Multilinear Filtering Based on a Hierarchical Structure of Covariance Matrices

Andrzej Szwabe,

Pawel Misiorek,

Michal Ciesielczyk

Abstrakt

We propose a novel model of multilinear filtering based on a hierarchical structure of covariance matrices – each matrix being extracted from the input tensor in accordance to a specific set-theoretic model of data generalization, such as derivation of expectation values. The experimental analysis results presented in this paper confirm that the investigated approaches to tensor-based data representation and processing outperform the standard collaborative filtering approach in the ‘cold-start’ personalized recommendation scenario (of very sparse input data). Furthermore, it has been shown that the proposed method is superior to standard tensor-based frameworks such as N-way Random Indexing (NRI) and Higher-Order Singular Value Decomposition (HOSVD) in terms of both the AUROC measure and computation time.

Słowa kluczowe: tensor-based data modeling, multilinear PCA, random indexing, dimensionality reduction, multilinear data filtering, higher-order SVD

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