iCVI-ARTMAP: Accelerating and improving clustering using adaptive resonance theory predictive mapping and incremental cluster validity indices

This paper presents an adaptive resonance theory predictive mapping (ARTMAP) model which uses incremental cluster validity indices (iCVIs) to perform unsupervised learning, namely iCVI-ARTMAP. Incorporating iCVIs to the decision-making and many-to-one mapping capabilities of ARTMAP can improve the choices of clusters to which samples are incrementally assigned. These improvements are accomplished by intelligently performing the operations of swapping sample assignments between clusters, splitting and merging clusters, and caching the values of variables when iCVI values need to be recomputed. Using recursive formulations enables iCVI-ARTMAP to considerably reduce the computational burden associated with cluster validity index (CVI)-based offline clustering. Depending on the iCVI and the data set, it can achieve running times up to two orders of magnitude shorter than when using batch CVI computations. In this work, the incremental versions of Calinski-Harabasz, WB-index, Xie-Beni, Davies-Bouldin, Pakhira-Bandyopadhyay-Maulik, and negentropy increment were integrated into fuzzy ARTMAP. Experimental results show that, with proper choice of iCVI, iCVI-ARTMAP outperformed fuzzy adaptive resonance theory (ART), dual vigilance fuzzy ART, kmeans, spectral clustering, Gaussian mixture models and hierarchical agglomerative clustering algorithms in most of the synthetic benchmark data sets. It also performed competitively on real world image benchmark data sets when clustering on projections and on latent spaces generated by a deep clustering model. Naturally, the performance of iCVI-ARTMAP is subject to the selected iCVI and its suitability to the data at hand; fortunately, it is a general model wherein other iCVIs can be easily embedded.