# Simplex Clustering via sBeta with Applications to Online Adjustment of Black-Box Predictions

arXiv: https://arxiv.org/abs/2208.00287 · HTML: https://mlsanity.com/paper/2208.00287/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 83 references that are in the map.
- First posted on arXiv 30 Jul 2022.

## Builds on (most cited first, 30 of 33)

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- [Prototype Rectification for Few-Shot Learning](https://mlsanity.com/paper/1911.10713/) (2019)
- [Laplacian Regularized Few-Shot Learning](https://mlsanity.com/paper/2006.15486/) (2020)
- [Transductive Information Maximization For Few-Shot Learning](https://mlsanity.com/paper/2008.11297/) (2020)
- [Deep clustering: On the link between discriminative models and K-means](https://mlsanity.com/paper/1810.04246/) (2018)
- [An Information-Theoretic Analysis of Hard and Soft Assignment Methods for Clustering](https://mlsanity.com/paper/1302.1552/) (2013)
- [Strategies for Training Large Vocabulary Neural Language Models](https://mlsanity.com/paper/1512.04906/) (2015)
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## Abstract (arXiv)

We explore clustering the softmax predictions of deep neural networks and introduce a novel probabilistic clustering method, referred to as k-sBetas. In the general context of clustering discrete distributions, the existing methods focused on exploring distortion measures tailored to simplex data, such as the KL divergence, as alternatives to the standard Euclidean distance. We provide a general maximum a posteriori (MAP) perspective of clustering distributions, emphasizing that the statistical models underlying the existing distortion-based methods may not be descriptive enough. Instead, we optimize a mixed-variable objective measuring data conformity within each cluster to the introduced sBeta density function, whose parameters are constrained and estimated jointly with binary assignment variables. Our versatile formulation approximates various parametric densities for modeling simplex data and enables the control of the cluster-balance bias. This yields highly competitive performances for the unsupervised adjustment of black-box model predictions in various scenarios. Our code and comparisons with the existing simplex-clustering approaches and our introduced softmax-prediction benchmarks are publicly available: https://github.com/fchiaroni/Clustering_Softmax_Predictions.