  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.
