{"type":"ScholarlyArticle","title":"Learning Multiple Maps from Conditional Ordinal Triplets","authors":[{"name":"Dung D. Le","slug":"dung-d-le","given":"Dung D.","family":"Le","affiliation":"School of Information Systems , Singapore Management University , Singapore"},{"name":"Hady W. Lauw","slug":"hady-w-lauw","given":"Hady W.","family":"Lauw","affiliation":"School of Information Systems , Singapore Management University , Singapore"}],"abstract":"Ordinal embedding seeks a low-dimensional representation of objects based on relative comparisons of their similarities.  This low-dimensional representation lends itself to visualization on a Euclidean map. Classical assumptions admit only one valid aspect of similarity. However, there are increasing scenarios involving ordinal comparisons that inherently reflect multiple aspects of similarity, which would be better represented by multiple maps. We formulate this problem as conditional ordinal embedding, which learns a distinct low-dimensional representation conditioned on each aspect, yet allows collaboration across aspects via a shared representation. Our geometric approach is novel in its use of a shared spherical representation and multiple aspect-specific projection maps on tangent hyperplanes. Experiments on public datasets showcase the utility of collaborative learning over baselines that learn multiple maps independently.","doi":"10.24963/ijcai.2019/390","url":"https://ijcai.org/proceedings/2019/390","pdf":"https://ijcai.org/proceedings/2019/0390.pdf","markdown":"https://ijcai.org/proceedings/2019/390.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/390","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 A-L","track":"Main track","number":390,"pages":{"first":2815,"last":2822},"keywords":["Machine Learning: Dimensionality Reduction and Manifold Learning","Machine Learning: Data Mining"],"videos":[],"references":[{"position":1,"raw":"[Absil et al., 2009] P-A Absil, Robert Mahony, and Rodolphe Sepulchre. Optimization algorithms on matrix manifolds. Princeton University Press, 2009.","title":"Optimization algorithms on matrix manifolds","authors":"P-A Absil, Robert Mahony, Rodolphe Sepulchre","year":"2009","venue":null,"doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Agarwal et al., 2007] Sameer Agarwal, Josh Wills, Lawrence Cayton, Gert Lanckriet, David J Kriegman, and Serge Belongie. Generalized non-metric multidimensional scaling. In AISTATS, pages 11-18, 2007.","title":"Generalized non-metric multidimensional scaling","authors":"Sameer Agarwal, Josh Wills, Lawrence Cayton, Gert Lanckriet, David J Kriegman, Serge Belongie","year":"2007","venue":"AISTATS","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Amid and Ukkonen, 2015] Ehsan Amid and Antti Ukko- nen. Multiview triplet embedding: Learning attributes in multiple maps. In ICML, pages 1472-1480, 2015.","title":"Ehsan Amid and Antti Ukkonen. Multiview triplet embedding: Learning attributes in multiple maps","authors":"Ukkonen Amid","year":"2015","venue":"ICML","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Argyriou et al., 2007] Andreas Argyriou, Theodoros Evge- niou, and Massimiliano Pontil. Multi-task feature learning. In NIPS, pages 41-48, 2007.","title":"Multi-task feature learning","authors":"Andreas Argyriou, Theodoros Evgeniou, Massimiliano Pontil","year":"2007","venue":"NIPS","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Bai et al., 2017] Song Bai, Xiang Bai, Longin Jan Latecki, and Qi Tian. Multidimensional scaling on multiple input distance matrices. In AAAI, pages 1281-1287, 2017.","title":"Multidimensional scaling on multiple input distance matrices","authors":"Song Bai, Xiang Bai, Longin, Jan Latecki, Qi Tian","year":"2017","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Bengio et al., 2013] Yoshua Bengio, Aaron Courville, and Pascal Vincent. Representation learning: A review and new perspectives. TPAMI, 35(8):1798-1828, 2013.","title":"Representation learning: A review and new perspectives","authors":"Yoshua Bengio, Aaron Courville, Pascal Vincent","year":"2013","venue":"TPAMI","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Blei et al., 2003] David M Blei, Andrew Y Ng, and Michael I Jordan. Latent dirichlet allocation. JMLR, 3(Jan):993-1022, 2003.","title":"Latent dirichlet allocation","authors":"Andrew Y David M Blei, Michael I Ng, Jordan","year":"2003","venue":"JMLR","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Bonnabel, 2013] Silvere Bonnabel. Stochastic gradient de- scent on riemannian manifolds. IEEE Transactions on Au- tomatic Control, 58(9):2217-2229, 2013.","title":"Stochastic gradient descent on riemannian manifolds","authors":"Silvere Bonnabel","year":"2013","venue":"IEEE Transactions on Automatic Control","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Caruana, 1997] Rich Caruana. Multitask learning. Machine Learning, 28(1):41-75, 1997.","title":"Multitask learning","authors":"Caruana","year":"1997","venue":"Machine Learning","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Cheng, 2013] Li Cheng. Riemannian similarity learning. In ICML, pages 540-548, 2013.","title":"Riemannian similarity learning","authors":"Li Cheng","year":"2013","venue":"ICML","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Estévez et al., 2009] Pablo A Estévez, Michel Tesmer, Claudio A Perez, and Jacek M Zurada. Normalized mu- tual information feature selection. IEEE Transactions on Neural Networks, 20(2):189-201, 2009.","title":"Normalized mutual information feature selection","authors":"Pablo A Estévez, Michel Tesmer, Claudio A Perez, Jacek M Zurada","year":"2009","venue":"IEEE Transactions on Neural Networks","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Ferreira et al., 2014] OP Ferreira, AN Iusem, and SZ Németh. Concepts and techniques of optimiza- tion on the sphere. TOP, 22(3):1148-1170, 2014.","title":"Concepts and techniques of optimization on the sphere","authors":"Ferreira","year":"2014","venue":"TOP","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Gilkey and others, 1975] Peter B Gilkey et al. The spectral geometry of a riemannian manifold. Journal of Differen- tial Geometry, 10(4):601-618, 1975.","title":"The spectral geometry of a riemannian manifold","authors":"Peter B Gilkey","year":"1975","venue":"Journal of Differential Geometry","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Gomes et al., 2011] Ryan G Gomes, Peter Welinder, An- dreas Krause, and Pietro Perona. Crowdclustering. In NIPS, pages 558-566, 2011.","title":"Crowdclustering","authors":"Peter Ryan G Gomes, Andreas Welinder, Pietro Krause, Perona","year":"2011","venue":"NIPS","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Le and Lauw, 2016] Dung D Le and Hady W Lauw. Eu- clidean co-embedding of ordinal data for multi-type visu- alization. In SDM, pages 396-404, 2016.","title":"Euclidean co-embedding of ordinal data for multi-type visualization","authors":"D Dung, Hady W Le, Lauw","year":"2016","venue":"SDM","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Le and Lauw, 2018] Dung D Le and Hady W Lauw. Mul- tiperspective graph-theoretic similarity measure. In Pro- ceedings of the 27th ACM International Conference on Information and Knowledge Management, pages 1223- 1232. ACM, 2018.","title":"Multiperspective graph-theoretic similarity measure","authors":"D Dung, Hady W Le, Lauw","year":"2018","venue":"Proceedings of the 27th ACM International Conference on Information and Knowledge Management","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Mardia, 1975] KV Mardia. Distribution theory for the von mises-fisher distribution and its application. In A Mod- ern Course on Statistical Distributions in Scientific Work, pages 113-130. Springer, 1975.","title":"Distribution theory for the von mises-fisher distribution and its application","authors":"; Kv Mardia, Mardia","year":"1975","venue":"A Modern Course on Statistical Distributions in Scientific Work","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[McFee and Lanckriet, 2011] Brian McFee and Gert Lanck- riet. Learning multi-modal similarity. JMLR, 12:491-523, 2011.","title":"Learning multi-modal similarity","authors":"Brian Mcfee, Gert Lanckriet","year":"2011","venue":"JMLR","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Parameswaran and Weinberger, 2010] Shibin Parameswaran and Kilian Q Weinberger. Large margin multi-task metric learning. In NIPS, pages 1867-1875, 2010.","title":"Large margin multi-task metric learning","authors":"Weinberger Parameswaran, Shibin Parameswaran, Kilian Q Weinberger","year":"2010","venue":"NIPS","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Tamuz et al., 2011] Omer Tamuz, Ce Liu, Ohad Shamir, Adam Kalai, and Serge J Belongie. Adaptively learning the crowd kernel. In ICML, pages 673-680, 2011.","title":"Adaptively learning the crowd kernel","authors":"Omer Tamuz, Ce Liu, Ohad Shamir, Adam Kalai, Serge J Belongie","year":"2011","venue":"ICML","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Terada and Luxburg, 2014] Yoshikazu Terada and Ulrike V Luxburg. Local ordinal embedding. In ICML, pages 847- 855, 2014.","title":"Local ordinal embedding","authors":"Yoshikazu Terada, Ulrike V Luxburg","year":"2014","venue":"ICML","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Van der Maaten and Hinton, 2012] Laurens Van der Maaten and Geoffrey Hinton. Visualizing non-metric similarities in multiple maps. Machine Learning, 87(1):33-55, 2012.","title":"Visualizing non-metric similarities in multiple maps","authors":"Van Der Maaten, Laurens Hinton, Geoffrey Van Der Maaten, Hinton","year":"2012","venue":"Machine Learning","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Van der Maaten and Weinberger, 2012] Laurens Van der Maaten and Kilian Weinberger. Stochastic triplet embedding. In MLSP, pages 1-6, 2012.","title":"Stochastic triplet embedding","authors":"Van Der Maaten, Laurens Weinberger, Kilian Van Der Maaten, Weinberger","year":"2012","venue":"MLSP","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Veit et al., 2017] Andreas Veit, Serge Belongie, and Theo- fanis Karaletsos. Conditional similarity networks. Com- puter Vision and Pattern Recognition (CVPR 2017), 2017.","title":"Conditional similarity networks. Computer Vision and Pattern Recognition","authors":"Andreas Veit, Serge Belongie, Theofanis Karaletsos","year":"2017","venue":null,"doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Weinberger and Saul, 2009] Kilian Q Weinberger and Lawrence K Saul. Distance metric learning for large mar- gin nearest neighbor classification. JMLR, 10:207-244, 2009.","title":"Distance metric learning for large margin nearest neighbor classification","authors":"Q Kilian, Lawrence K Weinberger, Saul","year":"2009","venue":"JMLR","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Wilber et al., 2014] Michael J Wilber, Iljung S Kwak, and Serge J Belongie. Cost-effective hits for relative similarity comparisons. In HCOMP, 2014.","title":"Cost-effective hits for relative similarity comparisons","authors":"J Michael, Iljung S Wilber, Serge J Kwak, Belongie","year":"2014","venue":"HCOMP","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Wills et al., 2009] Josh Wills, Sameer Agarwal, David Kriegman, and Serge Belongie. Toward a perceptual space for gloss. TOG, 28(4):103, 2009.","title":"Toward a perceptual space for gloss","authors":"Josh Wills, Sameer Agarwal, David Kriegman, Serge Belongie","year":"2009","venue":"TOG","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Wilson and Hancock, 2010] Richard C Wilson and Edwin R Hancock. Spherical embedding and classification. In Structural, Syntactic, and Statistical Pattern Recognition, pages 589-599. Springer, 2010.","title":"Spherical embedding and classification","authors":"C Richard, Edwin R Wilson, Hancock","year":"2010","venue":"Structural, Syntactic, and Statistical Pattern Recognition","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Wilson et al., 2010] Richard C Wilson, Edwin R Hancock, Elżbieta Pekalska, and Robert PW Duin. Spherical embed- dings for non-euclidean dissimilarities. In CVPR, pages 1903-1910, 2010.","title":"Spherical embeddings for non-euclidean dissimilarities","authors":"Edwin R Richard C Wilson, Elżbieta Hancock, Pekalska, Robert Pw Duin","year":"2010","venue":"CVPR","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Yang et al., 2013] Peipei Yang, Kaizhu Huang, and Cheng- Lin Liu. Geometry preserving multi-task metric learning. Machine Learning, 92(1):133-175, 2013.","title":"Geometry preserving multi-task metric learning","authors":"Peipei Yang, Kaizhu Huang, Cheng-Lin Liu","year":"2013","venue":"Machine Learning","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[Yang, 2007] Liu Yang. An overview of distance metric learning. In CVPR, 2007.","title":"An overview of distance metric learning","authors":"Liu Yang","year":"2007","venue":"CVPR","doi":null,"url":null,"internal_url":null},{"position":32,"raw":"[Yue et al., 2014] Yisong Yue, Chong Wang, Khalid El- Arini, and Carlos Guestrin. Personalized collaborative clustering. In WWW, pages 75-84, 2014.","title":"Personalized collaborative clustering","authors":"Yue","year":"2014","venue":"WWW","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}