# Latent Simplex Position Model: High Dimensional Multi-view Clustering with Uncertainty Quantification

arXiv: https://arxiv.org/abs/1903.09029 · HTML: https://mlsanity.com/paper/1903.09029/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Mar 2019.

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

- [Learning a Latent Simplex in Input-Sparsity Time](https://mlsanity.com/paper/2105.08005/) (2021)
- [clusterBMA: Bayesian model averaging for clustering](https://mlsanity.com/paper/2209.04117/) (2022)
- [Convex optimization over a probability simplex](https://mlsanity.com/paper/2305.09046/) (2023)

## Abstract (arXiv)

High dimensional data often contain multiple facets, and several clustering patterns can co-exist under different variable subspaces, also known as the views. While multi-view clustering algorithms were proposed, the uncertainty quantification remains difficult --- a particular challenge is in the high complexity of estimating the cluster assignment probability under each view, and sharing information among views. In this article, we propose an approximate Bayes approach --- treating the similarity matrices generated over the views as rough first-stage estimates for the co-assignment probabilities; in its Kullback-Leibler neighborhood, we obtain a refined low-rank matrix, formed by the pairwise product of simplex coordinates. Interestingly, each simplex coordinate directly encodes the cluster assignment uncertainty. For multi-view clustering, we let each view draw a parameterization from a few candidates, leading to dimension reduction. With high model flexibility, the estimation can be efficiently carried out as a continuous optimization problem, hence enjoys gradient-based computation. The theory establishes the connection of this model to a random partition distribution under multiple views. Compared to single-view clustering approaches, substantially more interpretable results are obtained when clustering brains from a human traumatic brain injury study, using high-dimensional gene expression data. KEY WORDS: Co-regularized Clustering, Consensus, PAC-Bayes, Random Cluster Graph, Variable Selection