{"type":"ScholarlyArticle","title":"Persistence Bag-of-Words for Topological Data Analysis","authors":[{"name":"Bartosz Zieliński","slug":"bartosz-zielinski","given":"Bartosz","family":"Zieliński","affiliation":"The Institute of Computer Science and Computer Mathematics ,"},{"name":"Michał Lipiński","slug":"micha-lipinski","given":"Michał","family":"Lipiński","affiliation":"The Institute of Computer Science and Computer Mathematics ,; Faculty of Mathematics and Computer Science , Jagiellonian University"},{"name":"Mateusz Juda","slug":"mateusz-juda","given":"Mateusz","family":"Juda","affiliation":"The Institute of Computer Science and Computer Mathematics ,"},{"name":"Matthias Zeppelzauer","slug":"matthias-zeppelzauer","given":"Matthias","family":"Zeppelzauer","affiliation":"Media Computing Group , Institute of Creative Media Technologies , St. Pölten University of Applied Sciences ,"},{"name":"Paweł Dłotko","slug":"pawe-d-otko","given":"Paweł","family":"Dłotko","affiliation":"Department of Mathematics and Swansea Academy of Advanced Computing , Swansea University"}],"abstract":"Persistent homology (PH) is a rigorous mathematical theory that provides a robust descriptor of data in the form of persistence diagrams (PDs). PDs exhibit, however, complex structure and are difficult to integrate in today's machine learning workflows. This paper introduces persistence bag-of-words: a novel and stable vectorized representation of PDs that enables the seamless integration with machine learning. Comprehensive experiments show that the new representation achieves state-of-the-art performance and beyond in much less time than alternative approaches.","doi":"10.24963/ijcai.2019/624","url":"https://ijcai.org/proceedings/2019/624","pdf":"https://ijcai.org/proceedings/2019/0624.pdf","markdown":"https://ijcai.org/proceedings/2019/624.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/624","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Machine Learning M-Z","track":"Main track","number":624,"pages":{"first":4489,"last":4495},"keywords":["Machine Learning: Dimensionality Reduction and Manifold Learning","Computer Vision: Recognition: Detection, Categorization, Indexing, Matching, Retrieval, Semantic Interpretation","Computer Vision: Statistical Methods and Machine Learning","Machine Learning: Classification"],"videos":[],"references":[{"position":1,"raw":"[Adams et al., 2017] Henry Adams, Sofya Chepushtanova, Tegan Emerson, Eric Hanson, Michael Kirby, Francis Motta, Rachel Neville, Chris Peterson, Patrick Shipman, and Lori Ziegelmeier. Persistence images: a stable vector representation of persistent homology. Journal of Machine Learning Research, 18(8):1-35, 2017.","title":"Persistence images: a stable vector representation of persistent homology","authors":"Henry Adams, Sofya Chepushtanova, Tegan Emerson, Eric Hanson, Michael Kirby, Francis Motta, Rachel Neville, Chris Peterson, Patrick Shipman, Lori Ziegelmeier","year":"2017","venue":"Journal of Machine Learning Research","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Anirudh et al., 2016] Rushil Anirudh, Vinay Venkataraman, Karthikeyan Natesan Ramamurthy, and Pavan Turaga. A rieman- nian framework for statistical analysis of topological persistence diagrams. In Proc. of IEEE CVPR -Workshops, pages 68-76, 2016.","title":"A riemannian framework for statistical analysis of topological persistence diagrams","authors":"Rushil Anirudh, Vinay Venkataraman, Karthikeyan Natesan Ramamurthy, Pavan Turaga","year":"2016","venue":"Proc. of IEEE CVPR -Workshops","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Baeza-Yates and Ribeiro-Neto, 1999] Ricardo Baeza-Yates and Berthier Ribeiro-Neto. Modern information retrieval, volume 463. ACM press New York, 1999.","title":"Modern information retrieval","authors":"Baeza-Yates, Ribeiro-Neto ; Baeza-Yates, Berthier Ribeiro-Neto","year":"1999","venue":"Ricardo","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Bauer et al., 2017] Ulrich Bauer, Michael Kerber, Jan Reining- haus, and Hubert Wagner. Phat-persistent homology algorithms toolbox. Journal of Symbolic Computation, 78:76-90, 2017.","title":"Phat-persistent homology algorithms toolbox","authors":"Bauer","year":"2017","venue":"Journal of Symbolic Computation","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Bubenik, 2015] Peter Bubenik. Statistical topological data analy- sis using persistence landscapes. JMLR, 16(1):77-102, 2015.","title":"Statistical topological data analysis using persistence landscapes","authors":"Peter Bubenik","year":"2015","venue":"JMLR","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Carrière et al., 2017] Mathieu Carrière, Marco Cuturi, and Steve Oudot. Sliced wasserstein kernel for persistence diagrams. In ICML, 2017.","title":"Sliced wasserstein kernel for persistence diagrams","authors":"Marco Mathieu Carrière, Steve Cuturi, Oudot","year":"2017","venue":"ICML","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[DeGol et al., 2016] Joseph DeGol, Mani Golparvar-Fard, and Derek Hoiem. Geometry-informed material recognition. In Proc. of CVPR, pages 1554-1562, 2016.","title":"Geometry-informed material recognition","authors":"Joseph Degol, Mani Golparvar-Fard, Derek Hoiem","year":"2016","venue":"Proc. of CVPR","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Dey et al., 2019] Tamal K. Dey, Dayu Shi, and Yusu Wang. Simba: An efficient tool for approximating rips-filtration persistence via simplicial batch collapse. J. Exp. Algorithmics, 24(1):1.5:1- 1.5:16, January 2019.","title":"Simba: An efficient tool for approximating rips-filtration persistence via simplicial batch collapse","authors":"K Tamal, Dayu Dey, Yusu Shi, Wang","year":"2019","venue":"J. Exp. Algorithmics","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Donatini et al., 1998] Pietro Donatini, Patrizio Frosini, and Al- berto Lovato. Size functions for signature recognition. In Proc. SPIE, volume 3454, pages 178-183, 1998.","title":"Size functions for signature recognition","authors":"Pietro Donatini, Patrizio Frosini, Alberto Lovato","year":"1998","venue":"Proc. SPIE","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Edelsbrunner and Harer, 2010] Herbert Edelsbrunner and John Harer. Computational topology: an introduction. American Mathematical Soc., 2010.","title":"Computational topology: an introduction","authors":"Harer Edelsbrunner, Herbert Edelsbrunner, John Harer","year":"2010","venue":null,"doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Ferri et al., 1998] Massimo Ferri, Patrizio Frosini, Alberto Lovato, and Chiara Zambelli. Point selection: A new comparison scheme for size functions (with an application to monogram recogni- tion). In Computer Vision -ACCV'98. LNCS., volume 1351, pages 329-337. Springer, 1998.","title":"Point selection: A new comparison scheme for size functions (with an application to monogram recognition)","authors":"Massimo Ferri, Patrizio Frosini, Alberto Lovato, Chiara Zambelli","year":"1998","venue":"Computer Vision -ACCV'98","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Ferri, 2017] Massimo Ferri. Persistent topology for natural data analysis -a survey. In Towards Integrative Machine Learn- ing and Knowledge Extraction, pages 117-133, Cham, 2017. Springer International Publishing.","title":"Persistent topology for natural data analysis -a survey","authors":"Massimo Ferri","year":"2017","venue":"Towards Integrative Machine Learning and Knowledge Extraction","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Gameiro et al., 2014] Marcio Gameiro, Yasuaki Hiraoka, Shun- suke Izumi, Miroslav Kramàr, Konstantin Mischaikow, and Vidit Nanda. A topological measurement of protein compressibility. Japan J.of Industrl. and Appl. Mathem., 32(1):1-17, 2014.","title":"A topological measurement of protein compressibility","authors":"Marcio Gameiro, Yasuaki Hiraoka, Shunsuke Izumi, Miroslav Kramàr, Konstantin Mischaikow, Vidit Nanda","year":"2014","venue":"Japan J.of Industrl. and Appl. Mathem","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Gidea and Katz, 2018] Marian Gidea and Yuri Katz. Topological data analysis of financial time series: Landscapes of crashes. Physica A: Statistical Mechanics and its Applications, 491:820- 834, 2018.","title":"Topological data analysis of financial time series: Landscapes of crashes","authors":"Katz Gidea, Marian Gidea, Yuri Katz","year":"2018","venue":"Physica A: Statistical Mechanics and its Applications","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Hofer et al., 2017] Christoph Hofer, Roland Kwitt, Marc Nietham- mer, and Andreas Uhl. Deep learning with topological signatures. In Advances in Neural Information Processing Systems, pages 1633-1643, 2017.","title":"Deep learning with topological signatures","authors":"Christoph Hofer, Roland Kwitt, Marc Niethammer, Andreas Uhl","year":"2017","venue":"Advances in Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Kerber et al., 2017] Michael Kerber, Dmitriy Morozov, and Arnur Nigmetov. Geometry helps to compare persistence diagrams. Journal of Experimental Algorithmics (JEA), 22:1-4, 2017.","title":"Geometry helps to compare persistence diagrams","authors":"Kerber","year":"2017","venue":"Journal of Experimental Algorithmics (JEA)","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Khrulkov and Oseledets, 2018] Valentin Khrulkov and Ivan Os- eledets. Geometry score: A method for comparing generative adversarial networks. In Proc. of the 35th ICML, volume 80, pages 2621-2629. PMLR, 2018.","title":"Geometry score: A method for comparing generative adversarial networks","authors":"Valentin Khrulkov, Ivan Oseledets","year":"2018","venue":"Proc. of the 35th ICML","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Lacombe et al., 2018] Théo Lacombe, Marco Cuturi, and Steve Oudot. Large scale computation of means and clusters for persis- tence diagrams using optimal transport. arXiv:1805.08331, 2018.","title":"Large scale computation of means and clusters for persistence diagrams using optimal transport","authors":"Théo Lacombe, Marco Cuturi, Steve Oudot","year":"2018","venue":null,"doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Le and Yamada, 2018] Tam Le and Makoto Yamada. Persistence fisher kernel: A riemannian manifold kernel for persistence di- agrams. In Adv. in Neural Inf. Proc. Sys., pages 10028-10039, 2018.","title":"Persistence fisher kernel: A riemannian manifold kernel for persistence diagrams","authors":"Tam Le, Makoto Yamada","year":"2018","venue":"Adv. in Neural Inf. Proc. Sys","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Lee et al., 2017] Yongjin Lee, Senja D. Barthel, Paweł Dłotko, S. Mohamad Moosavi, Kathryn Hess, and Berend Smit. Quanti- fying similarity of pore-geometry in nanoporous materials. Na- ture Communications, 8(15396), 2017.","title":"Quantifying similarity of pore-geometry in nanoporous materials","authors":"Yongjin Lee, Senja D Barthel, Paweł Dłotko, S Mohamad Moosavi, Kathryn Hess, Berend Smit","year":"2017","venue":"Nature Communications","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Li et al., 2014] Chunyuan Li, Maks Ovsjanikov, and Frédéric Chazal. Persistence-based structural recognition. In IEEE CVPR, pages 2003-2010. IEEE, 2014.","title":"Persistence-based structural recognition","authors":"Chunyuan Li, Maks Ovsjanikov, Frédéric Chazal","year":"2014","venue":"IEEE CVPR","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Maria et al., 2014] Clément Maria, Jean-Daniel Boissonnat, Marc Glisse, and Mariette Yvinec. The gudhi library: Simplicial com- plexes and persistent homology. In International Congress on Mathematical Software, pages 167-174. Springer, 2014.","title":"The gudhi library: Simplicial complexes and persistent homology","authors":"Clément Maria, Jean-Daniel Boissonnat, Marc Glisse, Mariette Yvinec","year":"2014","venue":"International Congress on Mathematical Software","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[McCallum and Nigam, 1998] Andrew McCallum and Kamal Nigam. A comparison of event models for naive bayes text classification. In AAAI-98 workshop on learning for text categorization, volume 752, pages 41-48, 1998.","title":"A comparison of event models for naive bayes text classification","authors":"Andrew Mccallum, Kamal Nigam","year":"1998","venue":"AAAI-98 workshop on learning for text categorization","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Nasrabadi, 2007] Nasser M. Nasrabadi. Pattern recognition and machine learning. J. of electronic imaging, 16(4):049901, 2007.","title":"Pattern recognition and machine learning","authors":"M Nasser, Nasrabadi","year":"2007","venue":"J. of electronic imaging","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Perronnin et al., 2010] Florent Perronnin, Jorge Sénchez, and Yan Liu Xerox. Large-scale image categorization with explicit data embedding. In Computer Vision and Pattern Recognition (CVPR), 2010 IEEE Conference on, pages 2297-2304. IEEE, 2010.","title":"Large-scale image categorization with explicit data embedding","authors":"Florent Perronnin, Jorge Sénchez, Yan Liu, Xerox","year":"2010","venue":"Computer Vision and Pattern Recognition (CVPR), 2010 IEEE Conference on","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Reininghaus et al., 2015] Jan Reininghaus, Stefan Huber, Ulrich Bauer, and Roland Kwitt. A stable multi-scale kernel for topo- logical machine learning. In 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 4741-4748, June 2015.","title":"A stable multi-scale kernel for topological machine learning","authors":"Reininghaus","year":"2015","venue":"IEEE Conference on Computer Vision and Pattern Recognition (CVPR)","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Rieck et al., 2018] Bastian Rieck, Matteo Togninalli, Christian Bock, Michael Moor, Max Horn, Thomas Gumbsch, and Karsten Borgwardt. Neural persistence: A complexity measure for deep neural networks using algebraic topology. arXiv:1812.09764, 2018.","title":"Neural persistence: A complexity measure for deep neural networks using algebraic topology","authors":"Bastian Rieck, Matteo Togninalli, Christian Bock, Michael Moor, Max Horn, Thomas Gumbsch, Karsten Borgwardt","year":"2018","venue":null,"doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Sivic and Zisserman, 2003] Josef Sivic and Andrew Zisserman. Video google: A text retrieval approach to object matching in videos. In IEEE ICCV, 2003, pages 1470-1477. IEEE, 2003.","title":"Video google: A text retrieval approach to object matching in videos","authors":"Zisserman Sivic, Josef Sivic, Andrew Zisserman","year":"2003","venue":"IEEE ICCV","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Van Gemert et al., 2008] Jan C. Van Gemert, Jan-Mark Geuse- broek, Cor J. Veenman, and Arnold W. M. Smeulders. Kernel codebooks for scene categorization. In European conference on computer vision, pages 696-709. Springer, 2008.","title":"Kernel codebooks for scene categorization","authors":"Jan C Van Gemert, Jan-Mark Geusebroek, Cor J Veenman, Arnold W M Smeulders","year":"2008","venue":"European conference on computer vision","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Vedaldi and Fulkerson, 2008] Andrea Vedaldi and Brian Fulker- son. VLFeat: An open and portable library of computer vision algorithms. http://www.vlfeat.org/, 2008.","title":"Andrea Vedaldi and Brian Fulkerson. VLFeat: An open and portable library of computer vision algorithms","authors":"Fulkerson Vedaldi","year":"2008","venue":null,"doi":null,"url":"http://www.vlfeat.org/,2008","internal_url":null},{"position":31,"raw":"[Zeppelzauer et al., 2017] Matthias Zeppelzauer, Bartosz Zieliński, Mateusz Juda, and Markus Seidl. A study on topological de- scriptors for the analysis of 3d surface texture. Comp. Vision and Image Underst., 2017.","title":"A study on topological descriptors for the analysis of 3d surface texture","authors":"Matthias Zeppelzauer, Bartosz Zieliński, Mateusz Juda, Markus Seidl","year":"2017","venue":"Comp. Vision and Image Underst","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}