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The cerebellum constitutes a vital part of the human brain system that possesses the capability to model highly nonlinear physical dynamics. The cerebellar model articulation controller (CMAC) associative memory network is a computational model inspired by the neuropbysiological properties of the cerebellum, and it has been widely used for control, optimization, and various pattern recognition tasks. However, the CMAC network's highly regularized computing structure often leads to the following: l) a suboptimal modeling accuracy, 21 poor memory utilization, and 3) the generalization-accuracy dilemma. Previous attempts to address these shortcomings have limited success and the proposed solutions often introduce a high operational complexity to the CMAC network. This paper presents a novel neurophysiologically inspired associative memory architecture named pseudo-self-evolving CMAC (PSECMAC) that nonuniformly allocates its computing cells to overcome the architectural deficiencies encountered by the CMAC network. The nonuniform memory allocation scheme employed by the proposed PSECMAC network is inspired by the cerebellar experience-driven synaptic plasticity phenomenon observed in the cerebellum, where significantly higher densities of synaptic connections are located in the frequently accessed regions. In the PSECMAC network, this biological synaptic plasticity phenomenon is emulated by employing a data-driven adaptive memory quantization scheme that defines its computing structure. A neighborhood-based activation process is subsequently implemented to facilitate the learning and computation of the PSECMAC structure. The training stability of the PSECMAC network is theoretically assured by the proof of its learning convergence, which will be presented in this paper. The performance of the proposed network is subsequently benchmarked against the CMAC network and several representative CMAC variants on three real-life applications, namely, pricing of currency futures option, banking failure classification, and modeling of the glucose-insulin dynamics of the human glucose metabolic process. The experimental results have strongly demonstrated the effectiveness of the PSECMAC network in addressing the architectural deficiencies of the CMAC network by achieving significant improvements in the memory utilization, output accuracy as well as the generalization capability of the network. Index Terms--Associative memory, brain inspired, cerebellar model articulation controller (CMAC), cerebellum, learning convergence, multiresolution, neural networks, pseudo-self-evolving CMAC (PSECMAC).

Earlier clustering techniques such as the modified learning vector quantization (MLVQ) and the fuzzy Kohonen partitioning (FKP) techniques have focused on the derivation of a certain set of parameters so as to define the fuzzy sets in terms of an algebraic function. The fuzzy membership functions thus generated are uniform, normal, and convex. Since any irregular training data is clustered into uniform fuzzy sets (Gaussian, triangular, or trapezoidal), the clustering may not be exact and some amount of information may be lost. In this paper, two clustering techniques using a Kohonen-like self-organizing neural network architecture, namely, the unsupervised discrete clustering technique (UDCT) and the supervised discrete clustering technique (SDCT), are proposed. The UDCT and SDCT algorithms reduce this data loss by introducing nununiform, normal fuzzy sets that are not necessarily convex. The training data range is divided into discrete points at equal intervals, and the membership value corresponding to each discrete point is generated. Hence, the fuzzy sets obtained contain pairs of values, each pair corresponding to a discrete point and its membership grade. Thus, it can be argued that fuzzy membership functions generated using this kind of a discrete methodology provide a more accurate representation of the actual input data. This fact has been demonstrated by comparing the membership functions generated by the UDCT and SDCT algorithms against those generated by the MLVQ, FKP, and pseudofuzzy Kohonen partitioning (PFKP) algorithms. In addition to these clustering techniques, a novel pattern classifying network called the Yager fuzzy neural network (FNN) is proposed in this paper. This network corresponds completely to the Yager inference rule and exhibits remarkable generalization abilities. A modified version of the pseudo-outer product (POP)-Yager FNN called the modified Yager FNN is introduced that eliminates the drawbacks of the earlier network and yields superior performance. Extensive experiments have been conducted to test the effectiveness of these two networks, using various clustering algorithms. It follows that the SDCT and UDCT clustering algorithms are particularly suited to networks based on the Yager inference rule. Index Terms--Anderson's Iris data, automatic derivation, fuzzy clustering, fuzzy Kohonen partitioning (FKP), fuzzy pattern classification, membership function, modified learning vector quantization (MLVQ), noise modeling and cancellation, normal and convex fuzzy sets, pseudofuzzy partition, self-organizing feature maps, supervised and unsupervised learning, traffic prediction and modeling, triangular and trapezoidal fuzzy sets, Yager inference rule, Yager rule network.

The cerebellar model articulation controller (CMAC) neural network (NN) is a well-established computational model of the human cerebellum. Nevertheless, there are two major drawbacks associated with the uniform quantization scheme of the CMAC network. They are the following: 1) a constant output resolution associated with the entire input space and 2) the generalization-accuracy dilemma. Moreover, the size of the CMAC network is an exponential function of the number of inputs. Depending on the characteristics of the training data, only a small percentage of the entire set of CMAC memory cells is utilized. Therefore, the efficient utilization of the CMAC memory is a crucial issue. One approach is to quantize the input space nonuniformly. For existing nonuniformly quantized CMAC systems, there is a tradeoff between memory efficiency and computational complexity. Inspired by the underlying organizational mechanism of the human brain, this paper presents a novel CMAC architecture named hierarchically clustered adaptive quantization CMAC (HCAQ-CMAC). HCAQ-CMAC employs hierarchical clustering for the nonuniform quantization of the input space to identify significant input segments and subsequently allocating more memory cells to these regions. The stability of the HCAQ-CMAC network is theoretically guaranteed by the proof of its learning convergence. The performance of the proposed network is subsequently benchmarked against the original CMAC network, as well as two other existing CMAC variants on two real-life applications, namely, automated control of car maneuver and modeling of the human blood glucose dynamics. The experimental results have demonstrated that the HCAQ-CMAC network offers an efficient memory allocation scheme and improves the generalization and accuracy of the network output to achieve better or comparable performances with smaller memory usages. Index Terms--Cerebellar model articulation controller (CMAC), hierarchical clustering, hierarchically clustered adaptive quantization CMAC (HCAQ-CMAC), learning convergence, nonuniform quantization.

As an associative memory neural network model, the cerebellar model articulation controller (CMAC) has attractive properties of fast learning and simple computation, but its rigid structure makes it difficult to approximate certain functions. This research attempts to construct a novel neural fuzzy CMAC, in which Bayesian Ying-Yang (BYY) learning is introduced to determine the optimal fuzzy sets, and a truth-value restriction inference scheme is subsequently employed to derive the truth values of the rule weights of implication rules. The BYY is motivated from the famous Chinese ancient Ying-Yang philosophy: everything in the universe can be viewed as a product of a constant conflict between opposites--Ying and Yang, a perfect status is reached when Ying and Yang achieve harmony. The proposed fuzzy CMAC (FCMAC)-BYY enjoys the following advantages. First, it has a higher generalization ability because the fuzzy rule sets are systematically optimized by BYY; second, it reduces the memory requirement of the network by a significant degree as compared to the original CMAC; and third, it provides an intuitive fuzzy logic reasoning and has clear semantic meanings. The experimental results on some benchmark datasets show that the proposed FCMAC-BYY outperforms the existing representative techniques in the research literature. Index Terms--Bayesian Ying-Yang (BYY) learning, cerebellar model articulation controller (CMAC), fuzzy rule set, neural networks, truth-value restriction (TVR).

Neural fuzzy networks proposed in the literature can be broadly classified into two groups. The first group is essentially fuzzy systems with self-tuning capabilities and requires an initial rule base to be specified prior to training, [7]. The second group of neural fuzzy networks, on the other hand, is able to automatically formulate the fuzzy rules from the numerical training data. Examples are the Falcon-ART, [12] and the POPFNN family of networks, [14]. A cluster analysis is first performed on the training data and the fuzzy rules are subsequently derived through the proper connections of these computed clusters. This correspondence proposes two new networks: Falcon-FKP and Falcon-PFKP. They are extensions of the Falcon-ART network, [12] and aimed to overcome the shortcomings faced by the Falcon-ART network itself, i.e., poor classification ability when the classes of input data are very similar to each other, termination of training cycle depends heavily on a preset error parameter, the fuzzy rule base of the Falcon-ART network may not be consistent Nauck, [13], there is no control over the number of fuzzy rules generated, and learning efficiency may deteriorate by using complementarily coded training data. These deficiencies are essentially inherent to the fuzzy ART, [3] clustering technique employed by the Falcon-ART network. Hence, two clustering techniques--Fuzzy Kohonen Partitioning (FKP) and its pseudo variant PFKP, [1] are synthesized with the basic Falcon structure to compute the fuzzy sets and to automatically derive the fuzzy rules from the training data. The resultant neural fuzzy networks are Falcon-FKP and Falcon-PFKP, respectively. These two proposed networks have a lean and efficient training algorithm and consistent fuzzy rule bases. Extensive simulations are conducted using the two networks and their performances are encouraging when benchmarked against other neural and neural fuzzy systems. Index Terms--Classification, convergence, Falcon-ART, Falcon-FKP, Falcon-PFKP, fuzzy rules, iris data, LVQ, noise tolerance, noisy data, prediction, traffic modeling.

Existing neural fuzzy (neuro-fuzzy) networks proposed in the literature can be broadly classified into two groups. The first group is essentially fuzzy systems with self-tuning capabilities and requires an initial rule base to be specified prior to training. The second group of neural fuzzy networks, on the other hand, is able to automatically formulate the fuzzy rules from the numerical training data. No initial rule base needs to be specified prior to training. A cluster analysis is first performed on the training data and the fuzzy rules are subsequently derived through the proper connections of these computed clusters. However, most existing neural fuzzy systems (whether they belong to the first or second group) encountered one or more of the following major problems. They are 1) inconsistent rule-base; 2) heuristically defined node operations; 3) susceptibility to noisy training data and the stability-plasticity dilemma; and 4) needs for prior knowledge such as the number of clusters to be computed. Hence, a novel neural fuzzy system that is immune to the above-mentioned deficiencies is proposed in this paper. This new neural fuzzy system is named the generic self-organizing fuzzy neural network (GenSoFNN). The GenSoFNN network has strong noise tolerance capability by employing a new clustering technique known as discrete incremental clustering (DIC). The fuzzy rule base of the GenSoFNN network is consistent and compact as GenSoFNN has built-in mechanisms to identify and prune redundant and/or obsolete rules. Extensive simulations were conducted using the proposed GenSoFNN network and its performance is encouraging when benchmarked against other neural and neural fuzzy systems. Index Terms--Backpropagation (BP), compact and consistent rule-base, compositional rule inference (CRI), generic self-organizing fuzzy neural network (GenSoFNN), laser data, learning vector quantization (LVQ), noise tolerance, one-pass learning, rule pruning, traffic modeling and prediction, 2-spiral.