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

Georgii Novikov, Alexander Gneushev, Alexey Kadeishvili, Ivan Oseledets

TL;DR

This work tackles efficient storage and fast retrieval in large vector databases by employing tensor-train (TT) low-rank decompositions to compress point clouds. It introduces a probabilistic compression framework that uses the Sliced Wasserstein loss and a Nearest-Neighbor Distance loss to train TT cores, achieving order-invariant representations with respect to point ordering. A key insight is the emergence of a hierarchical TT structure, enabling a beam-search-like ANN method and making TT suitable for out-of-distribution detection via distance-based scores. Experimental results on MVTEC AD and a Deep1B subset show memory savings and improved pixel-level metrics (and competitive image-level metrics) relative to coreset-based approaches, along with a proof-of-concept TT-based indexing for ANN that outperforms a baseline method in recall across several ranks.

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.

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

TL;DR

This work tackles efficient storage and fast retrieval in large vector databases by employing tensor-train (TT) low-rank decompositions to compress point clouds. It introduces a probabilistic compression framework that uses the Sliced Wasserstein loss and a Nearest-Neighbor Distance loss to train TT cores, achieving order-invariant representations with respect to point ordering. A key insight is the emergence of a hierarchical TT structure, enabling a beam-search-like ANN method and making TT suitable for out-of-distribution detection via distance-based scores. Experimental results on MVTEC AD and a Deep1B subset show memory savings and improved pixel-level metrics (and competitive image-level metrics) relative to coreset-based approaches, along with a proof-of-concept TT-based indexing for ANN that outperforms a baseline method in recall across several ranks.

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.
Paper Structure (21 sections, 19 equations, 3 figures, 1 table, 1 algorithm)

This paper contains 21 sections, 19 equations, 3 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Method
  3. Point Cloud Tensorization.
  4. Sliced Wasserstein Loss.
  5. Nearest-Neighbor Distance
  6. OOD Detection with TT Point Cloud.
  7. Approximate Nearest-Neighbor Search.
  8. Hierarchical Structure.
  9. Experiments
  10. Toy Examples
  11. MVTec Dataset
  12. Approximate Nearest Neighbors
  13. Related Work
  14. Conclusion
  15. Appendix
  16. ...and 6 more sections

Figures (3)

  • Figure 1: Diagram of the TT point cloud in Penrose graphical notation. Each tensor is depicted as a vertex, and each vertex has as many edges as the dimensionality of the corresponding tensor. Two tensors are connected with a common edge if these two tensors are contracted along the corresponding dimension.
  • Figure 2: Three toy point clouds (blue points) consisting of 8192 vectors each, and its compressed TT-point cloud approximation (orange points).
  • Figure 3: (a, b, c, d): Comparison of different characteristics of the index search structure for GNO-IMI and TT-point cloud with varying TT-ranks. On the x-axis, we plot TT-rank (upper value) and the fraction of parameters of the TT point cloud relative to the number of parameters in GNO-IMI (bottom value). (e, f): Two-dimensional PCA projections of the original point cloud (e) and TT-point cloud (f).