Unsupervised Multiway Data Analysis: A Literature Survey

By Evrim Acar, Bülent Yener. IEEE Transactions on Knowledge and Data Engineering, 2009

458 citations recorded by the source corpus.

Subfields: Computational Mathematics, Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/5979666682daad35c7cf72e139902c000cbd6b37

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The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

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In Computer Vision and Pattern Recognition

In Signal Processing

Citations in the corpus

Probabilistic Models for Incomplete Multi-dimensional Arrays (2009, methodology): “In each step only one of the matrices is optimized, while keeping others intact, refer to (Acar & Yener, 2007) for more details.”
Structure of the Hessian matrix and an economical implementation of Newton’s method in the problem of canonical approximation of tensors (2010, background): “The same approach is required for data processing in such diverse fields as spectroscopy, neuroscience, image processing, social network modeling, and real�time process monitoring (see [ 3 ]).”
Tensor-Based Formulation and Nuclear Norm Regularization for Multienergy Computed Tomography (2013, methodology): “We propose an iterative reconstruction method for the multi-energy CT problem where we model the multi-spectral unknown as a low rank 3-way (third order) tensor.”
Limestone: High-throughput candidate phenotype generation via tensor factorization (2014, background): “…in their paper [48]), we focus on the CP decomposition for two primary reasons: (i) it is a well-known and commonly applied tensor factorization model [55], and (ii) the resulting structure ( R rank-one tensors) is well-suited for capturing medical concepts in a concise and interpretable manner.”
MACH: Fast Randomized Tensor Decompositions (2009, background): “Two recent surveys of tensor decompositions and their applications are [26],[2], with a wealth of references on the topic.”
Tensor Decompositions and Applications (2009, unknown): “The inner product of two same-sized tensors X , Y ∈ R I 1 × I 2 × ··· × I N is the sum of the products of their entries, i.e., It follows immediately that ⟨ X , X ⟩ = ∥ X ∥ 2 .”
Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions (2016, unknown): “ol for blind signal separation in vastly diverse branches of signal processing and machine learning, such as in audio and speech processing, biomedical engineering, chemometrics, and machine learning [5,153,193,239]. It is also routinely used in exploratory data analysis, where the rank-1 terms capt”
New ALS Methods With Extrapolating Search Directions and Optimal Step Size for Complex-Valued Tensor Decompositions (2011, methodology): “Computationally, ALS is a classical and unsophisticated method for CP [3], [17], [20], [28].”
Tensor Decompositions for Signal Processing Applications: From two-way to multiway component analysis (2014, background): “The signiﬁcant interest in tensors and their fast emerging applications are reﬂected in books [7,8,12,19–21] and tutorial papers [22–29] covering various aspects of multiway analysis.”
From Frequency to Meaning: Vector Space Models of Semantics (2010, background): “For an overview of tensor decompositions, see the surveys of Kolda and Bader (2009) or Acar and Yener (2009). Turney (2007) gives an empirical evaluation of how well four different Tucker decomposition algorithms scale up for large sparse third-order tensors.”
Temporal Link Prediction Using Matrix and Tensor Factorizations (2010, methodology): “ix factorizations that capture the underlying patterns in multi-way data sets and have proved to be successful in diverse disciplines including chemometrics, neuroscience and social network analysis [Acar and Yener 2009; Kolda and Bader 2009]. Moreover, CP yields a highly interpretable factorization”
Big Data Analysis with Signal Processing on Graphs: Representation and processing of massive data sets with irregular structure (2014, background): “on graphs but rather view data as multi-dimensional arrays [ 2], [3], [4].”
Multilayer networks (2013, methodology): “In the computer-science and computational linear-algebra communities, tensor-decomposition methods [114, 186] and multiway data analysis [3] have been used to study various types of multilayer networks (see Sections 4.”
Learning Multi-Way Relations via Tensor Decomposition With Neural Networks (2018, methodology): “We focus on Tucker decomposition (Kolda and Bader 2009; Acar and Yener 2009), a well-known tensor decomposition, which is most often calculated using the alternating least squares (ALS) method (Lathauwer, Moor, and Vandewalle 2000).”
Algorithms for nonnegative matrix and tensor factorizations: a unified view based on block coordinate descent framework (2013, background): “A few other decomposition models of higher order tensors have been studied, and interested 601 readers are referred to [1,61].”
A survey of multilinear subspace learning for tensor data (2011, background): “Acar and Yener [34] surveys unsupervised multiway data analysis for discovering structures in higher-order data sets in applications such as chemistry, neuroscience, and social network analysis.”
Low-Rank Explicit QTT Representation of the Laplace Operator and Its Inverse (2012, background): “Nonlinear low-parametric approximations of multidimensional arrays, or tensors, find numerous applications in data analysis [26, 5, 1] and scientific computing [20].”