GNaN: A natural neighbor search algorithm based on universal gravitation

The natural neighbor (NaN) method and its search algorithm (NaN-Searching) are widely used in many fields, including pattern recognition and image processing. NaN-Searching fundamentally overcomes the problem of the conventional nearest neighbor algorithm in selecting parameters for datasets with arbitrary shapes and achieves good results. However, this algorithm uses the conventional distance metric as the neighbor judgment criterion, which cannot accurately reflect the overall structure of the dataset in the process of neighbor search. Inspired by Newton's law of universal gravitation, we propose a NaN search algorithm based on universal gravitation (GNaN-Searching). Our algorithm calculates gravitation using the structural features of data points in the dataset, it utilizes the gravitation between data as the neighbor judgment criterion, and inherits the no-parameter and dynamic neighborhood characteristics of the NaN search algorithm. Experimental results show that the natural neighborhood graph obtained by our method has a high performance in the representation of manifold data. We also applied the new method to clustering and outlier detection and achieved satisfactory results.