Tensor Decomposition with Unaligned Observations

Runshi Tang; Tamara Kolda; Anru R. Zhang

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arXiv · 2410.14046

Tensor Decomposition with Unaligned Observations

Runshi Tang·Tamara Kolda·Anru R. Zhang

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Abstract

This paper presents a canonical polyadic (CP) tensor decomposition that addresses unaligned observations. The mode with unaligned observations is represented using functions in a reproducing kernel Hilbert space (RKHS). We introduce a versatile loss function that effectively accounts for various types of data, including binary, integer-valued, and positive-valued types. Additionally, we propose an optimization algorithm for computing tensor decompositions with unaligned observations, along with a stochastic gradient method to enhance computational efficiency. A sketching algorithm is also introduced to further improve efficiency when using the $\ell_2$ loss function. To demonstrate the efficacy of our methods, we provide illustrative examples using both synthetic data and an early childhood human microbiome dataset.

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BibTeX RIS

Runshi Tang, Tamara Kolda, Anru R. Zhang. 2024-10-17. Tensor Decomposition with Unaligned Observations. https://arxiv.org/abs/2410.14046

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