NDLI: Multiresolution Tensor Decompositions with Mode Hierarchies

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Multiresolution Tensor Decompositions with Mode Hierarchies

Content Provider	ACM Digital Library
Author	Candan, K. Selçuk Schifanella, Claudio Sapino, Maria Luisa
Copyright Year	2014
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.
Starting Page	1
Ending Page	38
Page Count	38
File Format	PDF
ISSN	15564681
e-ISSN	1556472X
DOI	10.1145/2532169
Volume Number	8
Issue Number	2
Journal	ACM Transactions on Knowledge Discovery from Data (TKDD)
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2014-06-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	PARAFAC Tensor decomposition Tucker Multiresolution
Content Type	Text
Resource Type	Article
Subject	Computer Science

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3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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