Parallel Total Variation Distance Estimation with Neural Networks for Merging Over-Clusterings

TL;DR

This paper introduces a neural network-based method for efficiently estimating total variation distances between over-clustered data subsets, enabling improved merging decisions in image and point cloud datasets.

Contribution

The paper presents a novel neural network approach that estimates pairwise TVDs with reduced memory, improving over existing methods for merging over-clusterings.

Findings

TVD estimates lead to better merge decisions than state-of-the-art representations.

Memory usage is significantly reduced by the proposed neural network design.

Method generalizes well to different data modalities, including images and point clouds.

Abstract

We consider the initial situation where a dataset has been over-partitioned into $k$ clusters and seek a domain independent way to merge those initial clusters. We identify the total variation distance (TVD) as suitable for this goal. By exploiting the relation of the TVD to the Bayes accuracy we show how neural networks can be used to estimate TVDs between all pairs of clusters in parallel. Crucially, the needed memory space is decreased by reducing the required number of output neurons from $k^2$ to $k$. On realistically obtained over-clusterings of ImageNet subsets it is demonstrated that our TVD estimates lead to better merge decisions than those obtained by relying on state-of-the-art unsupervised representations. Further the generality of the approach is verified by evaluating it on a a point cloud dataset.