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Summarizing Fuzzy Tensors with Sub-Tensors

Published: 07 June 2023 Publication History

Abstract

Disjunctive box cluster models summarize n-way Boolean tensors with some of their sub-tensors. Mirkin and Kramarenko proposed that regression model, for n ∈ {2, 3}, and algorithms relying on hill climbing to discover good sub-tensors, according to ordinary least squares. This article generalizes that work to n-way fuzzy tensors, details significant performance improvements, better starting points for hill climbing if n ≥ 3, a greedy ranking of the discovered sub-tensors in descending order of contribution to the summary, and the use of the elbow method to truncate the ordered list.

References

[1]
Sanjar Karaev and Pauli Miettinen. 2016. Cancer: Another Algorithm for Subtropical Matrix Factorization. In Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases (ECML PKDD 2016). Springer, 576--592.
[2]
Lucas Maciel, Jônatas Alves, Vinícius Fernandes dos Santos, and Loïc Cerf. 2020. Climbing the Hill with ILP to Grow Patterns in Fuzzy Tensors. International Journal of Computational Intelligence Systems 13, 1 (2020), 1036--1047.
[3]
Boris G. Mirkin and Andrey V. Kramarenko. 2011. Approximate Bicluster and Tricluster Boxes in the Analysis of Binary Data. In Proceedings of the 13th. International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing (RSFDGrC 2011). Springer, 248--256.
[4]
Changlin Wan, Wennan Chang, Tong Zhao, Sha Cao, and Chi Zhang. 2020. Geometric All-way Boolean Tensor Decomposition. In Advances in Neural Information Processing Systems (NeurIPS 2020). Curran Associates, Inc., 2848--2857.

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    cover image ACM Conferences
    SAC '23: Proceedings of the 38th ACM/SIGAPP Symposium on Applied Computing
    March 2023
    1932 pages
    ISBN:9781450395175
    DOI:10.1145/3555776
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    Published: 07 June 2023

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    Author Tags

    1. disjunctive box cluster model
    2. fuzzy tensor
    3. ordinary least squares
    4. hill climbing
    5. elbow method

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