Advances in Nonnegative Matrix Decomposition with Application to Cluster Analysis

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dc.contributor Aalto-yliopisto fi
dc.contributor Aalto University en
dc.contributor.advisor Yang, Zhirong, Dr., Aalto University, Department of Information and Computer Science, Finland
dc.contributor.author Zhang, He
dc.date.accessioned 2014-09-09T09:00:17Z
dc.date.available 2014-09-09T09:00:17Z
dc.date.issued 2014
dc.identifier.isbn 978-952-60-5829-0 (electronic)
dc.identifier.isbn 978-952-60-5828-3 (printed)
dc.identifier.issn 1799-4942 (electronic)
dc.identifier.issn 1799-4934 (printed)
dc.identifier.issn 1799-4934 (ISSN-L)
dc.identifier.uri https://aaltodoc.aalto.fi/handle/123456789/13964
dc.description.abstract Nonnegative Matrix Factorization (NMF) has found a wide variety of applications in machine learning and data mining. NMF seeks to approximate a nonnegative data matrix by a product of several low-rank factorizing matrices, some of which are constrained to be nonnegative. Such additive nature often results in parts-based representation of the data, which is a desired property especially for cluster analysis.  This thesis presents advances in NMF with application in cluster analysis. It reviews a class of higher-order NMF methods called Quadratic Nonnegative Matrix Factorization (QNMF). QNMF differs from most existing NMF methods in that some of its factorizing matrices occur twice in the approximation. The thesis also reviews a structural matrix decomposition method based on Data-Cluster-Data (DCD) random walk. DCD goes beyond matrix factorization and has a solid probabilistic interpretation by forming the approximation with cluster assigning probabilities only. Besides, the Kullback-Leibler divergence adopted by DCD is advantageous in handling sparse similarities for cluster analysis.  Multiplicative update algorithms have been commonly used for optimizing NMF objectives, since they naturally maintain the nonnegativity constraint of the factorizing matrix and require no user-specified parameters. In this work, an adaptive multiplicative update algorithm is proposed to increase the convergence speed of QNMF objectives.  Initialization conditions play a key role in cluster analysis. In this thesis, a comprehensive initialization strategy is proposed to improve the clustering performance by combining a set of base clustering methods. The proposed method can better accommodate clustering methods that need a careful initialization such as the DCD.  The proposed methods have been tested on various real-world datasets, such as text documents, face images, protein, etc. In particular, the proposed approach has been applied to the cluster analysis of emotional data. en
dc.format.extent 94 + app. 94
dc.format.mimetype application/pdf en
dc.language.iso en en
dc.publisher Aalto University en
dc.publisher Aalto-yliopisto fi
dc.relation.ispartofseries Aalto University publication series DOCTORAL DISSERTATIONS en
dc.relation.ispartofseries 127/2014
dc.relation.haspart [Publication 1]: Zhirong Yang, He Zhang, Zhijian Yuan, and Erkki Oja. Kullback-Leibler divergence for nonnegative matrix factorization. In Proceedings of 21st International Conference on Artificial Neural Networks (ICANN), pages 250–257, Espoo, Finland, June 2011. DOI: 10.1007/978-3-642-21735-7_31
dc.relation.haspart [Publication 2]: He Zhang, Tele Hao, Zhirong Yang, and Erkki Oja. Pairwise clustering with t-PLSI. In Proceedings of 22nd International Conference on Artificial Neural Networks (ICANN), pages 411–418, Lausanne, Switzerland, September 2012. DOI: 10.1007/978-3-642-33266-1_51
dc.relation.haspart [Publication 3]: Zhirong Yang, He Zhang, and Erkki Oja. Online Projective Nonnegative Matrix Factorization for large datasets. In Proceedings of 19th International Conference on Neural Information Processing (ICONIP), pages 285–290, Doha, Qatar, November 2012. DOI: 10.1007/978-3-642-34487-9_35
dc.relation.haspart [Publication 4]: He Zhang, Zhirong Yang, and Erkki Oja. Adaptive multiplicative updates for projective nonnegative matrix factorization. In Proceedings of 19th International Conference on Neural Information Processing (ICONIP), pages 277–284, Doha, Qatar, November 2012. DOI: 10.1007/978-3-642-34487-9_34
dc.relation.haspart [Publication 5]: He Zhang, Zhirong Yang, and Erkki Oja. Adaptive Multiplicative Updates for quadratic nonnegative matrix factorization. Neurocomputing, 134: 206–213, 2014. DOI: 10.1016/j.neucom.2013.06.047
dc.relation.haspart [Publication 6]: He Zhang, Zhirong Yang, and Erkki Oja. Improving cluster analysis by co-initializations. Pattern Recognition Letters, 45: 71–77, 2014. DOI: DOI: 10.1016/j.patrec.2014.03.001
dc.relation.haspart [Publication 7]: He Zhang, Teemu Ruokolainen, Jorma Laaksonen, Christina Hochleitner, and Rudolf Traunmüller. Gaze- and speech-enhanced content-based image retrieval in image tagging. In Proceedings of 21st International Conference on Artificial Neural Networks (ICANN), pages 373–380, Espoo, Finland, June 2011. DOI: 10.1007/978-3-642-21738-8_48
dc.relation.haspart [Publication 8]: He Zhang, Eimontas Augilius, Timo Honkela, Jorma Laaksonen, Hannes Gamper, and Henok Alene. Analyzing emotional semantics of abstract art using low-level image features. In Proceedings of 10th International Symposium on Intelligent Data Analysis (IDA), pages 413–423, Porto, Portugal, October 2011. DOI: 10.1007/978-3-642-24800-9_38
dc.relation.haspart [Publication 9]: He Zhang, Zhirong Yang, Mehmet Gönen, Markus Koskela, Jorma Laaksonen, Timo Honkela, and Erkki Oja. Affective abstract image classification and retrieval using multiple kernel learning. In Proceedings of 20th International Conference on Neural Information Processing (ICONIP), pages 166–175, Daegu, South Korea, November 2013. DOI: 10.1007/978-3-642-42051-1_22
dc.subject.other Computer science en
dc.title Advances in Nonnegative Matrix Decomposition with Application to Cluster Analysis en
dc.type G5 Artikkeliväitöskirja fi
dc.contributor.school Perustieteiden korkeakoulu fi
dc.contributor.school School of Science en
dc.contributor.department Tietojenkäsittelytieteen laitos fi
dc.contributor.department Department of Information and Computer Science en
dc.subject.keyword nonnegative matrix factorization en
dc.subject.keyword cluster analysis en
dc.subject.keyword multiplicative update rule en
dc.subject.keyword constrained optimization en
dc.subject.keyword initialization condition en
dc.subject.keyword image classification and retrieval en
dc.subject.keyword affective computing en
dc.subject.keyword image emotion en
dc.identifier.urn URN:ISBN:978-952-60-5829-0
dc.type.dcmitype text en
dc.type.ontasot Doctoral dissertation (article-based) en
dc.type.ontasot Väitöskirja (artikkeli) fi
dc.contributor.supervisor Oja, Erkki, Aalto Distinguished Prof., Aalto University, Department of Information and Computer Science, Finland
dc.opn Cemgil, Ali Taylan, Associate Prof., Bogazici University, Turkey
dc.date.dateaccepted 2014-06-27
dc.rev Zdunek, Rafal, Research Scientist Ph.D., Wroclaw University of Technology, Poland
dc.rev Mørup, Morten, Associate Prof., Ph.D., DTU Compute, Denmark
dc.date.defence 2014-09-19


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