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Unsupervised Multiway Data Analysis: A Literature Survey
Abstract
Two-way arrays or matrices are often not enough to represent all the information in the data and standard two-way analysis techniques commonly applied on matrices may fail to find the underlying structures in multi-modal datasets. Multiway data analysis has recently become popular as an exploratory analysis tool in discovering the structures in higher-order datasets, where data have more than two modes. We provide a review of significant contributions in the literature on multiway models, algorithms as well as their applications in diverse disciplines including chemometrics, neuroscience, social network analysis, text mining and computer vision.
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Cites
Golub, G. (2012) · doi:10.56021/9781421407944 · Cited by 34,505
Tensor Decompositions and Applications
Kolda, T. G., & Bader, B. W. (2009) · SIAM Review · doi:10.1137/07070111x · Cited by 10,301
Kernel Methods for Pattern Analysis
Shawe-Taylor, J., & Cristianini, N. (2004) · Cambridge University Press eBooks · doi:10.1017/cbo9780511809682 · Cited by 6,587
Carroll, J. D., & Chang, J.-J. (1970) · Psychometrika · doi:10.1007/bf02310791 · Cited by 4,678
A Multilinear Singular Value Decomposition
De Lathauwer, L., De Moor, B., & Vandewalle, J. (2000) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/s0895479896305696 · Cited by 4,106
Two-dimensional pca: a new approach to appearance-based face representation and recognition
Yang, J., Zhang, D., Frangi, A. F., & Yang, J.-Y. (2004) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2004.1261097 · Cited by 3,563
Some Mathematical Notes on Three-Mode Factor Analysis
Tucker, L. R. (1966) · Psychometrika · doi:10.1007/bf02289464 · Cited by 3,492
PARAFAC. Tutorial and applications
Bro, R. (1997) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/s0169-7439(97)00032-4 · Cited by 2,814
Harshman, R. A. (1970) · Cited by 2,255
On the Best Rank-1 and Rank-(R1 ,R2 ,. . .,RN) Approximation of Higher-Order Tensors
De Lathauwer, L., De Moor, B., & Vandewalle, J. (2000) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/s0895479898346995 · Cited by 1,567
Lubin, A., & Harris, C. W. (1965) · The American Journal of Psychology · doi:10.2307/1420518 · Cited by 1,363
The Expression of a Tensor or a Polyadic as a Sum of Products
Hitchcock, F. L. (1927) · Journal of Mathematics and Physics · doi:10.1002/sapm192761164 · Cited by 1,345
A new efficient method for determining the number of components in PARAFAC models
Bro, R., & Kiers, H. A. L. (2003) · Journal of Chemometrics · doi:10.1002/cem.801 · Cited by 1,257
Andersson, C. A., & Bro, R. (2000) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/s0169-7439(00)00071-x · Cited by 1,229
Introduction to Factor Analysis: What It Is and How to Do It.
Harper, D., Kim, J.-O., & Mueller, C. W. (1980) · Contemporary Sociology · doi:10.2307/2066279 · Cited by 1,186
Multi‐Way Analysis with Applications in the Chemical Sciences
Smilde, A., Bro, R., & Geladi, P. (2004) · Wiley eBooks · doi:10.1002/0470012110 · Cited by 1,176
Multilinear Analysis of Image Ensembles: TensorFaces
Vasilescu, M. A. O., & Terzopoulos, D. (2002) · Lecture Notes in Computer Science · doi:10.1007/3-540-47969-4_30 · Cited by 836
Singular Values and Eigenvalues of Tensors: A Variational Approach
Lim, L. (2006) · IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing · doi:10.1109/camap.2005.1574201 · Cited by 789
Paatero, P. (1999) · Journal of Computational and Graphical Statistics · doi:10.1080/10618600.1999.10474853 · Cited by 756
Principal Component Analysis of Three-Mode Data by Means of Alternating Least Squares Algorithms
Kroonenberg, P. M., & de Leeuw, J. (1980) · Psychometrika · doi:10.1007/bf02293599 · Cited by 724
Multiway calibration. Multilinear PLS
Bro, R. (1996) · Journal of Chemometrics · doi:10.1002/(sici)1099-128x(199601)10:1<47::aid-cem400>3.0.co;2-c · Cited by 714
Practical aspects of PARAFAC modeling of fluorescence excitation‐emission data
Andersen, C. M., & Bro, R. (2003) · Journal of Chemometrics · doi:10.1002/cem.790 · Cited by 605
Paatero, P. (1999) · Journal of Computational and Graphical Statistics · doi:10.2307/1390831 · Cited by 510
Beyond streams and graphs: dynamic tensor analysis
Sun, J., Tao, D., & Faloutsos, C. (2006) · Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining · doi:10.1145/1150402.1150445 · Cited by 462
Rank-One Approximation to High Order Tensors
Zhang, T., & Golub, G. H. (2001) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/s0895479899352045 · Cited by 430
Centering and scaling in component analysis
Bro, R., & Smilde, A. K. (2003) · Journal of Chemometrics · doi:10.1002/cem.773 · Cited by 428
Generalized Low Rank Approximations of Matrices
Ye, J. (2005) · Machine Learning · doi:10.1007/s10994-005-3561-6 · Cited by 428
PARAFAC2—Part I. A direct fitting algorithm for the PARAFAC2 model
Kiers, H. A. L., ten Berge, J. M. F., & Bro, R. (1999) · Journal of Chemometrics · doi:10.1002/(sici)1099-128x(199905/08)13:3/4<275::aid-cem543>3.0.co;2-b · Cited by 412
Sequential Karhunen-Loeve basis extraction and its application to images
Levey, A., & Lindenbaum, M. (2000) · IEEE Transactions on Image Processing · doi:10.1109/83.855432 · Cited by 377
Orthogonal Tensor Decompositions
Kolda, T. G. (2001) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/s0895479800368354 · Cited by 376
Multilinear subspace analysis of image ensembles
Vasilescu, M. A. O., & Terzopoulos, D. (2003) · 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings. · doi:10.1109/cvpr.2003.1211457 · Cited by 375
Decomposing EEG data into space–time–frequency components using Parallel Factor Analysis
Miwakeichi, F., Martı́nez-Montes, E., Valdés-Sosa, P. A., Nishiyama, N., Mizuhara, H., & Yamaguchi, Y. (2004) · NeuroImage · doi:10.1016/j.neuroimage.2004.03.039 · Cited by 374
A comparison of algorithms for fitting the PARAFAC model
Tomasi, G., & Bro, R. (2006) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2004.11.013 · Cited by 372
A weighted non-negative least squares algorithm for three-way ‘PARAFAC’ factor analysis
Paatero, P. (1997) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/s0169-7439(97)00031-2 · Cited by 340
CubeSVD: a novel approach to personalized Web search
Sun, J.-T., Zeng, H.-J., Liu, H., Lu, Y., & Chen, Z. (2005) · Proceedings of the 14th international conference on World Wide Web - WWW '05 · doi:10.1145/1060745.1060803 · Cited by 338
Multiple Invariants and Generalized Rank of a P‐Way Matrix or Tensor
Hitchcock, F. L. (1928) · Journal of Mathematics and Physics · doi:10.1002/sapm19287139 · Cited by 338
Concurrent EEG/fMRI analysis by multiway Partial Least Squares
Martı́nez-Montes, E., Valdés-Sosa, P. A., Miwakeichi, F., Goldman, R. I., & Cohen, M. S. (2004) · NeuroImage · doi:10.1016/j.neuroimage.2004.03.038 · Cited by 326
PARAFAC2—Part II. Modeling chromatographic data with retention time shifts
Bro, R., Andersson, C. A., & Kiers, H. A. L. (1999) · Journal of Chemometrics · doi:10.1002/(sici)1099-128x(199905/08)13:3/4<295::aid-cem547>3.0.co;2-y · Cited by 323
Lavit, C., Escoufier, Y., Sabatier, R., & Traissac, P. (1994) · Computational Statistics & Data Analysis · doi:10.1016/0167-9473(94)90134-1 · Cited by 293
Coppi, R., & Bolasco, S. (1989) · Medical Entomology and Zoology · Cited by 285
Cattell, R. B. (1944) · Psychometrika · doi:10.1007/bf02288739 · Cited by 279
Parallel Factor Analysis as an exploratory tool for wavelet transformed event-related EEG
Mørup, M., Hansen, L. K., Herrmann, C. S., Parnas, J., & Arnfred, S. M. (2006) · NeuroImage · doi:10.1016/j.neuroimage.2005.08.005 · Cited by 269
Multiway analysis of epilepsy tensors
Acar, E., Aykut-Bingol, C., Bingol, H., Bro, R., & Yener, B. (2007) · Bioinformatics · doi:10.1093/bioinformatics/btm210 · Cited by 267
Self-citationRank, decomposition, and uniqueness for 3-way and n -way arrays
Kruskal, J. B. (1989) · Medical Entomology and Zoology · Cited by 253
Higher-Order Web Link Analysis Using Multilinear Algebra
Kolda, T. G., Bader, B. W., & Kenny, J. P. (2006) · Fifth IEEE International Conference on Data Mining (ICDM'05) · doi:10.1109/icdm.2005.77 · Cited by 252
Multiway analysis in the food industry. Models, algorithms and applications
Bro-Jorgensen, R. (1998) · UvA-DARE (University of Amsterdam) · Cited by 240
Multilinear image analysis for facial recognition
Vasilescu, M. A. O., & Terzopoulos, D. (2003) · Object recognition supported by user interaction for service robots · doi:10.1109/icpr.2002.1048350 · Cited by 229
Review on Multiway Analysis in Chemistry—2000–2005
Bro, R. (2006) · Critical Reviews in Analytical Chemistry · doi:10.1080/10408340600969965 · Cited by 224
Ceulemans, E., & Kiers, H. A. L. (2006) · British Journal of Mathematical and Statistical Psychology · doi:10.1348/000711005x64817 · Cited by 216
Weighted Least Squares Fitting Using Ordinary Least Squares Algorithms
Kiers, H. A. L. (1997) · Psychometrika · doi:10.1007/bf02295279 · Cited by 199
Timmerman, M. E., & Kiers, H. A. L. (2000) · British Journal of Mathematical and Statistical Psychology · doi:10.1348/000711000159132 · Cited by 185
Distributed Clustering Using Collective Principal Component Analysis
Kargupta, H., Huang, W., Sivakumar, K., & Johnson, E. (2001) · Knowledge and Information Systems · doi:10.1007/pl00011677 · Cited by 161
Kolda, T. G., & Bader, B. W. (2006) · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · Cited by 154
The TOPHITS Model for Higher-Order Web Link Analysis∗
Kolda, T. G., & Bader, B. W. (2006) · Cited by 153
Mørup, M., Hansen, L. K., & Arnfred, S. (2007) · Journal of Neuroscience Methods · doi:10.1016/j.jneumeth.2006.11.008 · Cited by 146
Canonical decomposition of ictal scalp EEG reliably detects the seizure onset zone
Vos, M. D., Vergult, A., Lathauwer, L. D., Clercq, W. D., Huffel, S. V., Dupont, P. J., Palmini, A., & Paesschen, W. V. (2007) · NeuroImage · doi:10.1016/j.neuroimage.2007.04.041 · Cited by 134
Temporal Analysis of Semantic Graphs Using ASALSAN
Bader, B. W., Harshman, R. A., & Kolda, T. G. (2007) · Proceedings · doi:10.1109/icdm.2007.54 · Cited by 130
Robust iterative fitting of multilinear models
Vorobyov, S. A., Rong, Y., Sidiropoulos, N. D., et al. (2005) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2005.850343 · Cited by 123
Rodgers, J. L., Coppi, R., Bolasco, S., Critchley, F., Escofier, Y., Heiser, W. J., Lauro, N., & Meulman, J. J. (1990) · Journal of the American Statistical Association · doi:10.2307/2289633 · Cited by 121
Modeling and Multiway Analysis of Chatroom Tensors
Acar, E., Camtepe, S. A., Krishnamoorthy, M. S., et al. (2005) · Lecture notes in computer science · doi:10.1007/11427995_21 · Cited by 119
Self-citationEEG correlates of emotional tasks related to attentional demands
Cole, H. W., & Ray, W. J. (1985) · International Journal of Psychophysiology · doi:10.1016/0167-8760(85)90017-0 · Cited by 102
Cross-language information retrieval using PARAFAC2
Chew, P. A., Bader, B. W., Kolda, T. G., & Abdelalí, A. (2007) · ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD) · doi:10.1145/1281192.1281211 · Cited by 99
Structure-seeking multilinear methods for the analysis of fMRI data
Andersen, A. H., & Rayens, W. S. (2004) · NeuroImage · doi:10.1016/j.neuroimage.2004.02.026 · Cited by 99
Maximum likelihood fitting using ordinary least squares algorithms
Bro, R., Sidiropoulos, N. D., & Smilde, A. K. (2002) · Journal of Chemometrics · doi:10.1002/cem.734 · Cited by 98
A Tensor Approximation Approach to Dimensionality Reduction
Wang, H., & Ahuja, N. (2007) · International Journal of Computer Vision · doi:10.1007/s11263-007-0053-0 · Cited by 83
2-Dimensional Singular Value Decomposition for 2D Maps and Images
Ding, C. H. Q., & Ye, J. (2005) · doi:10.1137/1.9781611972757.4 · Cited by 75
Decomposing event-related potentials: A new topographic components model
Möcks, J. (1988) · Biological Psychology · doi:10.1016/0301-0511(88)90020-8 · Cited by 71
Compact representation of multidimensional data using tensor rank-one decomposition
Wang, H., & Ahuja, N. (2004) · Cited by 69
STATIS, a three-way method for data analysis. Application to environmental data
Stanimirova, I., Walczak, B., Massart, D. L., Simeonov, V., Saby, C. A., & Crescenzo, E. D. (2004) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/j.chemolab.2004.03.005 · Cited by 56
Collective Sampling and Analysis of High Order Tensors for Chatroom Communications
Acar, E., Camtepe, S. A., & Yener, B. (2006) · Lecture notes in computer science · doi:10.1007/11760146_19 · Cited by 55
Self-citationTensor-CUR decompositions for tensor-based data
Mahoney, M. W., Maggioni, M., & Petros Drineas, B. (2006) · ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD) · doi:10.1145/1150402.1150440 · Cited by 51
Multi-way modelling of high-dimensionality electroencephalographic data
Estienne, F., Matthijs, N., Massart, D. L., Ricoux, P., & Leibovici, D. (2001) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/s0169-7439(01)00140-x · Cited by 41
Kernel-based multifactor analysis for image synthesis and recognition
Li, Y., Du, Y., & Lin, X. (2005) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2005.131 · Cited by 32
Computational analysis of epileptic focus localization
Acar, E., Bingöl, C. A., Bingol, H. O., & Yener, B. (2006) · Cited by 22
Self-citationCuBatch, a MATLAB® interface for n-mode data analysis
Gourvénec, S., Tomasi, G., Durville, C., Crescenzo, E. D., Saby, C. A., Massart, D. L., Bro, R., & Oppenheim, G. (2004) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/j.chemolab.2004.01.027 · Cited by 10
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Metadata
- Authors
- Acar, E., & Yener, B.
- Venue
- IEEE Transactions on Knowledge and Data Engineering
- Published
- 2009-01
- Volume
- 21
- Issue
- 1
- Pages
- 6-20
- ISSN
- 1041-4347 (ISSN-L)
- OpenAlex
- W2140862024
- Cited by
- 434
- References
- 75
- FWCI
- 8.70
- Type
- journal article
- Language
- en
- Open access
- closed
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