ABSTRACT

Tensors are multi-dimensional generalizations of matrices, and so can have non-numeric entries. Extremely large and sparse coupled tensors arise in numerous important applications that require the analysis of large, diverse, and partially related data. The effective analysis of coupled tensors requires the development of algorithms and associated software that can identify the core relations that exist among the different tensor modes, and scale to extremely large datasets. The objective of this project is to develop theory and algorithms for (coupled) sparse and low-rank tensor factorization, and associated scalable software toolkits to make such analysis possible. The research in the project is centered on three major thrusts. The first is designed to make novel theoretical contributions in the area of coupled tensor factorization, by developing multi-way compressed sensing methods for dimensionality reduction with perfect latent model reconstruction. Methods to handle missing values, noisy input, and coupled data will also be developed. The second thrust focuses on algorithms and scalability on modern architectures, which will enable the efficient analysis of coupled tensors with millions and billions of non-zero entries, using the map-reduce paradigm, as well as hybrid multicore architectures. An open-source coupled tensor factorization toolbox (HTF- Hybrid Tensor Factorization) will be developed that will provide robust and high-performance implementations of these algorithms. Finally, the third thrust focuses on evaluating and validating the effectiveness of these coupled factorization algorithms on a NeuroSemantics application whose goal is to understand how human brain activity correlates with text reading & understanding by analyzing fMRI and MEG brain image datasets obtained while reading various text passages.

Given triplets of facts (subject-verb-object), like ('Washington' 'is the capital of' 'USA'), can we find patterns, new objects, new verbs, anomalies? Can we correlate these with brain scans of people reading these words, to discover which parts of the brain get activated, say, by tool-like nouns ('hammer'), or action-like verbs ('run')?
We propose a unified "coupled tensor" factorization framework to systematically mine such datasets. Unique challenges in these settings include
(a) tera- and peta-byte scaling issues,
(b) distributed fault-tolerant computation,
(c) large proportions of missing data, and
(d) insufficient theory and methods for big sparse tensors.
The Intellectual Merit of this effort is exactly the solution to the above four challenges.

The Broader Impact is the derivation of new scientific hypotheses on how the brain works and how it processes language (from the never-ending language learning (NELL) and NeuroSemantics projects) and the development of scalable open source software for coupled tensor factorization. Our tensor analysis methods can also be used in many other settings, including recommendation systems and computer-network intrusion/anomaly detection.

KEYWORDS:
Data mining; map/reduce; read-the-web; neuro-semantics; tensors.

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