LAAT: Locally Aligned Ant Technique for discovering multiple faint low dimensional structures of varying density

TL;DR

This paper introduces LAAT, a biologically inspired ant colony optimization method that effectively detects multiple low-dimensional manifolds in noisy, high-dimensional data, outperforming existing techniques.

Contribution

LAAT is a novel ant colony-based algorithm that captures local manifold directions and recovers multiple structures in noisy datasets, including astronomical data.

Findings

LAAT outperforms state-of-the-art noise reduction methods.

Effective in detecting multiple manifolds in noisy environments.

Validated on synthetic and real datasets, including cosmological simulations.

Abstract

Dimensionality reduction and clustering are often used as preliminary steps for many complex machine learning tasks. The presence of noise and outliers can deteriorate the performance of such preprocessing and therefore impair the subsequent analysis tremendously. In manifold learning, several studies indicate solutions for removing background noise or noise close to the structure when the density is substantially higher than that exhibited by the noise. However, in many applications, including astronomical datasets, the density varies alongside manifolds that are buried in a noisy background. We propose a novel method to extract manifolds in the presence of noise based on the idea of Ant colony optimization. In contrast to the existing random walk solutions, our technique captures points that are locally aligned with major directions of the manifold. Moreover, we empirically show that the biologically inspired formulation of ant pheromone reinforces this behavior enabling it to recover multiple manifolds embedded in extremely noisy data clouds. The algorithm performance in comparison to state-of-the-art approaches for noise reduction in manifold detection and clustering is demonstrated, on several synthetic and real datasets, including an N-body simulation of a cosmological volume.