Ant colony mapping for dimensionality reduction to discrete spaces

Dimensionality reduction is a widely used technique in AI with various application areas. It maps feature vectors of high dimension to a space of lower dimension so that the new representation maintains some meaningful properties of the original data (i.e., similar vectors have similar new representations). This paper considers the problem of dimensionality reduction to discrete spaces. A novel distributed, stochastic ’swarm intelligence’ algorithm, Ant Colony Mapping (ACOM), is proposed to generate approximate solutions to the problem. ACOM is a generalisation of the brood-sorting behaviour of certain ant species that results in the spatial clustering of objects. After demonstrating ACOM’s basic behaviour, the algorithm’s performance on 2D lattice topologies is analysed in terms of the number of ants and the number of problem parameters. The performance is compared to that of a recent, local search-enhanced Steady-State Genetic Algorithm, namely Steady-State Memetic Algorithm (SSMA), as a baseline, both in terms of solution quality and computational budget. Additional experiments compare ACOM, an annealed variant, and an LAS-ACOM hybrid with non-evolutionary grid-sorting baselines on a random-RGB benchmark. Annealing and hybridisation improve ACOM’s alignment quality, but global baselines remain stronger; in exchange, ACOM uses local operations with constant complexity rather than the cubic complexity of assignment-based methods.