Unsupervised Multiway Data Analysis: A Literature Survey

Abstract

Multiway data analysis captures multilinear structures in higher-order datasets, where data have more than two modes. Standard two-way methods commonly applied on matrices often fail to find the underlying structures in multiway arrays. With increasing number of application areas, multiway data analysis has become popular as an exploratory analysis tool. We provide a review of significant contributions in literature on multiway models, algorithms as well as their applications in diverse disciplines including chemometrics, neuroscience, computer vision, and social network analysis.

Extended HALS algorithm for nonnegative Tucker decomposition and its applications for multiway analysis and classification

“…The simulation results are illustrated in Fig. 3 + from the corresponding basis components a (1) s , a (2) f , a (3) t and a (4) c . The relationship between two components can be evaluated via the Joint Rate index explained in details in [52].…”

“…The relationship between two components can be evaluated via the Joint Rate index explained in details in [52]. For example, to measure the relationship between spatial components a (1) s and category component a (4) c , we compute the Joint Rate index defined as the ratio of the total energy of all the rank-one tensors to which both components a (1) s and a (4) c contribute, and the total energy of all the rank-one tensors in which the component a (4) c interacts…”

“…Tensor decompositions are emerging as novel and promising tools for exploratory analysis of multidimen-sional data in diverse disciplines including text mining, neuroscience, computer vision, and social networks analysis [1][2][3][4]. Tensor decompositions capture multilinear structures in higher-order data-sets, where the data have more than two modes [5][6][7][8][9].…”

“…Tensor decompositions capture multilinear structures in higher-order data-sets, where the data have more than two modes [5][6][7][8][9]. Tensor decompositions and multi-way analysis allow naturally to extract hidden (latent) components and investigate complex relationships among them, for example, in exploration of social networks [4,10,11].…”

Exploring commonalities across participants in the neural representation of objects

“…In this work we are interested in examining similarity structure for internal representation of objects across people, thus focusing on multiway data (i.e., objects-byvoxels-by-people). Multiway data analysis requires special considerations; standard two-way analysis methods often fail to find underlying structure in multiway arrays [Acar and Yener, 2009]. Several solutions have been proposed to examine similarity structure for multiway data, such as INDSCAL procedure [Carroll and Chang, 1970], or PAR-AFAC procedure [Harshman, 1970].…”