Tensor-based anomaly detection: An interdisciplinary survey

Knowledge-Based Systems - Tập 98 - Trang 130-147 - 2016
Hadi Fanaee-T1, João Gama2
1Laboratory of Artificial Intelligence and Decision Support/ INESC TEC and FCUP/University of Porto, Rua Dr. Roberto Frias, Porto 4200-465, Portugal
2Laboratory of Artificial Intelligence and Decision Support/ INESC TEC and FEP/University of Porto, Rua Dr. Roberto Frias, Porto 4200-465, Portugal

Tài liệu tham khảo

Chandola, 2009, Anomaly detection: a survey, ACM Comput. Surv., 41, 15, 10.1145/1541880.1541882 Dong, 2010, Identification of temporal and spatial variations of water quality in Sanya Bay, China by three-way principal component analysis, Environ. Earth Sci., 60, 1673, 10.1007/s12665-009-0301-4 Cid, 2011, Modelling spatial and temporal variations in the water quality of an artificial water reservoir in the semiarid midwest of argentina, Anal. Chim. Acta, 705, 243, 10.1016/j.aca.2011.06.013 Panagakis, 2010, Non-negative multilinear principal component analysis of auditory temporal modulations for music genre classification, IEEE Trans. Audio Speech Lang. Process., 18, 576, 10.1109/TASL.2009.2036813 Hu, 2011, Incremental tensor subspace learning and its applications to foreground segmentation and tracking, Int. J. Comput. Vis., 91, 303, 10.1007/s11263-010-0399-6 Mujica, 2008, Multivariate statistics process control for dimensionality reduction in structural assessment, Mech. Syst. Signal Process., 22, 155, 10.1016/j.ymssp.2007.05.001 Wang, 2008, A comparative study of multilinear principal component analysis for face recognition, 1 Costantini, 2008, Higher order svd analysis for dynamic texture synthesis, IEEE Trans. Image Process., 17, 42, 10.1109/TIP.2007.910956 Acar, 2005, Modeling and multiway analysis of chatroom tensors, 256 Andersen, 2004, Structure-seeking multilinear methods for the analysis of fmri data, NeuroImage, 22, 728, 10.1016/j.neuroimage.2004.02.026 Baum, 2013, Enzyme activity measurement via spectral evolution profiling and parafac, Anal. Chim. Acta, 778, 1, 10.1016/j.aca.2013.03.029 Nomikos, 1994, Monitoring batch processes using multiway principal component analysis, AIChE J., 40, 1361, 10.1002/aic.690400809 Mørup, 2011, Applications of tensor (multiway array) factorizations and decompositions in data mining, Data Min. Knowl. Discov., 1, 24, 10.1002/widm.1 Kolda, 2009, Tensor decompositions and applications, SIAM Rev., 51, 455, 10.1137/07070111X Sun, 2006, Window-based tensor analysis on high-dimensional and multi-aspect streams, vol. 6, 1076 Sun, 2006, Beyond streams and graphs: dynamic tensor analysis, 374 Sun, 2008, Incremental tensor analysis: theory and applications, ACM Trans. Knowl. Discov. Data, 2, 11, 10.1145/1409620.1409621 Lee, 2014, Online monitoring and interpretation of periodic diurnal and seasonal variations of indoor air pollutants in a subway station using parallel factor analysis (parafac), Energy Build., 68, 87, 10.1016/j.enbuild.2013.09.022 Tran, 2012, Video detection anomaly via low-rank and sparse decompositions, 17 Koutra, 2012, Tensorsplat: spotting latent anomalies in time, 144 Panisson, 2014, Mining concurrent topical activity in microblog streams, 3 Acar, 2007, Seizure recognition on epilepsy feature tensor, 4273 Renard, 2008, Improvement of target detection methods by multiway filtering, IEEE Trans. Geosci. Remote Sens., 46, 2407, 10.1109/TGRS.2008.918419 Wang, 2014, Discovering urban spatio-temporal structure from time-evolving traffic networks, 93 Chuang, 2009, Using MPCA of spectra model for fault detection in a hot strip mill, J. Mater. Process. Technol., 209, 4162, 10.1016/j.jmatprotec.2008.10.008 Prada, 2012, Three-way analysis of structural health monitoring data, Neurocomputing, 80, 119, 10.1016/j.neucom.2011.07.030 Khosravi, 2008, Multiway principal component analysis (mpca) for upstream/downstream classification of voltage sags gathered in distribution substations, 297 Ho, 2014, Limestone: high-throughput candidate phenotype generation via tensor factorization, J. Biomed. Inform., 52, 199, 10.1016/j.jbi.2014.07.001 Fanaee-T, 2015, Eigenevent: an algorithm for event detection from complex data streams in syndromic surveillance, Intell. Data Anal., 19, 10.3233/IDA-150734 Bai, 2013, A multiway model for predicting earthquake ground motion, 219 Mu, 2011, Empirical discriminative tensor analysis for crime forecasting, 293 Kosanovich, 1994, Multi-way PCA applied to an industrial batch process, vol. 2, 1294 Nomikos, 1995, Multivariate spc charts for monitoring batch processes, Technometrics, 37, 41, 10.1080/00401706.1995.10485888 Kourti, 1995, Analysis, monitoring and fault diagnosis of batch processes using multiblock and multiway PLS, J. Process Control, 5, 277, 10.1016/0959-1524(95)00019-M Chen, 2003, Three-way data analysis with time lagged window for on-line batch process monitoring, Korean J. Chem. Eng., 20, 1000, 10.1007/BF02706928 GUO, 2013, Mpca fault detection method based on multiblock statistics for uneven-length batch processes, J. Comput. Inf. Syst., 9, 7181 Wise, 2001, Application of parafac2 to fault detection and diagnosis in semiconductor etch, J. Chemom., 15, 285, 10.1002/cem.689 Wise, 1999, A comparison of principal component analysis, multiway principal component analysis, trilinear decomposition and parallel factor analysis for fault detection in a semiconductor etch process, J. Chemom., 13, 379, 10.1002/(SICI)1099-128X(199905/08)13:3/4<379::AID-CEM556>3.0.CO;2-N Zhifeng, 2007, Online supervision of penicillin cultivations based on rolling mpca, Chin. J. Chem. Eng., 15, 92, 10.1016/S1004-9541(07)60039-1 Hu, 2009, Batch process monitoring with tensor factorization, J. Process Control, 19, 288, 10.1016/j.jprocont.2008.03.003 Singh, 2009, Multi-way modeling of wastewater data for performance evaluation of sewage treatment plant-a case study, Chemom. Intell. Lab. Syst., 95, 18, 10.1016/j.chemolab.2008.07.013 Amigo, 2008, On-line parallel factor analysis. a step forward in the monitoring of bioprocesses in real time, Chemom. Intell. Lab. Syst., 92, 44, 10.1016/j.chemolab.2007.12.001 Mori, 2014, Quality relevant nonlinear batch process performance monitoring using a kernel based multiway non-Gaussian latent subspace projection approach, J. Process Control, 24, 57, 10.1016/j.jprocont.2013.10.017 Lee, 2003, On-line batch process monitoring using a consecutively updated multiway principal component analysis model, Comput. Chem. Eng., 27, 1903, 10.1016/S0098-1354(03)00151-0 Yoo, 2004, On-line monitoring of batch processes using multiway independent component analysis, Chemom. Intell. Lab. Syst., 71, 151, 10.1016/j.chemolab.2004.02.002 Gallagher, 1996, Application of multi-way principal components analysis to nuclear waste storage tank monitoring, Comput. Chem. Eng., 20, S739, 10.1016/0098-1354(96)00131-7 Urtubia, 2012, Detection of abnormal fermentations in wine process by multivariate statistics and pattern recognition techniques, J. Biotechnol., 159, 336, 10.1016/j.jbiotec.2011.09.031 Barbieri, 2002, A three-way principal factor analysis for assessing the time variability of freshwaters related to a municipal water supply, Chemom. Intell. Lab. Syst., 62, 89, 10.1016/S0169-7439(02)00007-2 Singh, 2006, Multi-way modeling of hydro-chemical data of an alluvial river system-a case study, Anal. Chim. Acta, 571, 248, 10.1016/j.aca.2006.04.080 Singh, 2007, Multi-way partial least squares modeling of water quality data, Anal. Chim. Acta, 584, 385, 10.1016/j.aca.2006.11.038 Engle, 2014, Three-way compositional analysis of water quality monitoring data, Environ. Ecol. Stat., 21, 565, 10.1007/s10651-013-0268-x Singh, 2007, Exploring groundwater hydrochemistry of alluvial aquifers using multi-way modeling, Anal. Chim. Acta, 596, 171, 10.1016/j.aca.2007.06.001 Stanimirova, 2005, Modeling of environmental four-way data from air quality control, Chemom. Intell. Lab. Syst., 77, 115, 10.1016/j.chemolab.2004.11.005 Singh, 2006, Multi-way data analysis of soils irrigated with wastewater–a case study, Chemom. Intell. Lab. Syst., 83, 1, 10.1016/j.chemolab.2006.01.001 Andrade, 2007, 3-way characterization of soils by procrustes rotation, matrix-augmented principal components analysis and parallel factor analysis, Anal. Chim. Acta, 603, 20, 10.1016/j.aca.2007.09.043 Li, 2011, Robust tensor subspace learning for anomaly detection, Int. J. Mach. Learn. Cybern., 2, 89, 10.1007/s13042-011-0017-0 Zhao, 2013, Kernelization of tensor-based models for multiway data analysis: processing of multidimensional structured data, IEEE Signal Process. Mag., 30, 137, 10.1109/MSP.2013.2255334 Li, 2010, Infrared moving target detection and tracking based on tensor locality preserving projection, Infrared Phys. Technol., 53, 77, 10.1016/j.infrared.2009.09.009 Zhang, 2011, Visual tracking via dynamic tensor analysis with mean update, Neurocomputing, 74, 3277, 10.1016/j.neucom.2011.05.006 Li, 2011, Tensor-based covariance matrices for object tracking, 1681 Zhou, 2012, Higher-order SVD analysis for crowd density estimation, Comput. Vis. Image Underst., 116, 1014, 10.1016/j.cviu.2012.05.005 Kobayashi, 2009, Three-way auto-correlation approach to motion recognition, Pattern Recognit. Lett., 30, 212, 10.1016/j.patrec.2008.09.006 Araujo, 2014, Com2: fast automatic discovery of temporal (comet) communities, 271 Mao, 2014, Malspot: multi2 malicious network behavior patterns analysis, 1 Kim, 2009, Higher-order PCA for anomaly detection in large-scale networks, 85 Maruhashi, 2011, Multiaspectforensics: pattern mining on large-scale heterogeneous networks with tensor analysis, 203 Papalexakis, 2012, Parcube: sparse parallelizable tensor decompositions, 521 Kolda, 2008, Scalable tensor decompositions for multi-aspect data mining, 363 Bader, 2007, Temporal analysis of semantic graphs using asalsan, 33 Maruhashi, 2014, Multiaspectspotting: spotting anomalous behavior within count data using tensor, 474 Matsubara, 2012, Fast mining and forecasting of complex time-stamped events, 271 Fanaee-T, 2012, Event and anomaly detection using tucker3 decomposition, 8 Glass, 2010, Automatically identifying the sources of large internet events, 108 Peng, 2011, Temporal relation co-clustering on directional social network and author-topic evolution, Knowl. Inf. Syst., 26, 467, 10.1007/s10115-010-0289-9 Xu, 2015, Bayesian nonparametric models for multiway data analysis, IEEE Trans. Pattern Anal. Mach. Intell., 37, 475, 10.1109/TPAMI.2013.201 Papalexakis, 2014, Spotting misbehaviors in location-based social networks using tensors, 551 Gauvin, 2014, Detecting the community structure and activity patterns of temporal networks: a non-negative tensor factorization approach, PLoS One, 9, e86028, 10.1371/journal.pone.0086028 Oliveira, 2013, Visualization of evolving social networks using actor-level and community-level trajectories, Expert Syst., 30, 306, 10.1111/exsy.12028 Chen, 2015, Fast and scalable multi-way analysis of massive neural data, IEEE Trans. Comput., 64, 707, 10.1109/TC.2013.2295806 Rosipal, 2009, Application of multi-way EEG decomposition for cognitive workload monitoring, 145 Miwakeichi, 2008, Decomposing EEG data into space-time-frequency components using parallel factor analysis and its relation with cerebral blood flow, 802 Mørup, 2006, Parallel factor analysis as an exploratory tool for wavelet transformed event-related EEG, NeuroImage, 29, 938, 10.1016/j.neuroimage.2005.08.005 Cong, 2013, Multi-domain feature extraction for small event-related potentials through nonnegative multi-way array decomposition from low dense array EEG, Int. J. Neural Syst., 23, 10.1142/S0129065713500068 Cong, 2012, Benefits of multi-domain feature of mismatch negativity extracted by non-negative tensor factorization from eeg collected by low-density array, Int. J. Neural Syst., 22, 10.1142/S0129065712500256 Beckmann, 2005, Tensorial extensions of independent component analysis for multisubject FMRI analysis, Neuroimage, 25, 294, 10.1016/j.neuroimage.2004.10.043 Bourennane, 2010, Improvement of classification for hyperspectral images based on tensor modeling, IEEE Geosci. Remote Sens. Lett., 7, 801, 10.1109/LGRS.2010.2048696 Renard, 2009, Dimensionality reduction based on tensor modeling for classification methods, IEEE Trans. Geosci. Remote Sens., 47, 1123, 10.1109/TGRS.2008.2008903 Zhang, 2008, Tensor methods for hyperspectral data analysis: a space object material identification study, J. Opt. Soc. Am. A, 25, 3001, 10.1364/JOSAA.25.003001 Zhang, 2011, A multifeature tensor for remote-sensing target recognition, IEEE Geosci. Remote Sens. Lett., 8, 374, 10.1109/LGRS.2010.2077272 Hemissi, 2013, Multi-spectro-temporal analysis of hyperspectral imagery based on 3-d spectral modeling and multilinear algebra, IEEE Trans. Geosci. Remote Sens., 51, 199, 10.1109/TGRS.2012.2200486 Shi, 2014, Stensr: spatio-temporal tensor streams for anomaly detection and pattern discovery, Knowl. Inf. Syst., 1 Hayashi, 2010, Exponential family tensor factorization for missing-values prediction and anomaly detection, 216 Prada, 2012, Dimensionality reduction for damage detection in engineering structures, Int. J. Mod. Phys. B, 26, 10.1142/S0217979212460046 Karssen, 2009, Fall detection in walking robots by multi-way principal component analysis, Robotica, 27, 249, 10.1017/S0263574708004645 Fanaee-T, 2015, Event detectionfrom traffic tensors: a hybrid model, Neurocomputing Tan, 2013, Traffic volume data outlier recovery via tensor model, Math. Probl. Eng., 2013, 10.1155/2013/164810 Tan, 2013, A tensor-based method for missing traffic data completion, Transp. Res. Part C: Emerg. Technol., 28, 15, 10.1016/j.trc.2012.12.007 Hall, 2012, Tensor-based temporal behavior analysis in pain medicine, vol. 1, 626 Li, 2010, Non-negative matrix and tensor factorization based classification of clinical microarray gene expression data, 438 Fanaee-T, 2013, An eigenvector-based hotspot detection, 251 Ramanathan, 2008 Leibovici, 2010, Spatio-temporal multiway decomposition using principal tensor analysis on k-modes: the r package ptak, J. Stat. Softw., 34, 1, 10.18637/jss.v034.i10 Leibovici, 2007, A method to classify ecoclimatic arid and semiarid zones in circum-Saharan Africa using monthly dynamics of multiple indicators, IEEE Trans. Geosci. Remote Sens., 45, 4000, 10.1109/TGRS.2007.908878 Unkel, 2011, Independent component analysis for three-way data with an application from atmospheric science, J. Agric. Biol. Environ. Stat., 16, 319, 10.1007/s13253-011-0055-9 Marklund, 2014, Development and comparison of spectral methods for passive acoustic anomaly detection in nuclear power plants, Appl. Acoust., 83, 100, 10.1016/j.apacoust.2014.03.014 Mesgarani, 2014, Mechanisms of noise robust representation of speech in primary auditory cortex, Proc. Natl. Acad. Sci. USA, 111, 6792, 10.1073/pnas.1318017111 Mesgarani, 2006, Discrimination of speech from nonspeech based on multiscale spectro-temporal modulations, IEEE Trans. Audio Speech Lang. Process., 14, 920, 10.1109/TSA.2005.858055 Nomikos, 1995, Multi-way partial least squares in monitoring batch processes, Chemom. Intell. Lab. Syst., 30, 97, 10.1016/0169-7439(95)00043-7 Nazarpour, 2006, Parallel space-time-frequency decomposition of EEG signals for brain computer interfacing Villez, 2008, Combining multiway principal component analysis (MPCA) and clustering for efficient data mining of historical data sets of sbr processes., Water Sci. Technol., 57, 10.2166/wst.2008.143 Tao, 2005, Supervised tensor learning, 8 Cai, 2006, Learning with Tensor Representation Kotsia, 2012, Higher rank support tensor machines for visual recognition, Pattern Recognit., 45, 4192, 10.1016/j.patcog.2012.04.033 Yan, 2007, Multilinear discriminant analysis for face recognition, IEEE Trans. Image Process., 16, 212, 10.1109/TIP.2006.884929 Rendle, 2010, Factorization machines, 995 Lu, 2011, A survey of multilinear subspace learning for tensor data, Pattern Recognit., 44, 1540, 10.1016/j.patcog.2011.01.004 Wold, 1987, Multi-way principal components-and PLS-analysis, J. Chemom., 1, 41, 10.1002/cem.1180010107 Chen, 2002, On-line batch process monitoring using dynamic PCA and dynamic PLS models, Chem. Eng. Sci., 57, 63, 10.1016/S0009-2509(01)00366-9 Marjanovic, 2006, Real-time monitoring of an industrial batch process, Comput. Chem. Eng., 30, 1476, 10.1016/j.compchemeng.2006.05.040 Li, 2006, On-line fault detection using svm-based dynamic MPLS for batch processes, Chin. J. Chem. Eng., 14, 754, 10.1016/S1004-9541(07)60007-X Guo, 2012, Tensor learning for regression, IEEE Trans. Image Process, 21, 816, 10.1109/TIP.2011.2165291 Zhou, 2013, Tensor regression with applications in neuroimaging data analysis, J. Am. Stat. Assoc., 108, 540, 10.1080/01621459.2013.776499 Zhu, 2014, A general framework for predictive tensor modeling with domain knowledge, Data Min. Knowl. Discov., 1 Rogers, 2013, Multilinear dynamical systems for tensor time series, 2634 Bahadori, 2014, Fast multivariate spatio-temporal analysis via low rank tensor learning, 3491 Yu, 2012, Multiway discrete hidden markov model-based approach for dynamic batch process monitoring and fault classification, AIChE J., 58, 2714, 10.1002/aic.12794 Thai-Nghe, 2011, Factorization models for forecasting student performance, 11 Thai-Nghe, 2011 Kouchaki, 2013, Tensor based singular spectrum analysis for nonstationary source separation, 1 Lee, 2003, Monitoring of a sequencing batch reactor using adaptive multiblock principal component analysis, Biotechnol. Bioeng., 82, 489, 10.1002/bit.10589 Yoo, 2004, Application of multiway ICA for on-line process monitoring of a sequencing batch reactor, Water Res., 38, 1715, 10.1016/j.watres.2004.01.006 Tian, 2009, Multiway kernel independent component analysis based on feature samples for batch process monitoring, Neurocomputing, 72, 1584, 10.1016/j.neucom.2008.09.003 Fanaee-T, 2015, Multi-aspect-streaming tensor analysis, Knowl.-Based Syst., 89, 332, 10.1016/j.knosys.2015.07.013 Majid, 2011, Aluminium process fault detection by multiway principal component analysis, Control Eng. Pract., 19, 367, 10.1016/j.conengprac.2010.12.005 Gao, 2012, On-line Monitoring of Batch Process with Multiway PCA/ICA, 239 Stefanov, 2003, Hierarchical multivariate analysis of cockle phenomena, J. Chemom., 17, 550, 10.1002/cem.825 Tucker, 1966, Some mathematical notes on three-mode factor analysis, Psychometrika, 31, 279, 10.1007/BF02289464 R.A. Harshman, Foundations of the PARAFAC Procedure: Models and Conditions for an “Explanatory” Multi-Modal Factor Analysis, UCLA Working Papers in Phonetics, vol. 16(1), 1970, p. 84. Carroll, 1970, Analysis of individual differences in multidimensional scaling via an n-way generalization of “eckart-young” decomposition, Psychometrika, 35, 283, 10.1007/BF02310791 Chen, 2014, On optimal low rank tucker approximation for tensors: the case for an adjustable core size, J. Global Optim., 1 De Lathauwer, 2000, A multilinear singular value decomposition, SIAM J. Matrix Anal Appl., 21, 1253, 10.1137/S0895479896305696 Kolda, 2009, Tensor decompositions and application, SIAM Rev., 51, 455, 10.1137/07070111X Carroll, 1989, Fitting of the latent class model via iteratively reweighted least squares candecomp with nonnegativity constraints, 463 Bader, 2008, Discussion tracking in enron email using parafac, 147 Kiers, 1993, An alternating least squares algorithm for parafac2 and three-way dedicom, Comput. Stat. Data Anal., 16, 103, 10.1016/0167-9473(93)90247-Q Chi, 2012, On tensors, sparsity, and nonnegative factorizations, SIAM J. Matrix Anal. Appl., 33, 1272, 10.1137/110859063 Lu, 2006, Multilinear principal component analysis of tensor objects for recognition, vol. 2, 776 Lv, 2014, Fault detection for batch processes based on segmentation mpca, vol. 1030, 1701 Peng, 2014, Ascs online fault detection and isolation based on an improved mpca, Chin. J. Mech. Eng., 27, 1047, 10.3901/CJME.2014.0529.106 Luo, 2014, Batch process monitoring with gtucker2 model, Ind. Eng. Chem. Res., 53, 15101, 10.1021/ie5015102 Kim, 2007, Nonnegative tucker decomposition, 1 Mørup, 2008, Algorithms for sparse nonnegative tucker decompositions, Neural Comput., 20, 2112, 10.1162/neco.2008.11-06-407 Süsstrunk, 2006, Dynamic texture analysis and synthesis using tensor decomposition, vol. 4292, 1161 Selli, 2004, Application of multi-way models to the time-resolved fluorescence of polycyclic aromatic hydrocarbons mixtures in water, Water Res., 38, 2269, 10.1016/j.watres.2004.01.042 Harshman, 1978, Models for analysis of asymmetrical relationships among n objects or stimuli Bader, 2006, vol. 119 Chu, 2009, Probabilistic models for incomplete multi-dimensional arrays, vol. 5, 89 Hayashi, 2012, Exponential family tensor factorization: an online extension and applications, Knowl. Inf. Syst., 33, 57, 10.1007/s10115-012-0517-6 Mørup, 2009, Automatic relevance determination for multi-way models, J. Chemom., 23, 352, 10.1002/cem.1223 Zhao, 2015, Bayesian cp factorization of incomplete tensors with automatic rank determination, IEEE Trans Pattern Anal. Mach. Intell., PP Porteous, 2008, Multi-hdp: a nonparametric Bayesian model for tensor factorization, 1487 Tao, 2008, Bayesian tensor approach for 3-d face modeling, IEEE Trans. Circuits Syst. Video Technol., 18, 1397, 10.1109/TCSVT.2008.2002825 Xiong, 2010, Temporal collaborative filtering with Bayesian probabilistic tensor factorization., vol. 10, 211 Rai, 2014, Scalable Bayesian low-rank decomposition of incomplete multiway tensors, 1800 Zhou, 2015, Bayesian factorizations of big sparse tensors, J. Am. Stat. Assoc., 110, 1562, 10.1080/01621459.2014.983233 He, 2005, Tensor subspace analysis, 499 Dai, 2006, Tensor embedding methods, vol. 21, 330 Luo, 2014, Tensor global-local preserving projections for batch process monitoring, Ind. Eng. Chem. Res., 53, 10166, 10.1021/ie403973w Zhang, 2007, Fault detection of nonlinear processes using multiway kernel independent component analysis, Ind. Eng. Chem. Res., 46, 7780, 10.1021/ie070381q Hu, 2008, Multivariate statistical process control based on multiway locality preserving projections, J. Process Control, 18, 797, 10.1016/j.jprocont.2007.11.002 Westerhuis, 1999, Comparing alternative approaches for multivariate statistical analysis of batch process data, J. Chemom., 13, 397, 10.1002/(SICI)1099-128X(199905/08)13:3/4<397::AID-CEM559>3.0.CO;2-I MacGregor, 2001, Multivariate image analysis for process monitoring and control, 17 Jackson, 1993, Stopping rules in principal components analysis: a comparison of heuristical and statistical approaches, Ecology, 2204, 10.2307/1939574 Efron, 1983, Estimating the error rate of a prediction rule: improvement on cross-validation, J. Am. Stat. Assoc., 78, 316, 10.1080/01621459.1983.10477973 Louwerse, 1999, Cross-validation of multiway component models, J. Chemom., 13, 491, 10.1002/(SICI)1099-128X(199909/10)13:5<491::AID-CEM537>3.0.CO;2-2 Bro, 2003, A new efficient method for determining the number of components in parafac models, J Chemom., 17, 274, 10.1002/cem.801 Timmerman, 2000, Three-mode principal components analysis: choosing the numbers of components and sensitivity to local optima, Br. J. Math. Stat. Psychol., 53, 1, 10.1348/000711000159132 Kiers, 2003, A fast method for choosing the numbers of components in tucker3 analysis, Br. J. Math. Stat. Psychol., 56, 119, 10.1348/000711003321645386 Andersson, 2000, The n-way toolbox for matlab, Chemom. Intell. Lab. Syst., 52, 1, 10.1016/S0169-7439(00)00071-X Harshman, 1984, An application of PARAFAC to a small sample problem, demonstrating preprocessing, orthogonality constraints, and split-half diagnostic techniques, 602 Ceulemans, 2006, Selecting among three-mode principal component models of different types and complexities: a numerical convex hull based method, Br. J. Math. Stat. Psychol., 59, 133, 10.1348/000711005X64817 Akaike, 1974, A new look at the statistical model identification, IEEE Trans. Autom. Control, 19, 716, 10.1109/TAC.1974.1100705 Schwarz, 1978, Estimating the dimension of a model, Ann. Stat., 6, 461, 10.1214/aos/1176344136 Karami, 2010, Best rank-r tensor selection using genetic algorithm for better noise reduction and compression of hyperspectral images, 169 Håstad, 1990, Tensor rank is np-complete, J. Algorithms, 11, 644, 10.1016/0196-6774(90)90014-6 Riu, 2003, Jack-knife technique for outlier detection and estimation of standard errors in parafac models, Chemom. Intell. Lab. Syst., 65, 35, 10.1016/S0169-7439(02)00090-4 P.M. Kroonenberg, et al., Three-mode Component and Scaling Models. Wiley StatsRef: Statistics Reference Online. (2015), 1–17. URL: http://dx.doi.org/10.1002/9781118445112.stat06459.pub2. Kroonenberg, 2008 Kiers, 2001, Three-way component analysis: principles and illustrative application, Psychol. Methods, 6, 84, 10.1037/1082-989X.6.1.84 Brockmeier, 2013, A greedy algorithm for model selection of tensor decompositions., 6113 Rashid, 2012, Nonlinear and non-Gaussian dynamic batch process monitoring using a new multiway kernel independent component analysis and multidimensional mutual information based dissimilarity approach, Ind. Eng. Chem. Res., 51, 10910, 10.1021/ie301002h Karami, 2011, Noise reduction of hyperspectral images using kernel non-negative tucker decomposition, IEEE J. Sel. Top. Signal Process., 5, 487, 10.1109/JSTSP.2011.2132692 Kourti, 2003, Abnormal situation detection, three-way data and projection methods; robust data archiving and modeling for industrial applications, Annu. Rev. Control, 27, 131, 10.1016/j.arcontrol.2003.10.004 Lu, 2004, PCA-based modeling and on-line monitoring strategy for uneven-length batch processes, Ind. Eng. Chem. Res., 43, 3343, 10.1021/ie030736f Kolda, 2005, Higher-order web link analysis using multilinear algebra, 8 Bader, 2007, Efficient matlab computations with sparse and factored tensors, SIAM J. Sci. Comput., 30, 205, 10.1137/060676489 Allen, 2012, Sparse higher-order principal components analysis, 27 Baskaran, 2012, Efficient and scalable computations with sparse tensors, 1 Zou, 2015, Gputensor: efficient tensor factorization for context-aware recommendations, Inf. Sci., 299, 159, 10.1016/j.ins.2014.12.004 Kang, 2012, Gigatensor: scaling tensor analysis up by 100 times-algorithms and discoveries, 316 Sidiropoulos, 2014, Parallel randomly compressed cubes: a scalable distributed architecture for big tensor decomposition, IEEE Signal Process Mag., 31, 57, 10.1109/MSP.2014.2329196 Inah, 2015, Haten2: Billion-scale tensor decompositions Papadimitriou, 2006, Optimal multi-scale patterns in time series streams, 647 Li, 2007, Robust visual tracking based on incremental tensor subspace learning, 1 Bader, 2008, Scenario discovery using nonnegative tensor factorization, 791 Acar, 2011, All-at-once Optimization for Coupled Matrix and Tensor Factorizations Zheng, 2012, Towards mobile intelligence: learning from GPS history data for collaborative recommendation, Artif. Intell., 184, 17, 10.1016/j.artint.2012.02.002 Ermiş, 2015, Link prediction in heterogeneous data via generalized coupled tensor factorization, Data Min. Knowl. Discov., 29, 203, 10.1007/s10618-013-0341-y Becker, 2012, Tensor-based preprocessing of combined eeg/meg data, 275 Cichocki, 2013, Tensor Decompositions: A New Concept in Brain Data Analysis? Swinnen, 2014, Incorporating higher dimensionality in joint decomposition of EEG and FMRI, 121 Khan, 2014, Bayesian multi-view tensor factorization, 656 Acar, 2013, Understanding data fusion within the framework of coupled matrix and tensor factorizations, Chemom. Intell. Lab. Syst., 129, 53, 10.1016/j.chemolab.2013.06.006 Lin, 2009, Metafac: community discovery via relational hypergraph factorization, 527 Yang, 2011, Like like alike: joint friendship and interest propagation in social networks, 537 Acar, 2013, Structure-revealing data fusion model with applications in metabolomics, 6023 E. Acar, Data Fusion Based on Coupled Matrix/Tensor Factorizations, 2015, (http://www.models.life.ku.dk/~acare/DataFusion). de Almeida, 2014, Distributed large-scale tensor decomposition, 26 Hu, 2015, Scalable Bayesian non-negative tensor factorization for massive count data, 53