germany CSIC Universidad de Sevilla Seville41092 Spain IBM Research Zurich Switzerland STMicroelectronics Agrate Italy Dresden01187 Germany Institute of Semiconductors and Microsystems TU Dresden Dresden Germany CNR-IMM Unit of Agrate Brianza via C. Olivetti 2 MB Agrate Brianza Italy Juelich Germany Torino Italy Department of Applied Science and Technology Politecnico di Torino Torino Italy National Laboratory of Solid State Microstructures School of Physics Collaborative Innovation Center of Advanced Microstructures Nanjing University Nanjing China Thuwal23955-6900 Saudi Arabia Department of Materials Science and Engineering Stanford University StanfordCA94305 United States Department of Engineering University of Cambridge CambridgeCB2 1PZ United Kingdom Unité Mixte de Physique CNRS Thales Université Paris-Saclay Palaiseau91767 France Electrical and Computer Engineering Department University of Southern California Los AngelesCA United States Institute of Neuroinformatics University of Zurich ETH Zurich Switzerland Hewlett Packard Laboratories Hewlett Packard Enterprise San JoseCA United States Department of Electrical Engineering University of Notre Dame Notre DameIN United States CEA LETI Université Grenoble Alpes Grenoble France CEA LIST Université Grenoble Alpes Grenoble France Department of Materials University of Oxford Parks Road OxfordOX1 3PH United Kingdom Institute of Physics University of Münster Heisenbergstr. 11 Heisenbergstr Münster48149 Germany Center for Soft Nanoscience University of Münster Münster48149 Germany The University of Manchester United Kingdom Department of Cognitive Sciences University of California Irvine IrvineCA United States Institute of Theoretica

Modern computation based on the von Neumann architecture is today a mature cutting-edge science. In the Von Neumann architecture, processing and memory units are implemented as separate blocks interchanging data intensively and continuously. This data transfer is responsible for a large part of the power consumption. The next generation computer technology is expected to solve problems at the exascale with 1018 calculations each second. Even though these future computers will be incredibly powerful, if they are based on von Neumann type architectures, they will consume between 20 and 30 megawatts of power and will not have intrinsic physically built-in capabilities to learn or deal with complex data as our brain does. These needs can be addressed by neuromorphic computing systems which are inspired by the biological concepts of the human brain. This new generation of computers has the potential to be used for the storage and processing of large amounts of digital information with much lower power consumption than conventional processors. Among their potential future applications, an important niche is moving the control from data centers to edge devices. The aim of this Roadmap is to present a snapshot of the present state of neuromorphic technology and provide an opinion on the challenges and opportunities that the future holds in the major areas of neuromorphic technology, namely materials, devices, neuromorphic circuits, neuromorphic algorithms, applications, and ethics. The Roadmap is a collection of perspectives where leading researchers in the neuromorphic community provide their own view about the current state and the future challenges for each research area. We hope that this Roadmap will be a useful resource by providing a concise yet comprehensive introduction to readers outside this field, for those who are just entering the field, as well as providing future perspectives for those who are well established in the neuromorphic computing community. © 2021,

关键词： data transfer

NL-Augmenter A Framework for Task-Sensitive Natural Language Augmentation

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arXiv 2021年

作者： Dhole, Kaustubh D. Gangal, Varun Gehrmann, Sebastian Gupta, Aadesh Li, Zhenhao Mahamood, Saad Mahendiran, Abinaya Mille, Simon Shrivastava, Ashish Tan, Samson Wu, Tongshuang Sohl-Dickstein, Jascha Choi, Jinho D. Hovy, Eduard Dušek, Ondřej Ruder, Sebastian Anand, Sajant Aneja, Nagender Banjade, Rabin Barthe, Lisa Behnke, Hanna Berlot-Attwell, Ian Boyle, Connor Brun, Caroline Sobrevilla Cabezudo, Marco Antonio Cahyawijaya, Samuel Chapuis, Emile Che, Wanxiang Choudhary, Mukund Clauss, Christian Colombo, Pierre Cornell, Filip Dagan, Gautier Das, Mayukh Dixit, Tanay Dopierre, Thomas Dray, Paul-Alexis Dubey, Suchitra Ekeinhor, Tatiana Giovanni, Marco Di Goyal, Tanya Gupta, Rishabh Hamla, Louanes Han, Sang Harel-Canada, Fabrice Honoré, Antoine Jindal, Ishan Joniak, Przemyslaw K. Kleyko, Denis Kovatchev, Venelin Krishna, Kalpesh Kumar, Ashutosh Langer, Stefan Lee, Seungjae Ryan Levinson, Corey James Liang, Hualou Liang, Kaizhao Liu, Zhexiong Lukyanenko, Andrey Marivate, Vukosi de Melo, Gerard Meoni, Simon Meyer, Maxime Mir, Afnan Moosavi, Nafise Sadat Muennighoff, Niklas Hon Mun, Timothy Sum Murray, Kenton Namysl, Marcin Obedkova, Maria Oli, Priti Pasricha, Nivranshu Pfister, Jan Plant, Richard Prabhu, Vinay Pais, Vasile Qin, Libo Raji, Shahab Rajpoot, Pawan Kumar Raunak, Vikas Rinberg, Roy Roberts, Nicholas Rodriguez, Juan Diego Roux, Claude Vasconcellos, P.H.S. Sai, Ananya B. Schmidt, Robin M. Scialom, Thomas Sefara, Tshephisho Shamsi, Saqib N. Shen, Xudong Shi, Yiwen Shi, Haoyue Shvets, Anna Siegel, Nick Sileo, Damien Simon, Jamie Singh, Chandan Sitelew, Roman Soni, Priyank Sorensen, Taylor Soto, William Srivastava, Aman Aditya Srivatsa, K.V. Sun, Tony Mukund Varma, T. Tabassum, A. Tan, Fiona Anting Teehan, Ryan Tiwari, Mo Tolkiehn, Marie Wang, Athena Wang, Zijian Wang, Zijie J. Wang, Gloria Wei, Fuxuan Wilie, Bryan Winata, Genta Indra Wu, Xinyi Wydmanski, Witold Xie, Tianbao Yaseen, Usama Yee, Michael A. Zhang, Jing Zhang, Yue ACKO Agara Amelia R&D New York United States Applied Research Laboratories The University of Texas at Austin United States Bloomberg Brigham Young University United States Carnegie Mellon University United States Center for Data and Computing in Natural Sciences Universität Hamburg Germany Charles River Analytics Charles University Prague Czech Republic Columbia University United States Council for Scientific and Industrial Research DeepMind United Kingdom Department of Computer Science University of Pretoria South Africa Drexel University United States Eberhard Karls University of Tübingen Germany Edinburgh Napier University United Kingdom Emory University United States Fablab by Inetum in Paris France Fraunhofer IAIS Germany Georgia Tech United States Google Brain United States Google Research United States Harbin Institute of Technology China Hasso Plattner Institute University of Potsdam Germany Hong Kong University of Science and Technology Hong Kong IBM Research IIT Delhi India IIT Madras India Illinois Mathematics and Science Academy United States Imperial College London United Kingdom Independent Indian Institute of Science Bangalore India Institut Teknologi Bandung Indonesia Institute of Data Science National University of Singapore Singapore International Institute of Information Technology Hyderabad India Jagiellonian University Poland Jean Monnet University France Johns Hopkins United States KTH Royal Institute of Technology Sweden KU Leuven Belgium MTS AI France Microsoft RedmondWA United States Mphasis NEXT Labs National University of Ireland Galway Ireland National University of Science and Technology Pakistan National University of Singapore Singapore Naver Labs Europe France Peking University China Politecnico di Milano University of Bologna Italy Polytechnic Institute of Paris France Pompeu Fabra University Spain Pontifical Catholic University of Minas Gerais Brazil Princeton University United States Rakuten India India Research Institu

data augmentation is an important component in the robustness evaluation of models in natural language processing (NLP) and in enhancing the diversity of the data they are trained on. In this paper, we present NL-Augmenter, a new participatory Python-based natural language augmentation framework which supports the creation of both transformations (modifications to the data) and filters (data splits according to specific features). We describe the framework and an initial set of 117 transformations and 23 filters for a variety of natural language tasks. We demonstrate the efficacy of NL-Augmenter by using several of its tranformations to analyze the robustness of popular natural language models. The infrastructure, datacards and robutstness analysis results are available publicly on the NL-Augmenter repository (https://***/GEM-benchmark/NL-Augmenter). © 2021, CC BY.

关键词： Python

On w-mixtures: Finite convex combinations of prescribed component distributions

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arXiv 2017年

作者： Nielsen, Frank Nock, Richard Sony Computer Science Laboratories Inc Japan Data61 The Australian National University The University of Sydney Australia

We consider the space of w-mixtures which is defined as the set of finite statistical mixtures sharing the same prescribed component distributions closed under convex combinations. The information geometry induced by the Bregman generator set to the Shannon negentropy on this space yields a dually flat space called the mixture family manifold. We show how the Kullback-Leibler (KL) divergence can be recovered from the corresponding Bregman divergence for the negentropy generator: That is, the KL divergence between any two w-mixtures amounts to a Bregman Divergence (BD) induced by the Shannon negentropy generator. Thus the KL divergence between two Gaussian Mixture Models (GMMs) sharing the same Gaussian components is equivalent to a Bregman divergence. This KL-BD equivalence on a mixture family manifold implies that we can perform optimal KL-averaging aggregation of w-mixtures without information loss. More generally, we prove that the statistical skew Jensen-Shannon divergence between w-mixtures is equivalent to a skew Jensen divergence between their corresponding parameters. Finally, we state several properties, divergence identities, and divergence inequalities relating to w-mixtures. Copyright © 2017, The Authors. All rights reserved.

关键词： Machine learning

Clustering in Hilbert simplex geometry

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arXiv 2017年

作者： Nielsen, Frank Sun, Ke Sony Computer Science Laboratories Inc. Japan Data61 Australia The Australian National University Australia

Clustering categorical distributions in the finite-dimensional probability simplex is a fundamental task met in many applications dealing with normalized histograms. Traditionally, the differential-geometric structures of the probability simplex have been used either by (i) setting the Riemannian metric tensor to the Fisher information matrix of the categorical distributions, or (ii) defining the dualistic information-geometric structure induced by a smooth dissimilarity measure, the Kullback-Leibler divergence. In this work, we introduce for clustering tasks a novel computationally-friendly framework for modeling geometrically the probability simplex: The Hilbert simplex geometry. In the Hilbert simplex geometry, the distance is the non-separable Hilbert's metric distance which satisfies the property of information monotonicity with distance level set functions described by polytope boundaries. We show that both the Aitchison and Hilbert simplex distances are norm distances on normalized logarithmic representations with respect to the 2 and variation norms, respectively. We discuss the pros and cons of those different statistical modelings, and benchmark experimentally these different kind of geometries for center-based k-means and k-center clustering. Furthermore, since a canonical Hilbert distance can be defined on any bounded convex subset of the Euclidean space, we also consider Hilbert's geometry of the elliptope of correlation matrices and study its clustering performances compared to Fröbenius and log-det divergences. Copyright © 2017, The Authors. All rights reserved.

关键词： Geometry