# Multi-Slice Clustering for 3-order Tensor Data

arXiv: https://arxiv.org/abs/2109.10803 · HTML: https://mlsanity.com/paper/2109.10803/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 26 references that are in the map.
- First posted on arXiv 22 Sep 2021.

## Builds on (most cited first, 4 of 4)

- [Multiway clustering via tensor block models](https://mlsanity.com/paper/1906.03807/) (2019)
- [Computational and Statistical Boundaries for Submatrix Localization in a Large Noisy Matrix](https://mlsanity.com/paper/1502.01988/) (2015)
- [Dynamic Tensor Clustering](https://mlsanity.com/paper/1708.07259/) (2017)
- [Algorithms for an Efficient Tensor Biclustering](https://mlsanity.com/paper/1903.04042/) (2019)

## Built on by (most cited first, 3 of 3)

- [Multiway clustering of 3-order tensor via affinity matrix](https://mlsanity.com/paper/2303.07757/) (2023)
- [DBSCAN of Multi-Slice Clustering for Third-Order Tensors](https://mlsanity.com/paper/2303.07768/) (2023)
- [Parallel Computation of Multi-Slice Clustering of Third-Order Tensors](https://mlsanity.com/paper/2309.17383/) (2023)

## Abstract (arXiv)

Several methods of triclustering of three dimensional data require the specification of the cluster size in each dimension. This introduces a certain degree of arbitrariness. To address this issue, we propose a new method, namely the multi-slice clustering (MSC) for a 3-order tensor data set. We analyse, in each dimension or tensor mode, the spectral decomposition of each tensor slice, i.e. a matrix. Thus, we define a similarity measure between matrix slices up to a threshold (precision) parameter, and from that, identify a cluster. The intersection of all partial clusters provides the desired triclustering. The effectiveness of our algorithm is shown on both synthetic and real-world data sets.