Incremental cluster validity index-guided online learning for performance and robustness to presentation order

In streaming data applications incoming samples are processed and discarded, therefore, intelligent decision-making is crucial for the performance of lifelong learning systems. In addition, the order in which samples arrive may heavily affect the performance of online (and offline) incremental learners. The recently introduced incremental cluster validity indices (iCVIs) provide valuable aid in addressing such class of problems. Their primary use-case has been cluster quality monitoring; nonetheless, they have been very recently integrated in a streaming clustering method to assist the clustering task itself. In this context, the work presented here introduces the first adaptive resonance theory (ART)-based model that uses iCVIs for unsupervised and semi-supervised online learning. Moreover, it shows for the first time how to use iCVIs to regulate ART vigilance via an iCVI-based match tracking mechanism. The model achieves improved accuracy and robustness to ordering effects by integrating an online iCVI framework as module B of a topological adaptive resonance theory predictive mapping (TopoARTMAP) -- thereby being named iCVI-TopoARTMAP -- and by employing iCVI-driven post-processing heuristics at the end of each learning step. The online iCVI framework provides assignments of input samples to clusters at each iteration in accordance to any of several iCVIs. The iCVI-TopoARTMAP maintains useful properties shared by ARTMAP models, such as stability, immunity to catastrophic forgetting, and the many-to-one mapping capability via the map field module. The performance (unsupervised and semi-supervised) and robustness to presentation order (unsupervised) of iCVI-TopoARTMAP were evaluated via experiments with a synthetic data set and deep embeddings of a real-world face image data set.

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.