Multiresolution Tensor Decompositions with Mode Hierarchies

Abstract

Tensors (multidimensional arrays) are widely used for representing high-order dimensional data, in applications ranging from social networks, sensor data, and Internet traffic. Multiway data analysis techniques, in particular tensor decompositions, allow extraction of hidden correlations among multiway data and thus are key components of many data analysis frameworks. Intuitively, these algorithms can be thought of as multiway clustering schemes, which consider multiple facets of the data in identifying clusters, their weights, and contributions of each data element. Unfortunately, algorithms for fitting multiway models are, in general, iterative and very time consuming. In this article, we observe that, in many applications, there is a priori background knowledge (or metadata) about one or more domain dimensions. This metadata is often in the form of a hierarchy that clusters the elements of a given data facet (or mode). We investigate whether such single-mode data hierarchies can be used to boost the efficiency of tensor decomposition process, without significant impact on the final decomposition quality. We consider each domain hierarchy as a guide to help provide higher-or lower-resolution views of the data in the tensor on demand and we rely on these metadata-induced multiresolution tensor representations to develop a multiresolution approach to tensor decomposition. In this article, we focus on an alternating least squares (ALS)-based implementation of the two most important decomposition models such as the PARAllel FACtors (PARAFAC, which decomposes a tensor into a diagonal tensor and a set of factor matrices) and the Tucker (which produces as result a core tensor and a set of dimension-subspaces matrices). Experiment results show that, when the available metadata is used as a rough guide, the proposed multiresolution method helps fit both PARAFAC and Tucker models with consistent (under different parameters settings) savings in execution time and memory consumption, while preserving the quality of the decomposition.

MTC: Multiresolution Tensor Completion from Partial and Coarse Observations

“…Multi-scale methods can interpolate from low-resolution to highresolution [23,25,30] or operate first on one part of the tensor and then progressively generalize to the whole tensor [29]. For example, Schifanella et al [25] exploits extra domain knowledge and develops a multiresolution method to improve CP and Tucker decomposition. Song et al [29] imputes the tensor from a small corner and gradually increases on all modes by multi-aspect streaming.…”

epiDMS: Data Management and Analytics for Decision-Making From Epidemic Spread Simulation Ensembles

“…epiDMS, a novel epidemic simulation data management system software framework [26], aims to address the key challenges underlying large epidemic spread simulations, which, today, hinder real-time and continuous analysis and decision-making during ongoing outbreaks. Unlike other dynamic modeling platforms, such as Berkeley Madonna [27], the services provided by epiDMS include (a) storage and indexing of large-ensemble simulation data sets and the corresponding models and (b) search and analysis of ensemble simulation data sets to enable ensemble-based decision support [28][29][30].…”

SentIta and Doxa: Italian Databases and Tools for Sentiment Analysis Purposes

“…The second part of the proposal concerns the use of advanced DM techniques such as tensor-based representations (of semantics, rather than words) by embodying syntactic roles (subjects, modifiers, verbs, and arguments) into its dimensions (see Figure 1). The complexity of algorithms for tensors is a major challenge in this level, although recent re-search has shown that background information can improve this issue (Schifanella et al, 2014). Advanced data analysis techniques on tensors allow operations that are suitable for the aim of this ongoing research project.…”