Nearest neighbor search in general metric spaces using a tree data structure with a simple heuristic

Area of Science:

• Computer Science
• Computational Geometry
• Data Structures

Background:

• Nearest neighbor search is crucial for many data mining and machine learning tasks.
• Existing algorithms often struggle with high-dimensional or non-Euclidean metric spaces.
• Efficiently searching large datasets remains a significant computational challenge.

Purpose of the Study:

• To introduce a new, efficient algorithm for nearest neighbor search in general metric spaces.
• To improve search performance by optimizing the pruning of search space.
• To demonstrate the algorithm's effectiveness on diverse datasets.

Main Methods:

• The algorithm recursively partitions data into Voronoi regions, organized in a tree structure.
• It leverages the triangular inequality to estimate minimum distances and prune search branches.
• A heuristic orders tree traversal based on estimated distances, enhancing search efficiency.

Main Results:

• The algorithm demonstrates significant efficiency gains on artificial and real-world datasets.
• Effective pruning of the search tree was achieved through the proposed heuristic.
• The method shows promise for applications in computational chemistry and other fields.

Conclusions:

• The presented algorithm offers a novel and efficient approach to nearest neighbor search in metric spaces.
• Recursive Voronoi partitioning and heuristic-guided search provide substantial performance improvements.
• This method is a valuable tool for large-scale data analysis and scientific computing.