Tensor-Train Point Cloud Compression and Efficient Approximate Nearest-Neighbor Search

TL;DR

This paper presents a novel tensor-train based approach for compressing point clouds and performing fast approximate nearest-neighbor searches, with applications in machine learning and out-of-distribution detection.

Contribution

It introduces a tensor-train decomposition method with a probabilistic interpretation and density estimation losses, enabling efficient point cloud compression and hierarchical structure for ANN search.

Findings

Effective point cloud compression using TT decomposition

Enhanced approximate nearest-neighbor search efficiency

Improved out-of-distribution detection performance

Abstract

Nearest-neighbor search in large vector databases is crucial for various machine learning applications. This paper introduces a novel method using tensor-train (TT) low-rank tensor decomposition to efficiently represent point clouds and enable fast approximate nearest-neighbor searches. We propose a probabilistic interpretation and utilize density estimation losses like Sliced Wasserstein to train TT decompositions, resulting in robust point cloud compression. We reveal an inherent hierarchical structure within TT point clouds, facilitating efficient approximate nearest-neighbor searches. In our paper, we provide detailed insights into the methodology and conduct comprehensive comparisons with existing methods. We demonstrate its effectiveness in various scenarios, including out-of-distribution (OOD) detection problems and approximate nearest-neighbor (ANN) search tasks.