survey

Public Access

Tensors for Data Mining and Data Fusion: Models, Applications, and Scalable Algorithms

Authors:

Evangelos E. Papalexakis,

Christos Faloutsos,

Nicholas D. SidiropoulosAuthors Info & Claims

ACM Transactions on Intelligent Systems and Technology (TIST), Volume 8, Issue 2

Article No.: 16, Pages 1 - 44

https://doi.org/10.1145/2915921

Published: 03 October 2016 Publication History

Abstract

Tensors and tensor decompositions are very powerful and versatile tools that can model a wide variety of heterogeneous, multiaspect data. As a result, tensor decompositions, which extract useful latent information out of multiaspect data tensors, have witnessed increasing popularity and adoption by the data mining community. In this survey, we present some of the most widely used tensor decompositions, providing the key insights behind them, and summarizing them from a practitioner’s point of view. We then provide an overview of a very broad spectrum of applications where tensors have been instrumental in achieving state-of-the-art performance, ranging from social network analysis to brain data analysis, and from web mining to healthcare. Subsequently, we present recent algorithmic advances in scaling tensor decompositions up to today’s big data, outlining the existing systems and summarizing the key ideas behind them. Finally, we conclude with a list of challenges and open problems that outline exciting future research directions.

References

[1]

Evrim Acar, Canan Aykut-Bingol, Haluk Bingol, Rasmus Bro, and Bülent Yener. 2007. Multiway analysis of epilepsy tensors. Bioinformatics 23, 13 (2007), i10--i18.

Digital Library

[2]

Evrim Acar, Seyit A. Çamtepe, Mukkai S. Krishnamoorthy, and Bülent Yener. 2005. Modeling and multiway analysis of chatroom tensors. In Intelligence and Security Informatics. Springer, 256--268. 10.1007/11427995_21

Digital Library

[3]

Evrim Acar, Daniel M. Dunlavy, and Tamara G. Kolda. 2009. Link prediction on evolving data using matrix and tensor factorizations. In Proceedings of the 2009 IEEE International Conference on Data Mining Workshops (ICDMW’09). 262--269.

Digital Library

[4]

Evrim Acar, Daniel M. Dunlavy, and Tamara G. Kolda. 2011. A scalable optimization approach for fitting canonical tensor decompositions. Journal of Chemometrics 25, 2 (2011), 67--86.

[5]

Evrim Acar, Daniel M. Dunlavy, Tamara G. Kolda, and Morten Mørup. 2010. Scalable tensor factorizations with missing data. In SIAM International Conference on Data Mining (SDM). SIAM, 701--712.

[6]

Evrim Acar, Daniel M. Dunlavy, Tamara G. Kolda, and Morten Mørup. 2011. Scalable tensor factorizations for incomplete data. Chemometrics and Intelligent Laboratory Systems 106, 1 (March 2011), 41--56.

[7]

Evrim Acar, Gözde Gurdeniz, Morten A. Rasmussen, Daniela Rago, Lars O. Dragsted, and Rasmus Bro. 2012. Coupled matrix factorization with sparse factors to identify potential biomarkers in metabolomics. In IEEE International Conference on Data Mining Workshops (ICDMW). IEEE, 1--8.

Digital Library

[8]

Evrim Acar, Tamara G. Kolda, and Daniel M. Dunlavy. 2011. All-at-once optimization for coupled matrix and tensor factorizations. In Proceedings of Mining and Learning with Graphs (MLG’11). https://www.cs.purdue.edu/mlg2011/papers/paper_4.pdf.

[9]

Evrim Acar, Anders J. Lawaetz, Morten Rasmussen, and Rasmus Bro. 2013. Structure-revealing data fusion model with applications in metabolomics. In 2013 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC’13). IEEE, 6023--6026.

[10]

Evrim Acar, Evangelos E. Papalexakis, Morten A. Rasmussen, Anders J. Lawaetz, Mathias Nilsson, and Rasmus Bro. 2014. Structure-revealing data fusion. BMC Bioinformatics 15, 1 (2014), 239.

[11]

Evrim Acar, George Plopper, and Bülent Yener. 2012. Coupled analysis of in vitro and histology tissue samples to quantify structure-function relationship. PloS One 7, 3 (2012), e32227.

[12]

Evrim Acar and Bülent Yener. 2009. Unsupervised multiway data analysis: A literature survey. IEEE Transactions on Knowledge and Data Engineering, 21, 1 (2009), 6--20.

Digital Library

[13]

Rakesh Agrawal, Behzad Golshan, and Evangelos Papalexakis. 2015a. A study of distinctiveness in web results of two search engines. In 24th International Conference on World Wide Web, Web Science Track. ACM.

Digital Library

[14]

Rakesh Agrawal, Behzad Golshan, and Evangelos Papalexakis. 2015b. Whither social networks for web search? In 21st ACM SIGKDD Conference on Knowledge Discovery and Data Mining. Sydney, Australia.

Digital Library

[15]

Animashree Anandkumar, Rong Ge, Daniel Hsu, Sham M. Kakade, and Matus Telgarsky. 2014. Tensor decompositions for learning latent variable models. Journal of Machine Learning Research 15, 1 (2014), 2773--2832.

Digital Library

[16]

Miguel Araujo, Spiros Papadimitriou, Stephan Günnemann, Christos Faloutsos, Prithwish Basu, Ananthram Swami, Evangelos E. Papalexakis, and Danai Koutra. 2014. Com2: Fast automatic discovery of temporal (‘comet’) communities. In Advances in Knowledge Discovery and Data Mining. Springer, 271--283. 978-3-319-06605-9_23

[17]

Woody Austin, Grey Ballard, and Tamara G. Kolda. 2016. Parallel tensor compression for large-scale scientific data. In Proceedings of the 30th IEEE International Parallel & Distributed Processing Symposium (IPDPS’16).

[18]

Brett W. Bader, Richard A. Harshman, and Tamara G. Kolda. 2007. Temporal analysis of semantic graphs using ASALSAN. In 7th IEEE International Conference on Data Mining, 2007 (ICDM’07). IEEE, 33--42.

Digital Library

[19]

Brett W. Bader and Tamara G. Kolda. 2007. Efficient MATLAB computations with sparse and factored tensors. SIAM Journal on Scientific Computing 30, 1 (Dec. 2007), 205--231.

Digital Library

[20]

Brett W. Bader and Tamara G. Kolda. 2015. MATLAB Tensor Toolbox Version 2.6. Available online. (February 2015). http://www.sandia.gov/&sim;tgkolda/TensorToolbox/.

[21]

Jonas Ballani, Lars Grasedyck, and Melanie Kluge. 2013. Black box approximation of tensors in hierarchical Tucker format. Linear Algebra and Its Applications 438, 2 (2013), 639--657.

[22]

Arindam Banerjee, Sugato Basu, and Srujana Merugu. 2007. Multi-way clustering on relation graphs. In SIAM International Conference on Data Mining (SDM). Vol. 7. SIAM, 145--156.

[23]

Alex Beutel, Abhimanu Kumar, Evangelos Papalexakis, Partha Pratim Talukdar, Christos Faloutsos, and Eric P. Xing. 2014. FLEXIFACT: Scalable flexible factorization of coupled tensors on hadoop. In SIAM International Conference on Data Mining (SDM). SIAM.

[24]

David M. Blei, Andrew Y. Ng, and Michael I. Jordan. 2003. Latent Dirichlet allocation. Journal of Machine Learning Research 3 (2003), 993--1022.

Digital Library

[25]

Stephen Boyd, Neal Parikh, Eric Chu, Borja Peleato, and Jonathan Eckstein. 2011. Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends in Machine Learning 3, 1 (2011), 1--122.

Digital Library

[26]

John W. Brewer. 1978. Kronecker products and matrix calculus in system theory. IEEE Transactions on Circuits and Systems 25, 9 (1978), 772--781.

[27]

Rasmus Bro. 1998. Multi-way Analysis in the Food Industry: Models, Algorithms, and Applications. Ph.D. Dissertation. Københavns Universitet’Københavns Universitet’, LUKKET: 2012 Det Biovidenskabelige Fakultet for Fødevarer, Veterinærmedicin og NaturressourcerFaculty of Life Sciences, LUKKET: 2012 Institut for FødevarevidenskabDepartment of Food Science, 2012 Institut for Fødevarevidenskab, 2012 Kvalitet og TeknologiDepartment of Food Science, Quality & Technology.

[28]

Rasmus Bro and Claus A. Andersson. 1998. Improving the speed of multiway algorithms: Part II: Compression. Chemometrics and Intelligent Laboratory Systems 42, 1 (1998), 105--113.

[29]

Rasmus Bro and Henk A. L. Kiers. 2003. A new efficient method for determining the number of components in PARAFAC models. Journal of Chemometrics 17, 5 (2003), 274--286.

[30]

Cesar F. Caiafa and Andrzej Cichocki. 2010. Generalizing the column--row matrix decomposition to multi-way arrays. Linear Algebra Applications 433, 3 (2010), 557--573.

[31]

J. Douglas Carroll and Jih-Jie Chang. 1970. Analysis of individual differences in multidimensional scaling via an N-way generalization of ‘Eckart-Young’ decomposition. Psychometrika 35, 3 (1970), 283--319.

[32]

J. Douglas Carroll, Sandra Pruzansky, and Joseph B. Kruskal. 1980. CANDELINC: A general approach to multidimensional analysis of many-way arrays with linear constraints on parameters. Psychometrika 45, 1 (1980), 3--24.

[33]

Kai-Wei Chang, Wen-tau Yih, and Christopher Meek. 2013. Multi-relational latent semantic analysis. In Proceedings of the 2013 Conference on Empirical Methods in Natural Language Processing (EMNLP’13). 1602--1612.

[34]

Kai-Wei Chang, Wen-tau Yih, Bishan Yang, and Christopher Meek. 2014. Typed tensor decomposition of knowledge bases for relation extraction. In Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP’14). 1568--1579.

[35]

Peter A. Chew, Brett W. Bader, Tamara G. Kolda, and Ahmed Abdelali. 2007. Cross-language information retrieval using PARAFAC2. In Proceedings of the 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM, 143--152.

Digital Library

[36]

Eric C. Chi and Tamara G. Kolda. 2012. On tensors, sparsity, and nonnegative factorizations. SIAM Journal of Matrix Analysis & Applications 33, 4 (2012), 1272--1299.

[37]

Luca Chiantini and Giorgio Ottaviani. 2012. On generic identifiability of 3-tensors of small rank. SIAM Journal of Matrix Analysis & Applications 33, 3 (2012), 1018--1037.

[38]

Joon Hee Choi and S. Vishwanathan. 2014. DFacTo: Distributed factorization of tensors. In Advances in Neural Information Processing Systems 27, Z. Ghahramani, M. Welling, C. Cortes, N. D. Lawrence, and K. Q. Weinberger (Eds.). Curran Associates, 1296--1304. http://papers.nips.cc/paper/5395-dfacto-distributed-factorization-of-tensors.pdf.

Digital Library

[39]

Andrzej Cichocki, Danilo Mandic, Lieven De Lathauwer, Guoxu Zhou, Qibin Zhao, Cesar Caiafa, and Huy Anh Phan. 2015. Tensor decompositions for signal processing applications: From two-way to multiway component analysis. IEEE Signal Processing Magazine 32, 2 (2015), 145--163.

[40]

Andrzej Cichocki, Rafal Zdunek, Anh Huy Phan, and S. Amari. 2009. Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-Way Data Analysis and Blind Source Separation. John Wiley & Sons.

Digital Library

[41]

Jeremy E. Cohen, Rodrigo Cabral Farias, and Pierre Comon. 2015. Fast decomposition of large nonnegative tensors. IEEE Signal Processing Letters 22, 7 (2015), 862--866.

[42]

Joao Paulo C. L. da Costa, Martin Haardt, and F. Romer. 2008. Robust methods based on the HOSVD for estimating the model order in PARAFAC models. In 5th Sensor Array and Multichannel Signal Processing Workshop, 2008 (SAM’08). IEEE, 510--514.

[43]

Ian Davidson, Sean Gilpin, Owen Carmichael, and Peter Walker. 2013. Network discovery via constrained tensor analysis of fMRI data. In Proceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM, 194--202.

Digital Library

[44]

André L. F. De Almeida and Alain Y. Kibangou. 2014. Distributed large-scale tensor decomposition. In 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP’14).

[45]

Lieven De Lathauwer, Bart De Moor, and Joos Vandewalle. 2000. A multilinear singular value decomposition. SIAM Journal on Matrix Analysis and Applications 21, 4 (2000), 1253--1278.

Digital Library

[46]

S. Deerwester, S. T. Dumais, G. W. Furnas, T. K. Landauer, and R. Harshman. 1990. Indexing by latent semantic analysis. Journal of the American Society for Information Science 41, 6 (Sept. 1990), 391--407.

[47]

Petros Drineas, Ravi Kannan, and Michael W. Mahoney. 2006. Fast Monte Carlo algorithms for matrices III: Computing a compressed approximate matrix decomposition. SIAM Journal on Computing 36, 1 (2006), 184.

Digital Library

[48]

Daniel M. Dunlavy, Tamara G. Kolda, and Evrim Acar. 2011. Temporal link prediction using matrix and tensor factorizations. ACM Transactions on Knowledge Discovery from Data 5, 2 (Feb. 2011).

Digital Library

[49]

Dóra Erdos and Pauli Miettinen. 2013. Walk’n’merge: A scalable algorithm for boolean tensor factorization. In 2013 IEEE 13th International Conference on Data Mining (ICDM’13). IEEE, 1037--1042.

[50]

Beyza Ermiş, Evrim Acar, and A. Taylan Cemgil. 2015. Link prediction in heterogeneous data via generalized coupled tensor factorization. Data Mining and Knowledge Discovery 29, 1 (2015), 203--236.

Digital Library

[51]

Lars Grasedyck. 2010. Hierarchical singular value decomposition of tensors. SIAM Journal of Matrix Analysis & Applications 31, 4 (2010), 2029--2054.

Digital Library

[52]

Lars Grasedyck, Daniel Kressner, and Christine Tobler. 2013. A literature survey of low-rank tensor approximation techniques. GAMM-Mitteilungen 36, 1 (2013), 53--78.

[53]

Wolfgang Hackbusch and Stefan Kühn. 2009. A new scheme for the tensor representation. Journal of Fourier Analysis and Applications 15, 5 (2009), 706--722.

[54]

Samantha Hansen, Todd Plantenga, and Tamara G. Kolda. 2015. Newton-based optimization for Kullback-Leibler nonnegative tensor factorizations. Optimization Methods and Software 30, 5 (April 2015), 1002--1029.

Digital Library

[55]

Richard A. Harshman. 1970. Foundations of the PARAFAC procedure: Models and conditions for an “explanatory” multimodal factor analysis. UCLA Working Papers in Phonetics 16 (1970), 1--84.

[56]

Richard A. Harshman. 1972. PARAFAC2: Mathematical and technical notes. UCLA Working Papers in Phonetics 22 (1972), 30--44.

[57]

Richard A. Harshman. 1978. Models for analysis of asymmetrical relationships among N objects or stimuli. In 1st Joint Meeting of the Psychometric Society and the Society for Mathematical Psychology. McMaster University, Hamilton, Ontario.

[58]

Richard A. Harshman. 1984. How can I know if its real? A Catalog of Diagnostics for Use with Three-Mode Factor Analysis and Multidimensional Scaling. 566--591.

[59]

Richard A. Harshman, Sungjin Hong, and Margaret E. Lundy. 2003. Shifted factor analysis—Part I: Models and properties. Journal of Chemometrics 17, 7 (2003), 363--378.

[60]

Lifang He, Xiangnan Kong, S. Yu Philip, Ann B. Ragin, Zhifeng Hao, and Xiaowei Yang. 2014. Dusk: A dual structure-preserving kernel for supervised tensor learning with applications to neuroimages. Matrix 3, 1 (2014), 2.

[61]

Frank L. Hitchcock. 1927. The expression of a tensor or a polyadic as a sum of products. Journal of Mathematics and Physics 6, 1 (1927), 164--189.

[62]

Joyce C. Ho, Joydeep Ghosh, and Jimeng Sun. 2014. Marble: High-throughput phenotyping from electronic health records via sparse nonnegative tensor factorization. In Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM, 115--124.

Digital Library

[63]

Furong Huang, Sergiy Matusevych, Anima Anandkumar, Nikos Karampatziakis, and Paul Mineiro. 2014. Distributed latent Dirichlet allocation via tensor factorization. Neural Information Processing Systems (NIPS) Optimization Workshop 2014.

[64]

Furong Huang, U. N. Niranjan, Mohammad Umar Hakeem, and Animashree Anandkumar. 2013. Fast detection of overlapping communities via online tensor methods. arXiv preprint arXiv:1309.0787 (2013).

[65]

ByungSoo Jeon, L. S. I. Jeon, and U. Kang. 2016. SCouT: Scalable coupled matrix-tensor factorization algorithm and discoveries. In International Conference on Data Engineering (ICDE). IEEE.

[66]

Inah Jeon, Evangelos E. Papalexakis, U. Kang, and Christos Faloutsos. 2015. Haten2: Billion-scale tensor decompositions. In International Conference on Data Engineering (ICDE).

[67]

Meng Jiang, Peng Cui, Fei Wang, Xinran Xu, Wenwu Zhu, and Shiqiang Yang. 2014. FEMA: Flexible evolutionary multi-faceted analysis for dynamic behavioral pattern discovery. In Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM, 1186--1195.

Digital Library

[68]

Tao Jiang and Nicholas D. Sidiropoulos. 2004. Kruskal’s permutation lemma and the identification of CANDECOMP/PARAFAC and bilinear models with constant modulus constraints. IEEE Transactions on Signal Processing 52, 9 (2004), 2625--2636.

Digital Library

[69]

U. Kang, Evangelos Papalexakis, Abhay Harpale, and Christos Faloutsos. 2012. Gigatensor: Scaling tensor analysis up by 100 times-algorithms and discoveries. In Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM, 316--324.

Digital Library

[70]

Alexandros Karatzoglou, Xavier Amatriain, Linas Baltrunas, and Nuria Oliver. 2010. Multiverse recommendation: N-dimensional tensor factorization for context-aware collaborative filtering. In Proceedings of the 4th ACM Conference on Recommender Systems. ACM, 79--86.

Digital Library

[71]

Henk A. L. Kiers. 1993. An alternating least squares algorithm for PARAFAC2 and three-way DEDICOM. Computational Statistics & Data Analysis 16, 1 (1993), 103--118.

Digital Library

[72]

Henk A. L. Kiers and Albert Kinderen. 2003. A fast method for choosing the numbers of components in Tucker3 analysis. British Journal of Mathematical and Statistical Psychology 56, 1 (2003), 119--125.

[73]

Henk A. L. Kiers. 1997. Weighted least squares fitting using ordinary least squares algorithms. Psychometrika 62, 2 (June 1997), 215--266.

[74]

Mijung Kim and K. Selçuk Candan. 2012. Decomposition-by-normalization (DBN): Leveraging approximate functional dependencies for efficient tensor decomposition. In Proceedings of the 21st ACM International Conference on Information and Knowledge Management. ACM, 355--364.

Digital Library

[75]

Eleftherios Kofidis and Phillip A. Regalia. 2002. On the best rank-1 approximation of higher-order supersymmetric tensors. SIAM Journal on Matrix Analysis & Applications 23, 3 (2002), 863--884.

Digital Library

[76]

Tamara G. Kolda and Brett W. Bader. 2009. Tensor decompositions and applications. SIAM Reviews 51, 3 (2009).

Digital Library

[77]

Tamara G. Kolda, Brett W. Bader, and Joseph P. Kenny. 2005. Higher-order web link analysis using multilinear algebra. In 5th IEEE International Conference on Data Mining. IEEE, 8--pp.

Digital Library

[78]

Tamara G. Kolda and Jackson R. Mayo. 2011. Shifted power method for computing tensor eigenpairs. SIAM Journal on Matrix Analysis & Applications 32, 4 (Oct. 2011), 1095--1124.

[79]

Tamara G. Kolda and Jimeng Sun. 2008. Scalable tensor decompositions for multi-aspect data mining. In 8th IEEE International Conference on Data Mining, 2008 (ICDM’08). IEEE, 363--372.

Digital Library

[80]

Daniel Kressner and Christine Tobler. 2012. Htucker--A matlab toolbox for tensors in hierarchical Tucker format. Mathicse, EPF Lausanne (2012).

[81]

Joseph B. Kruskal. 1977. Three-way arrays: Rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics. Linear Algebra and Its Applications 18, 2 (1977), 95--138.

[82]

Daniel D. Lee and H. Sebastian Seung. 1999. Learning the parts of objects by non-negative matrix factorization. Nature 401, 6755 (1999), 788--791.

[83]

Athanasios P. Liavas and Nicholas D. Sidiropoulos. 2015. Parallel algorithms for constrained tensor factorization via alternating direction method of multipliers. IEEE Transactions on Signal Processing, 63, 20 (2015), 5450--5463.

Digital Library

[84]

Yu-Ru Lin, Jimeng Sun, Paul Castro, Ravi Konuru, Hari Sundaram, and Aisling Kelliher. 2009. Metafac: Community discovery via relational hypergraph factorization. In Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM, 527--536.

Digital Library

[85]

Ji Liu, Przemyslaw Musialski, Peter Wonka, and Jieping Ye. 2013. Tensor completion for estimating missing values in visual data. IEEE Transactions on Pattern Analysis and Machine Intelligence, 35, 1 (2013), 208--220.

Digital Library

[86]

Haiping Lu, Konstantinos N. Plataniotis, and Anastasios N. Venetsanopoulos. 2011. A survey of multilinear subspace learning for tensor data. Pattern Recognition 44, 7 (2011), 1540--1551.

Digital Library

[87]

Machine Learning Department. 2016. Carnegie Mellon University. Read the Web. http://rtw.ml.cmu.edu/rtw/. (Last accessed: 2/13/2016).

[88]

Michael W. Mahoney, Mauro Maggioni, and Petros Drineas. 2008. Tensor-CUR decompositions for tensor-based data. SIAM Journal on Matrix Analysis & Applications 30, 3 (2008), 957--987.

Digital Library

[89]

Ching-Hao Mao, Chung-Jung Wu, Evangelos E. Papalexakis, Christos Faloutsos, and Tien-Cheu Kao. 2014. MalSpot: Multi2 malicious network behavior patterns analysis. In Pacific Asia Conference on Knowledge Discovery and Data Mining (PAKDD) 2014.

[90]

K. Maruhashi, F. Guo, and C. Faloutsos. 2011. MultiAspectForensics: Pattern mining on large-scale heterogeneous networks with tensor analysis. In Proceedings of the 3rd International Conference on Advances in Social Network Analysis and Mining.

Digital Library

[91]

Saskia Metzler and Pauli Miettinen. 2015. Clustering boolean tensors. Data Mining and Knowledge Discovery 29, 5 (2015), 1343--1373.

Digital Library

[92]

Pauli Miettinen. 2011. Boolean tensor factorizations. In 2011 IEEE 11th International Conference on Data Mining (ICDM’11). IEEE, 447--456.

Digital Library

[93]

Shahin Mohammadi, David Gleich, Tamara Kolda, and Ananth Grama. 2016. Triangular alignment (TAME): A tensor-based approach for higher-order network alignment. IEEE/ACM Transactions on Computational Biology and Bioinformatics (2016).

[94]

Morten Mørup and Lars Kai Hansen. 2009. Automatic relevance determination for multi-way models. Journal of Chemometrics 23, 7--8 (2009), 352--363.

[95]

Morten Mørup, Lars Kai Hansen, Sidse Marie Arnfred, Lek-Heng Lim, and Kristoffer Hougaard Madsen. 2008. Shift-invariant multilinear decomposition of neuroimaging data. NeuroImage 42, 4 (2008), 1439--1450.

[96]

Morten Mørup, Lars Kai Hansen, and Kristoffer Hougaard Madsen. 2011. Modeling latency and shape changes in trial based neuroimaging data. In 2011 Conference Record of the 45th Asilomar Conference on Signals, Systems and Computers (ASILOMAR’11). IEEE, 439--443.

[97]

Yang Mu, Wei Ding, Melissa Morabito, and Dacheng Tao. 2011. Empirical discriminative tensor analysis for crime forecasting. In Knowledge Science, Engineering and Management. Springer, 293--304.

Digital Library

[98]

Atsuhiro Narita, Kohei Hayashi, Ryota Tomioka, and Hisashi Kashima. 2012. Tensor factorization using auxiliary information. Data Mining and Knowledge Discovery 25, 2 (2012), 298--324.

Digital Library

[99]

Maximilian Nickel, Volker Tresp, and Hans-Peter Kriegel. 2011. A three-way model for collective learning on multi-relational data. In Proceedings of the 28th International Conference on Machine Learning (ICML’11). 809--816.

Digital Library

[100]

Maximilian Nickel, Volker Tresp, and Hans-Peter Kriegel. 2012. Factorizing YAGO: Scalable machine learning for linked data. In Proceedings of the 21st International Conference on World Wide Web. ACM, 271--280.

Digital Library

[101]

Dimitri Nion, Kleanthis N. Mokios, Nicholas D. Sidiropoulos, and Alexandros Potamianos. 2010. Batch and adaptive PARAFAC-based blind separation of convolutive speech mixtures. IEEE Transactions on Audio, Speech, and Language Processing, 18, 6 (2010), 1193--1207.

Digital Library

[102]

Dimitri Nion and Nicholas D. Sidiropoulos. 2009. Adaptive algorithms to track the PARAFAC decomposition of a third-order tensor. IEEE Transactions on Signal Processing, 57, 6 (2009), 2299--2310.

Digital Library

[103]

Ivan V. Oseledets. 2011. Tensor-train decomposition. SIAM Journal on Scientific Computing 33, 5 (2011), 2295--2317.

Digital Library

[104]

Pentti Paatero. 1997. A weighted non-negative least squares algorithm for three-way “PARAFAC” factor analysis. Chemometrics and Intelligent Laboratory Systems 38, 2 (Oct. 1997), 223--242.

[105]

Evangelia Pantraki and Constantine Kotropoulos. 2015. Automatic image tagging and recommendation via PARAFAC2. In 2015 IEEE 25th International Workshop on Machine Learning for Signal Processing (MLSP’15). IEEE, 1--6.

[106]

Evangelos E. Papalexakis and Christos Faloutsos. 2015. Fast efficient and scalable core consistency diagnostic for the PARAFAC decomposition for big sparse tensors. In 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP’15). IEEE.

[107]

Evangelos E. Papalexakis, Leman Akoglu, and Dino Ienco. 2013. Do more views of a graph help? Community detection and clustering in multi-graphs. In 2013 16th International Conference on Information Fusion (FUSION’13). IEEE, 899--905.

[108]

Evangelos E. Papalexakis, Christos Faloutsos, and Nicholas D. Sidiropoulos. 2012. ParCube: Sparse parallelizable tensor decompositions. In Machine Learning and Knowledge Discovery in Databases. Springer, 521--536.

[109]

Evangelos E. Papalexakis, Tom M. Mitchell, Nicholas D. Sidiropoulos, Christos Faloutsos, Partha Pratim Talukdar, and Brian Murphy. 2014. Turbo-SMT: Accelerating coupled sparse matrix-tensor factorizations by 200x. In SIAM International Conference on Data Mining (SDM). SIAM.

[110]

Evangelos E. Papalexakis, Nicholas D. Sidiropoulos, and Rasmus Bro. 2013. From k-means to higher-way co-clustering: Multilinear decomposition with sparse latent factors. IEEE Transactions on Signal Processing, 61, 2 (2013), 493--506.

Digital Library

[111]

Jing Peng, Daniel Dajun Zeng, Huimin Zhao, and Fei-yue Wang. 2010. Collaborative filtering in social tagging systems based on joint item-tag recommendations. In Proceedings of the 19th ACM International Conference on Information and Knowledge Management. ACM, 809--818.

Digital Library

[112]

Ioakeim Perros, Robert Chen, Richard Vuduc, and Jimeng Sun. 2015. Sparse hierarchical tucker factorization and its application to healthcare. In 2015 IEEE 15th International Conference on Data Mining (ICDM’15). IEEE.

Digital Library

[113]

Anh-Huy Phan and Andrzej Cichocki. 2009. Block decomposition for very large-scale nonnegative tensor factorization. In 2009 3rd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP’09). IEEE, 316--319.

[114]

Anh-Huy Phan, Petr Tichavský, and Andrzej Cichocki. 2013. Low complexity damped Gauss--Newton algorithms for CANDECOMP/PARAFAC. SIAM Journal on Matrix Analysis & Applications 34, 1 (Jan. 2013), 126--147.

[115]

Niranjay Ravindran, Nicholas D. Sidiropoulos, Shaden Smith, and George Karypis. 2014. Memory-efficient parallel computation of tensor and matrix products for big tensor decomposition. In 2014 48th Asilomar Conference on Signals, Systems and Computers. IEEE, 581--585.

[116]

Steffen Rendle. 2010. Factorization machines. In 2010 IEEE 10th International Conference on Data Mining (ICDM’10). IEEE, 995--1000.

Digital Library

[117]

Steffen Rendle and Lars Schmidt-Thieme. 2010. Pairwise interaction tensor factorization for personalized tag recommendation. In Proceedings of the 3rd ACM International Conference on Web Search and Data Mining. ACM, 81--90.

Digital Library

[118]

Ruslan Salakhutdinov and Andriy Mnih. 2008. Bayesian probabilistic matrix factorization using Markov chain Monte Carlo. In Proceedings of the 25th International Conference on Machine Learning. ACM, 880--887.

Digital Library

[119]

Aaron Schein, John Paisley, David M. Blei, and Hanna Wallach. 2015. Bayesian poisson tensor factorization for inferring multilateral relations from sparse dyadic event counts. In Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM, 1045--1054.

Digital Library

[120]

Amnon Shashua and Tamir Hazan. 2005. Non-negative tensor factorization with applications to statistics and computer vision. In Proceedings of the 22nd International Conference on Machine Learning. ACM, 792--799.

Digital Library

[121]

Kijung Shin and U. Kang. 2014. Distributed methods for high-dimensional and large-scale tensor factorization. In 2014 IEEE International Conference on Data Mining (ICDM’14). IEEE, 989--994.

Digital Library

[122]

Nicholas Sidiropoulos, Evangelos Papalexakis, and Christos Faloutsos. 2014. Parallel randomly compressed cubes: A scalable distributed architecture for big tensor decomposition. IEEE Signal Processing Magazine 31, 5 (2014), 57--70.

[123]

Nicholas D. Sidiropoulos and Rasmus Bro. 2000. On the uniqueness of multilinear decomposition of N-way arrays. Journal of Chemometrics 14, 3 (2000), 229--239.

[124]

Nicholas D. Sidiropoulos and Anastasios Kyrillidis. 2012. Multi-way compressed sensing for sparse low-rank tensors. IEEE Signal Processing Letters 19, 11 (2012), 757--760.

[125]

Ajit P. Singh and Geoffrey J. Gordon. 2008. Relational learning via collective matrix factorization. In Proceedings of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM, 650--658.

Digital Library

[126]

Age K. Smilde, Johan A. Westerhuis, and Ricard Boqué. 2000. Multiway multiblock component and covariates regression models. Journal of Chemometrics 14, 3 (2000), 301--331.

[127]

Shaden Smith, Niranjay Ravindran, Nicholas D. Sidiropoulos, and George Karypis. 2015. SPLATT: Efficient and parallel sparse tensor-matrix multiplication. In 29th IEEE International Parallel & Distributed Processing Symposium.

Digital Library

[128]

A. Stegeman, J. M. F. ten Berge, and L. De Lathauwer. 2006. Sufficient conditions for uniqueness in CANDECOMP/PARAFAC and INDSCAL with random component matrices. Psychometrika 71, 2 (2006), 219--229.

[129]

Fabian M. Suchanek, Gjergji Kasneci, and Gerhard Weikum. 2007. Yago: A core of semantic knowledge unifying wordnet and wikipedia. In 16th International World Wide Web Conference (WWW’07). 697--706.

Digital Library

[130]

Jimeng Sun, Dacheng Tao, and Christos Faloutsos. 2006. Beyond streams and graphs: Dynamic tensor analysis. In Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM, 374--383.

Digital Library

[131]

Jimeng Sun, Charalampos E. Tsourakakis, Evan Hoke, Christos Faloutsos, and Tina Eliassi-Rad. 2008. Two heads better than one: Pattern discovery in time-evolving multi-aspect data. Data Mining and Knowledge Discovery 17, 1 (2008), 111--128.

Digital Library

[132]

Jian-Tao Sun, Hua-Jun Zeng, Huan Liu, Yuchang Lu, and Zheng Chen. 2005. CubeSVD: A novel approach to personalized web search. In Proceedings of the 14th International Conference on World Wide Web. ACM, 382--390.

Digital Library

[133]

Yizhou Sun, Jiawei Han, Xifeng Yan, Philip S. Yu, and Tianyi Wu. 2011. Pathsim: Meta path-based top-k similarity search in heterogeneous information networks. International Conference on Very Large Data Bases (VLDB) (2011).

Digital Library

[134]

Dacheng Tao, Mingli Song, Xuelong Li, Jialie Shen, Jimeng Sun, Xindong Wu, Christos Faloutsos, and Stephen J. Maybank. 2008. Bayesian tensor approach for 3-D face modeling. IEEE Transactions on Circuits and Systems for Video Technology, 18, 10 (2008), 1397--1410.

Digital Library

[135]

Jos M. F. ten Berge and Nikolaos D. Sidiropoulos. 2002. On uniqueness in CANDECOMP/PARAFAC. Psychometrika 67, 3 (2002), 399--409.

[136]

Marieke E. Timmerman and Henk A. L. Kiers. 2000. Three-mode principal components analysis: Choosing the numbers of components and sensitivity to local optima. British Journal of Mathematical and Statistical Psychology 53, 1 (2000), 1--16.

[137]

Giorgio Tomasi and Rasmus Bro. 2005. PARAFAC and missing values. Chemometrics and Intelligent Laboratory Systems 75, 2 (2005), 163--180.

[138]

Giorgio Tomasi and Rasmus Bro. 2006. A comparison of algorithms for fitting the PARAFAC model. Computational Statistics & Data Analysis 50, 7 (2006), 1700--1734.

Digital Library

[139]

Charalampos E. Tsourakakis. 2010. MACH: Fast randomized tensor decompositions. In SIAM International Conference on Data Mining (SDM). SIAM, 689--700.

[140]

L. R. Tucker. 1966. Some mathematical notes on three-mode factor analysis. Psychometrika 31, 3 (1966), 279--311.

[141]

Alex M. Vasilescu and Demetri Terzopoulos. 2002. Multilinear analysis of image ensembles: Tensorfaces. Computer Vision ECCV 2002 (2002), 447--460.

Digital Library

[142]

Yilun Wang, Yu Zheng, and Yexiang Xue. 2014. Travel time estimation of a path using sparse trajectories. In Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD’14). ACM, New York, NY, 25--34.

Digital Library

[143]

Tom Wilderjans, Eva Ceulemans, and Iven Van Mechelen. 2009. Simultaneous analysis of coupled data blocks differing in size: A comparison of two weighting schemes. Computational Statistics & Data Analysis 53, 4 (2009), 1086--1098.

Digital Library

[144]

Liang Xiong, Xi Chen, Tzu-Kuo Huang, Jeff G. Schneider, and Jaime G. Carbonell. 2010. Temporal collaborative filtering with Bayesian probabilistic tensor factorization. In SIAM International Conference on Data Mining (SDM). Vol. 10. SIAM, 211--222.

[145]

Tatsuya Yokota, Andrzej Cichocki, and Yukihiko Yamashita. 2012. Linked PARAFAC/CP tensor decomposition and its fast implementation for multi-block tensor analysis. In Neural Information Processing. Springer, 84--91.

Digital Library

[146]

Fuzheng Zhang, Nicholas Jing Yuan, David Wilkie, Yu Zheng, and Xing Xie. 2015. Sensing the pulse of urban refueling behavior: A perspective from taxi mobility. ACM Transactions on Intelligent Systems and Technology (TIST) 6, 3 (2015), 37.

Digital Library

[147]

Q. Zhao, L. Zhang, and A. Cichocki. 2015. Bayesian CP factorization of incomplete tensors with automatic rank determination. IEEE Transactions on Pattern Analysis and Machine Intelligence, 37 (2015), 1751--1763.

Digital Library

[148]

Vincent Wenchen Zheng, Bin Cao, Yu Zheng, Xing Xie, and Qiang Yang. 2010. Collaborative filtering meets mobile recommendation: A user-centered approach. In AAAI International Conference on Artificial Intelligence (AAAI). Vol. 10. 236--241.

Digital Library

[149]

Vincent W. Zheng, Yu Zheng, Xing Xie, and Qiang Yang. 2012. Towards mobile intelligence: Learning from GPS history data for collaborative recommendation. Artificial Intelligence 184 (2012), 17--37.

Digital Library

[150]

Yu Zheng, Tong Liu, Yilun Wang, Yanmin Zhu, Yanchi Liu, and Eric Chang. 2014. Diagnosing New York City’s noises with ubiquitous data. In Proceedings of the 2014 ACM International Joint Conference on Pervasive and Ubiquitous Computing. ACM, 715--725.

Digital Library

Cited By

Li LHoefsloot HBakker BHorner DRasmussen MSmilde AAcar E(2024)Longitudinal Metabolomics Data Analysis Informed by Mechanistic ModelsMetabolites10.3390/metabo1501000215:1(2)Online publication date: 24-Dec-2024
https://doi.org/10.3390/metabo15010002
Pandey DVenugopal ALeib H(2024)Linear to multi-linear algebra and systems using tensorsFrontiers in Applied Mathematics and Statistics10.3389/fams.2023.12598369Online publication date: 5-Feb-2024
https://doi.org/10.3389/fams.2023.1259836
Li LYan SBakker BHoefsloot HChawes BHorner DRasmussen MSmilde AAcar E(2024)Analyzing postprandial metabolomics data using multiway models: a simulation studyBMC Bioinformatics10.1186/s12859-024-05686-w25:1Online publication date: 4-Mar-2024
https://doi.org/10.1186/s12859-024-05686-w
Show More Cited By

Index Terms

Tensors for Data Mining and Data Fusion: Models, Applications, and Scalable Algorithms

Recommendations

Tensor Completion Algorithms in Big Data Analytics

Tensor completion is a problem of filling the missing or unobserved entries of partially observed tensors. Due to the multidimensional character of tensors in describing complex datasets, tensor completion algorithms and their applications have received ...
Tensor Factorization with Total Variation and Tikhonov Regularization for Low-Rank Tensor Completion in Imaging Data
Abstract
The main aim of this paper is to study tensor factorization for low-rank tensor completion in imaging data. Due to the underlying redundancy of real-world imaging data, the low-tubal-rank tensor factorization (the tensor–tensor product of two ...
On the Nuclear Norm and the Singular Value Decomposition of Tensors

Finding the rank of a tensor is a problem that has many applications. Unfortunately, it is often very difficult to determine the rank of a given tensor. Inspired by the heuristics of convex relaxation, we consider the nuclear norm instead of the rank of ...

Comments

Information & Contributors

Information

Published In

cover image ACM Transactions on Intelligent Systems and Technology

ACM Transactions on Intelligent Systems and Technology Volume 8, Issue 2

Survey Paper, Special Issue: Intelligent Music Systems and Applications and Regular Papers

March 2017

407 pages

ISSN:2157-6904

EISSN:2157-6912

DOI:10.1145/3004291

Editor:
Yu Zheng
Microsoft Research, China

Issue’s Table of Contents

Copyright © 2016 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 03 October 2016

Accepted: 01 April 2016

Received: 01 February 2016

Published in TIST Volume 8, Issue 2

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Survey
Research
Refereed

Funding Sources

National Science Foundation

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

226
Total Citations
View Citations
8,033
Total Downloads

Downloads (Last 12 months)695
Downloads (Last 6 weeks)90

Reflects downloads up to 09 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Li LHoefsloot HBakker BHorner DRasmussen MSmilde AAcar E(2024)Longitudinal Metabolomics Data Analysis Informed by Mechanistic ModelsMetabolites10.3390/metabo1501000215:1(2)Online publication date: 24-Dec-2024
https://doi.org/10.3390/metabo15010002
Pandey DVenugopal ALeib H(2024)Linear to multi-linear algebra and systems using tensorsFrontiers in Applied Mathematics and Statistics10.3389/fams.2023.12598369Online publication date: 5-Feb-2024
https://doi.org/10.3389/fams.2023.1259836
Li LYan SBakker BHoefsloot HChawes BHorner DRasmussen MSmilde AAcar E(2024)Analyzing postprandial metabolomics data using multiway models: a simulation studyBMC Bioinformatics10.1186/s12859-024-05686-w25:1Online publication date: 4-Mar-2024
https://doi.org/10.1186/s12859-024-05686-w
Keshavarz ALakizadeh A(2024)PU-GNNInternational Journal of Intelligent Systems10.1155/2024/47496682024Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1155/2024/4749668
Yi ZXie M(2024)Polypharmacy side effect prediction based on semi-implicit graph variational auto-encoderJournal of Bioinformatics and Computational Biology10.1142/S021972002450020322:04Online publication date: 12-Sep-2024
https://doi.org/10.1142/S0219720024500203
Wu HQiao YLuo X(2024)A Fine-Grained Regularization Scheme for Nonnegative Latent Factorization of High-Dimensional and Incomplete TensorsIEEE Transactions on Services Computing10.1109/TSC.2024.3486171(1-15)Online publication date: 2024
https://doi.org/10.1109/TSC.2024.3486171
Qin WWang HZhang FMa WWang JHuang T(2024)Nonconvex Robust High-Order Tensor Completion Using Randomized Low-Rank ApproximationIEEE Transactions on Image Processing10.1109/TIP.2024.338528433(2835-2850)Online publication date: 10-Apr-2024
https://dl.acm.org/doi/10.1109/TIP.2024.3385284
Chen XZou YLi CXiao W(2024)A Deep Learning Based Lightweight Human Activity Recognition System Using Reconstructed WiFi CSIIEEE Transactions on Human-Machine Systems10.1109/THMS.2023.334869454:1(68-78)Online publication date: Feb-2024
https://doi.org/10.1109/THMS.2023.3348694
Benjamin JYang M(2024)Tensor-Based Possibilistic C-Means ClusteringIEEE Transactions on Fuzzy Systems10.1109/TFUZZ.2024.343573032:10(5939-5950)Online publication date: 1-Oct-2024
https://dl.acm.org/doi/10.1109/TFUZZ.2024.3435730
Qin WLuo X(2024)Asynchronous Parallel Fuzzy Stochastic Gradient Descent for High-Dimensional Incomplete Data RepresentationIEEE Transactions on Fuzzy Systems10.1109/TFUZZ.2023.330037032:2(445-459)Online publication date: Feb-2024
https://doi.org/10.1109/TFUZZ.2023.3300370
Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Article

Media

Figures

Other

Tables

View Issue’s Table of Contents