Neuroengineering of Clustering Algorithms

Cluster analysis can be broadly divided into multivariate data visualization, clustering algorithms, and cluster validation. This dissertation contributes neural network-based techniques to perform all three unsupervised learning tasks. Particularly, the first paper provides a comprehensive review on adaptive resonance theory (ART) models for engineering applications and provides context for the four subsequent papers. These papers are devoted to enhancements of ART-based clustering algorithms from (a) a practical perspective by exploiting the visual assessment of cluster tendency (VAT) sorting algorithm as a preprocessor for ART offline training, thus mitigating ordering effects; and (b) an engineering perspective by designing a family of multi-criteria ART models: dual vigilance fuzzy ART and distributed dual vigilance fuzzy ART (both of which are capable of detecting complex cluster structures), merge ART (aggregates partitions and lessens ordering effects in online learning), and cluster validity index vigilance in fuzzy ART (features a robust vigilance parameter selection and alleviates ordering effects in offline learning). The sixth paper consists of enhancements to data visualization using self-organizing maps (SOMs) by depicting in the reduced dimension and topology-preserving SOM grid information-theoretic similarity measures between neighboring neurons. This visualization\u27s parameters are estimated using samples selected via a single-linkage procedure, thereby generating heatmaps that portray more homogeneous within-cluster similarities and crisper between-cluster boundaries. The seventh paper presents incremental cluster validity indices (iCVIs) realized by (a) incorporating existing formulations of online computations for clusters\u27 descriptors, or (b) modifying an existing ART-based model and incrementally updating local density counts between prototypes. Moreover, this last paper provides the first comprehensive comparison of iCVIs in the computational intelligence literature --Abstract, page iv

A Survey of Adaptive Resonance Theory Neural Network Models for Engineering Applications

This survey samples from the ever-growing family of adaptive resonance theory (ART) neural network models used to perform the three primary machine learning modalities, namely, unsupervised, supervised and reinforcement learning. It comprises a representative list from classic to modern ART models, thereby painting a general picture of the architectures developed by researchers over the past 30 years. The learning dynamics of these ART models are briefly described, and their distinctive characteristics such as code representation, long-term memory and corresponding geometric interpretation are discussed. Useful engineering properties of ART (speed, configurability, explainability, parallelization and hardware implementation) are examined along with current challenges. Finally, a compilation of online software libraries is provided. It is expected that this overview will be helpful to new and seasoned ART researchers

Incremental Cluster Validity Index-Guided Online Learning for Performance and Robustness to Presentation Order

In streaming data applications, the incoming samples are processed and discarded, and therefore, intelligent decision-making is crucial for the performance of lifelong learning systems. In addition, the order in which the samples arrive may heavily affect the performance of 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 recently integrated in a streaming clustering method. 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 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 module as module B of a topological ART predictive mapping (TopoARTMAP)—thereby being named iCVI-TopoARTMAP—and using iCVI-driven postprocessing heuristics at the end of each learning step. The online iCVI module provides assignments of input samples to clusters at each iteration in accordance to any of the several iCVIs. The iCVI-TopoARTMAP maintains useful properties shared by the ART predictive mapping (ARTMAP) models, such as stability, immunity to catastrophic forgetting, and the many-to-one mapping capability via the map field module. The performance and robustness to the presentation order of iCVI-TopoARTMAP were evaluated via experiments with synthetic and real-world datasets

Incremental Cluster Validity Indices for Online Learning of Hard Partitions: Extensions and Comparative Study

Validation is one of the most important aspects of clustering, particularly when the user is designing a trustworthy or explainable system. However, most clustering validation approaches require batch calculation. This is an important gap because of the value of clustering in real-time data streaming and other online learning applications. Therefore, interest has grown in providing online alternatives for validation. This paper extends the incremental cluster validity index (iCVI) family by presenting incremental versions of Calinski-Harabasz (iCH), Pakhira-Bandyopadhyay-Maulik (iPBM), WB index (iWB), Silhouette (iSIL), Negentropy Increment (iNI), Representative Cross Information Potential (irCIP), Representative Cross Entropy (irH), and Conn_Index (iConn_Index). This paper also provides a thorough comparative study of correct, under- and over-partitioning on the behavior of these iCVIs, the Partition Separation (PS) index as well as four recently introduced iCVIs: incremental Xie-Beni (iXB), incremental Davies-Bouldin (iDB), and incremental generalized Dunn\u27s indices 43 and 53 (iGD43 and iGD53). Experiments were carried out using a framework that was designed to be as agnostic as possible to the clustering algorithms. The results on synthetic benchmark data sets showed that while evidence of most under-partitioning cases could be inferred from the behaviors of the majority of these iCVIs, over-partitioning was found to be a more challenging problem, detected by fewer of them. Interestingly, over-partitioning, rather then under-partitioning, was more prominently detected on the real-world data experiments within this study. The expansion of iCVIs provides significant novel opportunities for assessing and interpreting the results of unsupervised lifelong learning in real-time, wherein samples cannot be reprocessed due to memory and/or application constraints

A Study on Exploiting VAT to Mitigate Ordering Effects in Fuzzy ART

The clustering structures formed by Adaptive Resonance Theory (ART) and many other algorithms are dependent on input presentation/permutation order. In this work, we exploit Visual Assessment of cluster Tendency (VAT) as a pre-processor for Fuzzy ART in order to mitigate this problem. This approach is a global strategy that uses similarity-based ordering before clustering. Experimental results show that this framework improved peak and average performance, reduced the number of categories, and incurred less variability in the clustering outcome. By enhancing performance and reducing sensitivity to input order presentation, this approach is recommended when it is suitable to perform off-line incremental learning

Validity Index-Based Vigilance Test in Adaptive Resonance Theory Neural Networks

One of the distinguishing features of Adaptive Resonance Theory (ART) is that it relies on a second similarity check, called a vigilance test, to accept or reject a sample into a given category. Generic unsupervised versions of ART rely on a single layer vigilance test, whereas their supervised counterparts possess a second layer test based on classification errors that trigger a match tracking procedure regulated by an inter-ART block. This work uses a second layer vigilance test based on validity indices. A new sample is accepted into a category if its match function surpasses the vigilance test of both layers: the standard first check is based on minimum similarity, and the second check analyses whether setting that sample as belonging to the winner category results in an improvement of the current data partition according to the chosen validity index used as a cost function. Namely, if the new clustering state is superior to the previous one, then learning is allowed for the winning category. Otherwise, the algorithm proceeds as usual in ART implementations. Thus, this local greedy heuristic uses the validity index as a reinforcement signal, looking at the immediate reward to guide the learning of the ART categories without an additional external optimizer algorithm. A sweep analysis of the first layer vigilance parameter was performed and experiments indicate that the presented approach outperforms the standard Fuzzy ART neural network when samples are randomly presented. When samples are presented in a predefined order, Fuzzy ART obtains the best peak performance, however the modified approach was less sensitive to parameter variations

An Information-Theoretic-Cluster Visualization for Self-Organizing Maps

Improved data visualization will be a significant tool to enhance cluster analysis. In this paper, an information-theoretic-based method for cluster visualization using self-organizing maps (SOMs) is presented. The information-theoretic visualization (IT-vis) has the same structure as the unified distance matrix, but instead of depicting Euclidean distances between adjacent neurons, it displays the similarity between the distributions associated with adjacent neurons. Each SOM neuron has an associated subset of the data set whose cardinality controls the granularity of the IT-vis and with which the first- and second-order statistics are computed and used to estimate their probability density functions. These are used to calculate the similarity measure, based on Renyi\u27s quadratic cross entropy and cross information potential (CIP). The introduced visualizations combine the low computational cost and kernel estimation properties of the representative CIP and the data structure representation of a single-linkage-based grouping algorithm to generate an enhanced SOM-based visualization. The visual quality of the IT-vis is assessed by comparing it with other visualization methods for several real-world and synthetic benchmark data sets. Thus, this paper also contains a significant literature survey. The experiments demonstrate the IT-vis cluster revealing capabilities, in which cluster boundaries are sharply captured. Additionally, the information-theoretic visualizations are used to perform clustering of the SOM. Compared with other methods, IT-vis of large SOMs yielded the best results in this paper, for which the quality of the final partitions was evaluated using external validity indices

An Information Theoretic ART for Robust Unsupervised Learning

In this paper, an information-theoretic-based adaptive resonance theory (IT-ART) neural network architecture is presented. Each IT-ART category is defined by the first and second order statistics (mean and covariance matrix) of the cluster or class it represents. This information is used to estimate probability density functions (multivariate Gaussians) and compute the activation functions. The match function of the vigilance check is based on Renyi\u27s quadratic cross-entropy: it is the cross information potential. Experiments involving several real world and synthetic data sets were carried out to assess the performance of IT-ART, which was measured in terms of external validity indices. IT-ART expanded the range of successful vigilance parameter values in these tests