Arkade: Accelerating k-Nearest Neighbor Search with Non-Euclidean Distances using GPU Ray Tracing

Core Concepts

Arkade introduces two general reductions, Filter-Refine and Monotone Transformation, that enable k-nearest neighbor search with non-Euclidean distance functions to be accelerated using GPU ray tracing hardware.

Abstract

The paper proposes Arkade, a suite of two reductions that enable k-nearest neighbor (kNN) search with non-Euclidean distance functions to be accelerated using GPU ray tracing hardware. The key insights are: Filter-Refine Reduction: Decouples the kNN search into Filter and Refine phases, adapting a tree-based kNN algorithm for distances besides Euclidean distance. Exploits geometric properties of the distances to leverage ray tracing acceleration. Provides optimized implementations for L1, L∞, and general Lp distances. Monotone Transformation Reduction: Enables RT-based acceleration of kNN search for distance functions that do not hold the geometric properties favored by Filter-Refine. Transforms the input such that the original order of distances between the data points is preserved. Handles important examples like cosine distance or angular distance. The evaluations show that Arkade achieves speedups of 1.6x-200x and 1.3x-33.1x over various state-of-the-art GPU shader core and RT core baselines, respectively, across different datasets and distance functions.

Stats

"High-performance implementations of 𝑘-Nearest Neighbor Search (𝑘NN) in low dimensions use tree-based data structures." "Tree algorithms are hard to parallelize on GPUs due to their irregularity." "Newer Nvidia GPUs offer hardware support for tree operations through ray-tracing cores."

Quotes

"Recent works have proposed using RT cores to implement 𝑘NN search, but they all have a hardware-imposed constraint on the distance metric used in the search—the Euclidean distance." "We propose and implement two reductions to support 𝑘NN for a broad range of distances other than the Euclidean distance: Arkade Filter-Refine and Arkade Monotone Transformation."

Key Insights Distilled From

Arkade: k-Nearest Neighbor Search With Non-Euclidean Distances using GPU Ray Tracing

by Durga Mandar... at arxiv.org 04-23-2024

https://arxiv.org/pdf/2311.09168.pdf

Deeper Inquiries

How can the Arkade reductions be extended to handle higher dimensional data beyond 3D

To extend the Arkade reductions to handle higher dimensional data beyond 3D, we can leverage techniques such as dimensionality reduction. One approach could involve transforming the high-dimensional data into a lower-dimensional space using methods like Principal Component Analysis (PCA) or t-Distributed Stochastic Neighbor Embedding (t-SNE). By reducing the dimensionality of the data while preserving its essential characteristics, we can then apply the existing Arkade reductions designed for 3D data to the transformed dataset. This way, we can effectively handle higher-dimensional data in a manner similar to how we handle 3D data.

What are the limitations of the current Arkade reductions and how can they be addressed to support a wider range of distance functions, including non-metric distances

The current limitations of the Arkade reductions lie in their dependency on the Euclidean distance metric and the need for a predefined radius parameter. To support a wider range of distance functions, including non-metric distances, we can explore the following approaches: Custom Distance Functions: Allow users to define custom distance functions and corresponding geometric objects that can be efficiently processed by the Arkade reductions. This flexibility would enable the use of a variety of distance metrics beyond the Euclidean norm. Dynamic Radius Selection: Implement algorithms or heuristics to dynamically adjust the radius parameter based on the dataset characteristics and the chosen distance function. This adaptive approach can optimize the performance of the reductions for different scenarios. Incorporating Non-Metric Distances: Develop specific transformations or mappings for non-metric distances, similar to the Monotone Transformation for cosine distance, to align the non-metric distances with the capabilities of the Arkade reductions. This would involve finding ways to convert non-metric distances into a form compatible with the reductions. By addressing these limitations and incorporating these enhancements, the Arkade approach can be made more versatile and applicable to a broader range of distance functions, including non-metric distances.

Can the Arkade approach be generalized to accelerate other types of spatial queries beyond kNN, such as range searches or nearest neighbor joins

The Arkade approach can be generalized to accelerate other types of spatial queries beyond kNN, such as range searches or nearest neighbor joins, by adapting the core principles of the reductions to suit the requirements of these queries. Here are some ways to extend the Arkade approach for different spatial queries: Range Searches: For range searches, where the goal is to find all points within a specified distance from a query point, the Arkade reductions can be modified to filter and refine points based on a range criterion rather than a fixed number of nearest neighbors. By adjusting the filtering criteria and refining process, the reductions can efficiently handle range search queries. Nearest Neighbor Joins: Nearest neighbor joins involve finding the closest pair of points from two datasets. To support this query type, the Arkade approach can be enhanced to handle dual datasets and perform the necessary comparisons to identify the nearest neighbors from each dataset. By extending the reductions to consider pairs of points from different datasets, nearest neighbor joins can be accelerated using the Arkade framework. By customizing the Arkade approach to suit the specific requirements of range searches, nearest neighbor joins, and other spatial queries, it can serve as a versatile and efficient solution for a variety of spatial data processing tasks.