# EM Algorithms for Weighted-Data Clustering with Application to Audio-Visual Scene Analysis

arXiv: https://arxiv.org/abs/1509.01509 · HTML: https://mlsanity.com/paper/1509.01509/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Sep 2015.

## Built on by (most cited first, 6 of 6)

- [SWEM: Towards Real-Time Video Object Segmentation with Sequential Weighted Expectation-Maximization](https://mlsanity.com/paper/2208.10128/) (2022)
- [Toward a `Standard Model' of Machine Learning](https://mlsanity.com/paper/2108.07783/) (2021)
- [Multimodal Continuous Visual Attention Mechanisms](https://mlsanity.com/paper/2104.03046/) (2021)
- [Hierarchical Augmentation and Distillation for Class Incremental Audio-Visual Video Recognition](https://mlsanity.com/paper/2401.06287/) (2024)
- [Gaussian Mixture Estimation from Weighted Samples](https://mlsanity.com/paper/2106.05109/) (2021)
- [Towards Automated Animal Density Estimation with Acoustic Spatial Capture-Recapture](https://mlsanity.com/paper/2308.12859/) (2023)

## Abstract (arXiv)

Data clustering has received a lot of attention and numerous methods, algorithms and software packages are available. Among these techniques, parametric finite-mixture models play a central role due to their interesting mathematical properties and to the existence of maximum-likelihood estimators based on expectation-maximization (EM). In this paper we propose a new mixture model that associates a weight with each observed point. We introduce the weighted-data Gaussian mixture and we derive two EM algorithms. The first one considers a fixed weight for each observation. The second one treats each weight as a random variable following a gamma distribution. We propose a model selection method based on a minimum message length criterion, provide a weight initialization strategy, and validate the proposed algorithms by comparing them with several state of the art parametric and non-parametric clustering techniques. We also demonstrate the effectiveness and robustness of the proposed clustering technique in the presence of heterogeneous data, namely audio-visual scene analysis.