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Linked Component Analysis From Matrices to High-Order Tensors: Applications to Biomedical Data

Guoxu Zhou, Qibin Zhao, Yu Zhang, Tulay Adali, Shengli Xie, Andrzej Cichocki
2016 Proceedings of the IEEE  
We show how constrained multi-block tensor decomposition methods are able to extract similar or statistically dependent common features that are shared by all blocks, by incorporating the multiway nature  ...  Then, we discuss their important extensions and generalization to multi-block multiway (tensor) data.  ...  data via tensorization and decomposition of a high-order tensor into factor matrices and/or core tensors with low rank and low order [3] , [111] ; ability to perform all mathematical operations in feasible  ... 
doi:10.1109/jproc.2015.2474704 fatcat:7rhda5adurbt3d6bm2ryax6cy4

Bayesian Sparse Tucker Models for Dimension Reduction and Tensor Completion [article]

Qibin Zhao, Liqing Zhang, Andrzej Cichocki
2015 arXiv   pre-print
Tucker decomposition is the cornerstone of modern machine learning on tensorial data analysis, which have attracted considerable attention for multiway feature extraction, compressive sensing, and tensor  ...  To address these issues, we present a class of probabilistic generative Tucker models for tensor decomposition and completion with structural sparsity over multilinear latent space.  ...  decomposition of an incomplete tensor, the problem is ill-conditioned and has infinite solutions.  ... 
arXiv:1505.02343v1 fatcat:b3sbfv76yfbdhnlk7tjp3bxate

Tensor-based anomaly detection: An interdisciplinary survey

Hadi Fanaee-T, João Gama
2016 Knowledge-Based Systems  
However, if data includes tensor (multiway) structure (e.g. space-time-measurements), some meaningful anomalies may remain invisible with these methods.  ...  This survey aims to highlight the potential of tensor-based techniques as a novel approach for detection and identification of abnormalities and failures.  ...  Although estimation of tensor rank is an NP hard problem [185] , in the majority of cases, an optimal low-rank approximation is desirable.  ... 
doi:10.1016/j.knosys.2016.01.027 fatcat:lejxxae63jcutfx2ncahownt7e

Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions

Andrzej Cichocki, Namgil Lee, Ivan Oseledets, Anh-Huy Phan, Qibin Zhao, Danilo P. Mandic
2016 Foundations and Trends® in Machine Learning  
We provide the mathematical and graphical representations and interpretation of tensor networks, with the main focus on the Tucker and Tensor Train (TT) decompositions and their extensions or generalizations  ...  , multiway component analysis, multilinear blind source separation, tensor completion, linear/multilinear dimensionality reduction, large-scale optimization problems, symmetric eigenvalue decomposition  ...  Infinite Tucker decomposition: Nonparametric Bayesian models for multiway data analysis.  ... 
doi:10.1561/2200000059 fatcat:ememscddezeovamsoqrcpp33z4

Computational Creativity Based Video Recommendation

Wei Lu, Fu-lai Chung
2016 Proceedings of the 39th International ACM SIGIR conference on Research and Development in Information Retrieval - SIGIR '16  
Targeting at constructing a recommender system that can compromise between accuracy and creativity for users, a deep Bayesian probabilistic tensor framework for tag and item recommending is adopted.  ...  Tensor models offer effective approaches for complex multi-relational data learning and missing element completion.  ...  Through a scalable framework for tensor decomposition and completion, and through introducing Bayesian surprise into probabilistic ranking, we are able to recommend personalized items taking creativity  ... 
doi:10.1145/2911451.2914707 dblp:conf/sigir/LuC16 fatcat:pighwyqwi5f6xhtebwx2ewneem

Tensor Completion Algorithms in Big Data Analytics [article]

Qingquan Song, Hancheng Ge, James Caverlee, Xia Hu
2018 arXiv   pre-print
Tensor completion is a problem of filling the missing or unobserved entries of partially observed tensors.  ...  We characterize these advances from four perspectives: general tensor completion algorithms, tensor completion with auxiliary information (variety), scalable tensor completion algorithms (volume), and  ...  to X X X Ω Ω Ω = T T T Ω Ω Ω , where rank * denotes a speci c type of tensor rank based on the rank assumption of the given tensor T T T, X X X represents the completed low-rank tensor of T T T, and Ω  ... 
arXiv:1711.10105v2 fatcat:onu2bket3na3dmfsmzhc7byqku

A Bayesian Tensor Factorization Model via Variational Inference for Link Prediction [article]

Beyza Ermis, A. Taylan Cemgil
2014 arXiv   pre-print
Probabilistic approaches for tensor factorization aim to extract meaningful structure from incomplete data by postulating low rank constraints.  ...  This paper presents full Bayesian inference via VB on both single and coupled tensor factorization models. Our method can be run even for very large models and is easily implemented.  ...  In this study, to model a multiway data, we use non-negative variants of the two most widelyused low-rank tensor factorization models; the Tucker model [8] and the more restricted CANDE-COMP/PARAFAC  ... 
arXiv:1409.8276v1 fatcat:2j7hem634jdrjn6ql27lfknyyi

2020 Index IEEE Transactions on Knowledge and Data Engineering Vol. 32

2021 IEEE Transactions on Knowledge and Data Engineering  
Thangavel, M., +, TKDE Dec. 2020 2351-2362 Scalable Multiway Stream Joins in Hardware.  ...  ., +, TKDE March 2020 588-601 Microsoft Windows Scalable Multiway Stream Joins in Hardware.  ... 
doi:10.1109/tkde.2020.3038549 fatcat:75f5fmdrpjcwrasjylewyivtmu

Tensor Computation: A New Framework for High-Dimensional Problems in EDA

Zheng Zhang, Kim Batselier, Haotian Liu, Luca Daniel, Ngai Wong
2017 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  
open EDA problems where the use of tensor computation could be of advantage.  ...  This paper presents "tensor computation" as an alternative general framework for the development of efficient EDA algorithms and tools.  ...  This idea has been applied successfully to obtain polyadic decomposition [95] , [96] and Tucker decomposition [97] from incomplete data with automatic rank determination. • Low-Rank and Sparse Constraints  ... 
doi:10.1109/tcad.2016.2618879 fatcat:4li26hkadvex5c3xs3eb2ijwk4

Provable Sparse Tensor Decomposition [article]

Will Wei Sun and Junwei Lu and Han Liu and Guang Cheng
2016 arXiv   pre-print
We propose a novel sparse tensor decomposition method, namely Tensor Truncated Power (TTP) method, that incorporates variable selection into the estimation of decomposition components.  ...  The sparsity is achieved via an efficient truncation step embedded in the tensor power iteration.  ...  Scalable bayesian low-rank decomposition of incomplete multiway tensors. In International Conference on Machine Learning. Rendle, S. and Schmidt-Thieme, L. (2010) .  ... 
arXiv:1502.01425v3 fatcat:cfbyw2gqmzftzbzackviobyhva

Tensor Networks for Latent Variable Analysis. Part I: Algorithms for Tensor Train Decomposition [article]

Anh-Huy Phan, Andrzej Cichocki, Andre Uschmajew, Petr Tichavsky, George Luta, Danilo Mandic
2016 arXiv   pre-print
In this study, we present novel algorithms and applications of tensor network decompositions, with a particular focus on the tensor train decomposition and its variants.  ...  The novel algorithms developed for the tensor train decomposition update, in an alternating way, one or several core tensors at each iteration, and exhibit enhanced mathematical tractability and scalability  ...  Such tensor decompositions are natural extensions of matrix factorizations, which allows for most two-way factor analysis methods to be generalised to their multiway analysis counterparts.  ... 
arXiv:1609.09230v1 fatcat:2kfh7d6vabezfihdyfksvx4sy4

Regularized and Smooth Double Core Tensor Factorization for Heterogeneous Data [article]

Davoud Ataee Tarzanagh, George Michailidis
2021 arXiv   pre-print
We introduce a general tensor model suitable for data analytic tasks for heterogeneous datasets, wherein there are joint low-rank structures within groups of observations, but also discriminative structures  ...  data, since it provides more insightful decompositions than conventional tensor methods.  ...  The ill-posedness of the best low-rank approximation of a tensor was investigated in De Silva and Lim (2008) , while upper and lower bounds for tensor ranks have been studied in Alexeev et al. (2011)  ... 
arXiv:1911.10454v2 fatcat:y2tkhh2qmbce5iisznjlz6zii4

A Review of Relational Machine Learning for Knowledge Graphs

Maximilian Nickel, Kevin Murphy, Volker Tresp, Evgeniy Gabrilovich
2016 Proceedings of the IEEE  
The first is based on latent feature models such as tensor factorization and multiway neural networks. The second is based on mining observable patterns in the graph.  ...  In particular, we discuss two fundamentally different kinds of statistical relational models, both of which can scale to massive datasets.  ...  [76, 77] factorized adjacency tensors using the CP tensor decomposition to analyze the link structure of Web pages and Semantic Web data respectively.  ... 
doi:10.1109/jproc.2015.2483592 fatcat:uk6xvh5xljgf7aytfadzwzncsi

Tensor Graphical Model: Non-convex Optimization and Statistical Inference [article]

Xiang Lyu, Will Wei Sun, Zhaoran Wang, Han Liu, Jian Yang, Guang Cheng
2019 arXiv   pre-print
To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we assume the data follow a tensor normal distribution whose covariance has a Kronecker product structure.  ...  We consider the estimation and inference of graphical models that characterize the dependency structure of high-dimensional tensor-valued data.  ...  Acknowledgement Han Liu is grateful for the support of NSF CAREER Award DMS1454377, NSF IIS1408910, NSF IIS1332109, NIH R01MH102339, NIH R01GM083084, and NIH R01HG06841.  ... 
arXiv:1609.04522v2 fatcat:mrb6xax73rdj5apzryarnqgaqe

Unsupervised machine learning for exploratory data analysis in imaging mass spectrometry

Nico Verbeeck, Richard M. Caprioli, Raf Van de Plas
2019 Mass spectrometry reviews (Print)  
IMS does not require prior tagging of molecular targets and is able to measure a large number of ions concurrently in a single experiment.  ...  Imaging mass spectrometry (IMS) is a rapidly advancing molecular imaging modality that can map the spatial distribution of molecules with high chemical specificity.  ...  Although PARAFAC was originally developed as a multiway or tensor decomposition method, it can also be seen as a constrained two-way PCA model (Hanselmann et al., 2008) .  ... 
doi:10.1002/mas.21602 pmid:31602691 fatcat:lxna3i7wyvbn3lefbkafizdthu
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