In this paper, we present the factorization model PITF (Pairwise Interaction Tensor Factorization) which is a special case of the TD model with linear runtime both for learning and prediction. PITF explicitly models the pairwise interactions between users, items and tags. The model is learned with an adaption of the Bayesian personalized ranking (BPR) criterion which originally has been introduced for item recommendation. Empirically, we show on real world datasets that this model outperforms TD largely in runtime and even can achieve better prediction quality. Besides our lab experiments, PITF has also won the ECML/PKDD Discovery Challenge 2009 for graph-based tag recommendation.}, acmid = {1718498}, address = {New York, NY, USA}, author = {Rendle, Steffen and Schmidt-Thieme, Lars}, booktitle = {Proceedings of the third ACM international conference on Web search and data mining}, doi = {10.1145/1718487.1718498}, interhash = {ce8fbdf2afb954579cdb58104fb683a7}, intrahash = {10fe730b391b08031f3103f9cdbb6e1a}, isbn = {978-1-60558-889-6}, location = {New York, New York, USA}, numpages = {10}, pages = {81--90}, publisher = {ACM}, series = {WSDM '10}, title = {Pairwise interaction tensor factorization for personalized tag recommendation}, url = {http://doi.acm.org/10.1145/1718487.1718498}, year = 2010 } @inproceedings{rendle2010pairwise, abstract = {Tagging plays an important role in many recent websites. Recommender systems can help to suggest a user the tags he might want to use for tagging a specific item. Factorization models based on the Tucker Decomposition (TD) model have been shown to provide high quality tag recommendations outperforming other approaches like PageRank, FolkRank, collaborative filtering, etc. The problem with TD models is the cubic core tensor resulting in a cubic runtime in the factorization dimension for prediction and learning.
In this paper, we present the factorization model PITF (Pairwise Interaction Tensor Factorization) which is a special case of the TD model with linear runtime both for learning and prediction. PITF explicitly models the pairwise interactions between users, items and tags. The model is learned with an adaption of the Bayesian personalized ranking (BPR) criterion which originally has been introduced for item recommendation. Empirically, we show on real world datasets that this model outperforms TD largely in runtime and even can achieve better prediction quality. Besides our lab experiments, PITF has also won the ECML/PKDD Discovery Challenge 2009 for graph-based tag recommendation.}, acmid = {1718498}, address = {New York, NY, USA}, author = {Rendle, Steffen and Schmidt-Thieme, Lars}, booktitle = {Proceedings of the third ACM international conference on Web search and data mining}, doi = {10.1145/1718487.1718498}, interhash = {ce8fbdf2afb954579cdb58104fb683a7}, intrahash = {10fe730b391b08031f3103f9cdbb6e1a}, isbn = {978-1-60558-889-6}, location = {New York, New York, USA}, numpages = {10}, pages = {81--90}, publisher = {ACM}, title = {Pairwise interaction tensor factorization for personalized tag recommendation}, url = {http://doi.acm.org/10.1145/1718487.1718498}, year = 2010 } @article{kolda2009tensor, abstract = {This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or $N$-way array. Decompositions of higher-order tensors (i.e., $N$-way arrays with $N \geq 3$) have applications in psycho-metrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, and elsewhere. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decomposition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum of rank-one tensors, and the Tucker decomposition is a higher-order form of principal component analysis. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as well as nonnegative variants of all of the above. The N-way Toolbox, Tensor Toolbox, and Multilinear Engine are examples of software packages for working with tensors.}, author = {Kolda, Tamara G. and Bader, Brett W.}, doi = {10.1137/07070111X}, interhash = {b30bb2d42e1a05fc41370c50844822ad}, intrahash = {e52e5c7bff59fd01fb6497d3bb620077}, issn = {00361445}, journal = {SIAM Review}, number = 3, pages = {455--500}, publisher = {SIAM}, title = {Tensor Decompositions and Applications}, url = {http://dx.doi.org/10.1137/07070111X}, volume = 51, year = 2009 } @article{journals/siamrev/KoldaB09, author = {Kolda, Tamara G. and Bader, Brett W.}, ee = {http://dx.doi.org/10.1137/07070111X}, interhash = {b30bb2d42e1a05fc41370c50844822ad}, intrahash = {6b115affb18f3f1f99411596c03787f8}, journal = {SIAM Review}, number = 3, pages = {455-500}, title = {Tensor Decompositions and Applications.}, url = {http://dblp.uni-trier.de/db/journals/siamrev/siamrev51.html#KoldaB09}, volume = 51, year = 2009 } @inproceedings{Cai:2011:LTD:1935826.1935920, abstract = {Social tagging recommendation is an urgent and useful enabling technology for Web 2.0. In this paper, we present a systematic study of low-order tensor decomposition approach that are specifically targeted at the very sparse data problem in tagging recommendation problem. Low-order polynomials have low functional complexity, are uniquely capable of enhancing statistics and also avoids over-fitting than traditional tensor decompositions such as Tucker and Parafac decompositions. We perform extensive experiments on several datasets and compared with 6 existing methods. Experimental results demonstrate that our approach outperforms existing approaches.}, acmid = {1935920}, address = {New York, NY, USA}, author = {Cai, Yuanzhe and Zhang, Miao and Luo, Dijun and Ding, Chris and Chakravarthy, Sharma}, booktitle = {Proceedings of the fourth ACM international conference on Web search and data mining}, doi = {10.1145/1935826.1935920}, interhash = {414f80ad09d994af6f448446c04cd226}, intrahash = {52a9e5fd121bf7be4fa8670cc93a7197}, isbn = {978-1-4503-0493-1}, location = {Hong Kong, China}, numpages = {10}, pages = {695--704}, publisher = {ACM}, series = {WSDM '11}, title = {Low-order tensor decompositions for social tagging recommendation}, url = {http://doi.acm.org/10.1145/1935826.1935920}, year = 2011 } @inproceedings{marinho:ecml2009, abstract = {This paper describes our approach to the ECML/PKDD Discovery Challenge 2009. Our approach is a pure statistical model taking no content information into account. It tries to find latent interactions between users, items and tags by factorizing the observed tagging data. The factorization model is learned by the Bayesian Personal Ranking method (BPR) which is inspired by a Bayesian analysis of personalized ranking with missing data. To prevent overfitting, we ensemble the models over several iterations and hyperparameters. Finally, we enhance the top-n lists by estimating how many tags to recommend.}, address = {Bled, Slovenia}, author = {Rendle, Steffen and Schmidt-Thieme, Lars}, booktitle = {ECML PKDD Discovery Challenge 2009 (DC09)}, editor = {Eisterlehner, Folke and Hotho, Andreas and Jäschke, Robert}, interhash = {8485850cde1a6b61971cac27fa867845}, intrahash = {ceed045a84e121fa37384f797306d30f}, issn = {1613-0073}, month = {September}, pages = {235--242}, publisher = {CEUR Workshop Proceedings}, title = {Factor Models for Tag Recommendation in BibSonomy}, url = {http://sunsite.informatik.rwth-aachen.de/Publications/CEUR-WS/Vol-497/}, volume = 497, year = 2009 } @inproceedings{kdml2, abstract = {The discovery of communities or interrelations in social networks has become an important area of research. The increasing amount of information available in these networks and its decreasing life-time poses tight constraints on the information processing – storage of the data is often prohibited due to its sheer volume. In this paper we adapt a flexible approach for community discovery offering the integration of new information into the model. The continuous integration is combined with a time-based weighting of the data allowing for disposing obsolete information from the model building process. We demonstrate the usefulness of our approach by applying it on the popular Twitter network. The proposed solution can be directly fed with streaming data from Twitter, providing an up-todate community model.}, address = {Kassel, Germany}, author = {Bockermann, Christian and Jungermann., Felix}, booktitle = {Proceedings of LWA2010 - Workshop-Woche: Lernen, Wissen {\&} Adaptivitaet}, crossref = {lwa2010}, editor = {Atzmüller, Martin and Benz, Dominik and Hotho, Andreas and Stumme, Gerd}, interhash = {25e36bf796df1bd4c22a0a4b0c2d60cf}, intrahash = {e0e77b218030558331e985746e824da0}, presentation_end = {2010-10-05 16:22:30}, presentation_start = {2010-10-05 16:00:00}, room = {0446}, session = {kdml2}, title = {Stream-based Community Discovery via Relational Hypergraph Factorization on Evolving Networks}, track = {kdml}, url = {http://www.kde.cs.uni-kassel.de/conf/lwa10/papers/kdml2.pdf}, year = 2010 } @inproceedings{rendle2009learning, abstract = {Tag recommendation is the task of predicting a personalized list of tags for a user given an item. This is important for many websites with tagging capabilities like last.fm or delicious. In this paper, we propose a method for tag recommendation based on tensor factorization (TF). In contrast to other TF methods like higher order singular value decomposition (HOSVD), our method RTF ('ranking with tensor factorization') directly optimizes the factorization model for the best personalized ranking. RTF handles missing values and learns from pairwise ranking constraints. Our optimization criterion for TF is motivated by a detailed analysis of the problem and of interpretation schemes for the observed data in tagging systems. In all, RTF directly optimizes for the actual problem using a correct interpretation of the data. We provide a gradient descent algorithm to solve our optimization problem. We also provide an improved learning and prediction method with runtime complexity analysis for RTF. The prediction runtime of RTF is independent of the number of observations and only depends on the factorization dimensions. Besides the theoretical analysis, we empirically show that our method outperforms other state-of-the-art tag recommendation methods like FolkRank, PageRank and HOSVD both in quality and prediction runtime.}, address = {New York, NY, USA}, author = {Rendle, Steffen and Marinho, Leandro Balby and Nanopoulos, Alexandros and Schmidt-Thieme, Lars}, booktitle = {KDD '09: Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining}, doi = {10.1145/1557019.1557100}, interhash = {1cc85ca2ec82db2a3caf40fd1795a58a}, intrahash = {1bd672ffb8d6ba5589bb0c7deca09412}, isbn = {978-1-60558-495-9}, location = {Paris, France}, pages = {727--736}, publisher = {ACM}, title = {Learning optimal ranking with tensor factorization for tag recommendation}, url = {http://portal.acm.org/citation.cfm?doid=1557019.1557100}, year = 2009 } @inproceedings{rendle2009learning, abstract = {Tag recommendation is the task of predicting a personalized list of tags for a user given an item. This is important for many websites with tagging capabilities like last.fm or delicious. In this paper, we propose a method for tag recommendation based on tensor factorization (TF). In contrast to other TF methods like higher order singular value decomposition (HOSVD), our method RTF ('ranking with tensor factorization') directly optimizes the factorization model for the best personalized ranking. RTF handles missing values and learns from pairwise ranking constraints. Our optimization criterion for TF is motivated by a detailed analysis of the problem and of interpretation schemes for the observed data in tagging systems. In all, RTF directly optimizes for the actual problem using a correct interpretation of the data. We provide a gradient descent algorithm to solve our optimization problem. We also provide an improved learning and prediction method with runtime complexity analysis for RTF. The prediction runtime of RTF is independent of the number of observations and only depends on the factorization dimensions. Besides the theoretical analysis, we empirically show that our method outperforms other state-of-the-art tag recommendation methods like FolkRank, PageRank and HOSVD both in quality and prediction runtime.}, address = {New York, NY, USA}, author = {Rendle, Steffen and Balby Marinho, Leandro and Nanopoulos, Alexandros and Schmidt-Thieme, Lars}, booktitle = {KDD '09: Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining}, doi = {10.1145/1557019.1557100}, interhash = {1cc85ca2ec82db2a3caf40fd1795a58a}, intrahash = {1bd672ffb8d6ba5589bb0c7deca09412}, isbn = {978-1-60558-495-9}, location = {Paris, France}, pages = {727--736}, publisher = {ACM}, title = {Learning optimal ranking with tensor factorization for tag recommendation}, url = {http://portal.acm.org/citation.cfm?doid=1557019.1557100}, year = 2009 } @article{wiley2009, address = {DTU Informatics, Intelligent Signal Processing, Richard Petersens Plads, Bld. 321 2800 Kgs. Lyngby, Denmark}, author = {Mørup, Morten and Hansen, Lars Kai}, doi = {10.1002/cem.1223}, interhash = {a9c89408e829272eed988d01f0694612}, intrahash = {6f4df21cfb3f6f7da188b66dd61c0ad9}, journal = {Journal of Chemometrics}, number = {7-8}, pages = {352-363}, publisher = {Copyright © 2009 John Wiley & Sons, Ltd.}, title = {Automatic relevance determination for multi-way models}, url = {http://dx.doi.org/10.1002/cem.1223}, volume = 23, year = 2009 } @inproceedings{1557100, abstract = {Tag recommendation is the task of predicting a personalized list of tags for a user given an item. This is important for many websites with tagging capabilities like last.fm or delicious. In this paper, we propose a method for tag recommendation based on tensor factorization (TF). In contrast to other TF methods like higher order singular value decomposition (HOSVD), our method RTF ('ranking with tensor factorization') directly optimizes the factorization model for the best personalized ranking. RTF handles missing values and learns from pairwise ranking constraints. Our optimization criterion for TF is motivated by a detailed analysis of the problem and of interpretation schemes for the observed data in tagging systems. In all, RTF directly optimizes for the actual problem using a correct interpretation of the data. We provide a gradient descent algorithm to solve our optimization problem. We also provide an improved learning and prediction method with runtime complexity analysis for RTF. The prediction runtime of RTF is independent of the number of observations and only depends on the factorization dimensions. Besides the theoretical analysis, we empirically show that our method outperforms other state-of-the-art tag recommendation methods like FolkRank, PageRank and HOSVD both in quality and prediction runtime.}, address = {New York, NY, USA}, author = {Rendle, Steffen and Marinho, Leandro Balby and Nanopoulos, Alexandros and Schmidt-Thieme, Lars}, booktitle = {KDD '09: Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining}, doi = {http://doi.acm.org/10.1145/1557019.1557100}, interhash = {1cc85ca2ec82db2a3caf40fd1795a58a}, intrahash = {1bd672ffb8d6ba5589bb0c7deca09412}, isbn = {978-1-60558-495-9}, location = {Paris, France}, pages = {727--736}, publisher = {ACM}, title = {Learning optimal ranking with tensor factorization for tag recommendation}, url = {http://portal.acm.org/citation.cfm?id=1557019.1557100&coll=ACM&dl=ACM&type=series&idx=SERIES939&part=series&WantType=Proceedings&title=KDD}, year = 2009 } @inproceedings{1454017, address = {New York, NY, USA}, author = {Symeonidis, Panagiotis and Nanopoulos, Alexandros and Manolopoulos, Yannis}, booktitle = {RecSys '08: Proceedings of the 2008 ACM conference on Recommender systems}, doi = {http://doi.acm.org/10.1145/1454008.1454017}, interhash = {8ee38f4ffc05845fcb98f121fb265d48}, intrahash = {e93afe409833a632af02290bbe134cba}, isbn = {978-1-60558-093-7}, location = {Lausanne, Switzerland}, pages = {43--50}, publisher = {ACM}, title = {Tag recommendations based on tensor dimensionality reduction}, url = {http://portal.acm.org/citation.cfm?id=1454017}, year = 2008 } @inproceedings{WaAh04, author = {Wang, Hongcheng and Ahuja, Narendra}, booktitle = {ICPR (1)}, ee = {http://csdl.computer.org/comp/proceedings/icpr/2004/2128/01/212810044abs.htm}, interhash = {8e1acfd0bb4bb34d6bf26bd9a476019b}, intrahash = {b6ca9a81389eef7bc3c5d8c7141ec8db}, pages = {44-47}, title = {Compact Representation of Multidimensional Data Using Tensor Rank-One Decomposition.}, url = {http://vision.ai.uiuc.edu/~wanghc/papers/icpr04_tensor.pdf}, year = 2004 }