Cross-validation in fuzzy ARTMAP for large databases

Kernel Bayesian ART and ARTMAP

Adaptive Resonance Theory (ART) is one of the successful approaches to resolving "the plasticity-stability dilemma" in neural networks, and its supervised learning model called ARTMAP is a powerful tool for classification. Among several improvements, such as Fuzzy or Gaussian based models, the state of art model is Bayesian based one, while solving the drawbacks of others. However, it is known that the Bayesian approach for the high dimensional and a large number of data requires high computational cost, and the covariance matrix in likelihood becomes unstable. This paper introduces Kernel Bayesian ART (KBA) and ARTMAP (KBAM) by integrating Kernel Bayes' Rule (KBR) and Correntropy Induced Metric (CIM) to Bayesian ART (BA) and ARTMAP (BAM), respectively, while maintaining the properties of BA and BAM. The kernel frameworks in KBA and KBAM are able to avoid the curse of dimensionality. In addition, the covariance-free Bayesian computation by KBR provides the efficient and stable computational capability to KBA and KBAM. Furthermore, Correntropy-based similarity measurement allows improving the noise reduction ability even in the high dimensional space. The simulation experiments show that KBA performs an outstanding self-organizing capability than BA, and KBAM provides the superior classification ability than BAM, respectively.

Fuzzy ARTMAP prediction of biological activities for potential HIV-1 protease inhibitors using a small molecular data set

Obtaining satisfactory results with neural networks depends on the availability of large data samples. The use of small training sets generally reduces performance. Most classical Quantitative Structure-Activity Relationship (QSAR) studies for a specific enzyme system have been performed on small data sets. We focus on the neuro-fuzzy prediction of biological activities of HIV-1 protease inhibitory compounds when inferring from small training sets. We propose two computational intelligence prediction techniques which are suitable for small training sets, at the expense of some computational overhead. Both techniques are based on the FAMR model. The FAMR is a Fuzzy ARTMAP (FAM) incremental learning system used for classification and probability estimation. During the learning phase, each sample pair is assigned a relevance factor proportional to the importance of that pair. The two proposed algorithms in this paper are: 1) The GA-FAMR algorithm, which is new, consists of two stages: a) During the first stage, we use a genetic algorithm (GA) to optimize the relevances assigned to the training data. This improves the generalization capability of the FAMR. b) In the second stage, we use the optimized relevances to train the FAMR. 2) The Ordered FAMR is derived from a known algorithm. Instead of optimizing relevances, it optimizes the order of data presentation using the algorithm of Dagher et al. In our experiments, we compare these two algorithms with an algorithm not based on the FAM, the FS-GA-FNN introduced in [4], [5]. We conclude that when inferring from small training sets, both techniques are efficient, in terms of generalization capability and execution time. The computational overhead introduced is compensated by better accuracy. Finally, the proposed techniques are used to predict the biological activities of newly designed potential HIV-1 protease inhibitors.

An adaptive multiobjective approach to evolving ART architectures

In this paper, we present the evolution of adaptive resonance theory (ART) neural network architectures (classifiers) using a multiobjective optimization approach. In particular, we propose the use of a multiobjective evolutionary approach to simultaneously evolve the weights and the topology of three well-known ART architectures; fuzzy ARTMAP (FAM), ellipsoidal ARTMAP (EAM), and Gaussian ARTMAP (GAM). We refer to the resulting architectures as MO-GFAM, MO-GEAM, and MO-GGAM, and collectively as MO-GART. The major advantage of MO-GART is that it produces a number of solutions for the classification problem at hand that have different levels of merit [accuracy on unseen data (generalization) and size (number of categories created)]. MO-GART is shown to be more elegant (does not require user intervention to define the network parameters), more effective (of better accuracy and smaller size), and more efficient (faster to produce the solution networks) than other ART neural network architectures that have appeared in the literature. Furthermore, MO-GART is shown to be competitive with other popular classifiers, such as classification and regression tree (CART) and support vector machines (SVMs).

GFAM: Evolving Fuzzy ARTMAP neural networks

This paper focuses on the evolution of Fuzzy ARTMAP neural network classifiers, using genetic algorithms, with the objective of improving generalization performance (classification accuracy of the ART network on unseen test data) and alleviating the ART category proliferation problem (the problem of creating more than necessary ART network categories to solve a classification problem). We refer to the resulting architecture as GFAM. We demonstrate through extensive experimentation that GFAM exhibits good generalization and is of small size (creates few ART categories), while consuming reasonable computational effort. In a number of classification problems, GFAM produces the optimal classifier. Furthermore, we compare the performance of GFAM with other competitive ARTMAP classifiers that have appeared in the literature and addressed the category proliferation problem in ART. We illustrate that GFAM produces improved results over these architectures, as well as other competitive classifiers.

Experiments with Safe muARTMAP : effect of the network parameters on the network performance

Fuzzy ARTMAP (FAM) is currently considered to be one of the premier neural network architectures in solving classification problems. One of the limitations of Fuzzy ARTMAP that has been extensively reported in the literature is the category proliferation problem. That is, Fuzzy ARTMAP has the tendency of increasing its network size, as it is confronted with more and more data, especially if the data are of the noisy and/or overlapping nature. To remedy this problem a number of researchers have designed modifications to the training phase of Fuzzy ARTMAP that had the beneficial effect of reducing this category proliferation. One of these modified Fuzzy ARTMAP architectures was the one proposed by Gomez-Sanchez, and his colleagues, referred to as Safe muARTMAP. In this paper we present reasonable analytical arguments that demonstrate of how we should choose the range of some of the Safe muARTMAP network parameters. Through a combination of these analytical arguments and experimentation we were able to identify good default parameter values for some of the Safe muARTMAP network parameters. This feat would allow one to save computations when a good performing Safe muARTMAP network is needed to be identified for a new classification problem. Furthermore, we performed an exhaustive experimentation to find the best Safe muARTMAP network for a variety of problems (simulated and real problems), and we compared it with other best performing ART networks, including other ART networks that claim to resolve the category proliferation problem in Fuzzy ARTMAP. These experimental results allow one to make appropriate statements regarding the pair-wise comparison of a number of ART networks (including Safe muARTMAP).

Accurate and Fast Off and Online Fuzzy ARTMAP-Based Image Classification With Application to Genetic Abnormality Diagnosis

We propose and investigate the fuzzy ARTMAP neural network in off and online classification of fluorescence in situ hybridization image signals enabling clinical diagnosis of numerical genetic abnormalities. We evaluate the classification task (detecting a several abnormalities separately or simultaneously), classifier paradigm (monolithic or hierarchical), ordering strategy for the training patterns (averaging or voting), training mode (for one epoch, with validation or until completion) and model sensitivity to parameters. We find the fuzzy ARTMAP accurate in accomplishing both tasks requiring only very few training epochs. Also, selecting a training ordering by voting is more precise than if averaging over orderings. If trained for only one epoch, the fuzzy ARTMAP provides fast, yet stable and accurate learning as well as insensitivity to model complexity. Early stop of training using a validation set reduces the fuzzy ARTMAP complexity as for other machine learning models but cannot improve accuracy beyond that achieved when training is completed. Compared to other machine learning models, the fuzzy ARTMAP does not loose but gain accuracy when overtrained, although increasing its number of categories. Learned incrementally, the fuzzy ARTMAP reaches its ultimate accuracy very fast obtaining most of its data representation capability and accuracy by using only a few examples. Finally, the fuzzy ARTMAP accuracy for this domain is comparable with those of the multilayer perceptron and support vector machine and superior to those of the naive Bayesian and linear classifiers.

Data-partitioning using the Hilbert space filling curves: effect on the speed of convergence of Fuzzy ARTMAP for large database problems

The Fuzzy ARTMAP algorithm has been proven to be one of the premier neural network architectures for classification problems. One of the properties of Fuzzy ARTMAP, which can be both an asset and a liability, is its capacity to produce new nodes (templates) on demand to represent classification categories. This property allows Fuzzy ARTMAP to automatically adapt to the database without having to a priori specify its network size. On the other hand, it has the undesirable side effect that large databases might produce a large network size (node proliferation) that can dramatically slow down the training speed of the algorithm. To address the slow convergence speed of Fuzzy ARTMAP for large database problems, we propose the use of space-filling curves, specifically the Hilbert space-filling curves (HSFC). Hilbert space-filling curves allow us to divide the problem into smaller sub-problems, each focusing on a smaller than the original dataset. For learning each partition of data, a different Fuzzy ARTMAP network is used. Through this divide-and-conquer approach we are avoiding the node proliferation problem, and consequently we speedup Fuzzy ARTMAP's training. Results have been produced for a two-class, 16-dimensional Gaussian data, and on the Forest database, available at the UCI repository. Our results indicate that the Hilbert space-filling curve approach reduces the time that it takes to train Fuzzy ARTMAP without affecting the generalization performance attained by Fuzzy ARTMAP trained on the original large dataset. Given that the resulting smaller datasets that the HSFC approach produces can independently be learned by different Fuzzy ARTMAP networks, we have also implemented and tested a parallel implementation of this approach on a Beowulf cluster of workstations that further speeds up Fuzzy ARTMAP's convergence to a solution for large database problems.