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Pattern Analysis and Applications

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01.08.2014 | Theoretical Advances

Dimensionality reduction and topographic mapping of binary tensors

verfasst von: Jakub Mažgut, Peter Tiňo, Mikael Bodén, Hong Yan

Erschienen in: Pattern Analysis and Applications | Ausgabe 3/2014

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Abstract

In this paper, a decomposition method for binary tensors, generalized multi-linear model for principal component analysis (GMLPCA) is proposed. To the best of our knowledge at present there is no other principled systematic framework for decomposition or topographic mapping of binary tensors. In the model formulation, we constrain the natural parameters of the Bernoulli distributions for each tensor element to lie in a sub-space spanned by a reduced set of basis (principal) tensors. We evaluate and compare the proposed GMLPCA technique with existing real-valued tensor decomposition methods in two scenarios: (1) in a series of controlled experiments involving synthetic data; (2) on a real-world biological dataset of DNA sub-sequences from different functional regions, with sequences represented by binary tensors. The experiments suggest that the GMLPCA model is better suited for modelling binary tensors than its real-valued counterparts. Furthermore, we extended our GMLPCA model to the semi-supervised setting by forcing the model to search for a natural parameter subspace that represents a user-specified compromise between the modelling quality and the degree of class separation.

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The updating formulas of CSA and MPCA are similar, the only difference being that MPCA subtracts the mean from the data tensors.

As a term, we denote a short and widespread sequence of nucleotides that has or may have a biological significance.

R = [3 × 3] represents a natural parameter subspace spanned by 3-row and 3-column vectors.

\(\theta\)’s are fixed current values of the parameters and should be treated as constants.

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Titel: Dimensionality reduction and topographic mapping of binary tensors
verfasst von: Jakub Mažgut
Peter Tiňo
Mikael Bodén
Hong Yan
Publikationsdatum: 01.08.2014
Verlag: Springer London
Erschienen in: Pattern Analysis and Applications / Ausgabe 3/2014
Print ISSN: 1433-7541
Elektronische ISSN: 1433-755X
DOI: https://doi.org/10.1007/s10044-013-0317-y

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