Neuro-fuzzy [Jang,1997][Abraham,2005] are hybrid systems that combine the learning capacity of neural nets [Haykin,1999] with the linguistic interpretation of fuzzy inference systems [Ross,2004]. These systems have been evaluated quite intensively in machine learning tasks. This is mainly due to a number of factors: the applicability of learning algorithms developed for neural nets; the possibility of promoting implicit and explicit knowledge integration; and the possibility of extracting knowledge in the form of fuzzy rules. Most of the well known neuro-fuzzy systems, however, present limitations regarding the number of inputs allowed or the limited (or nonexistent) form to create their own structure and rules [Nauck,1997][Nauck,19 98][Vuorimaa,1994][Zhang,1995]. This paper describes a new class of neuro-fuzzy models, called Hierarchical Neuro-Fuzzy BSP Systems (HNFB). These models employ the BSP partitioning (Binary Space Partitioning) of the input space [Chrysanthou,1996] and have been developed to bypass traditional drawbacks of neuro-fuzzy systems. This paper introduces the HNFB models based on supervised learning algorithm. These models were evaluated in many benchmark applications related to classification and time-series forecasting. A second paper, entitled Hierarchical Neuro-Fuzzy Systems Part II, focuses on hierarchical neuro-fuzzy models based on reinforcement learning algorithms.
Hierarchical Neuro-Fuzzy Systems
This section presents the new class of neuro-fuzzy systems that are based on hierarchical partitioning. Two sub-sets of hierarchical neuro-fuzzy systems (HNF) have been developed, according to the learning process used: supervised learning models (HNFB [Souza,2002b][Vellasco,2004], HNFB-1 [Gonçalves,2006], HNFB-Mamdani HNFB-Mamdani [Bezerra,2005]); and reinforcement learning models (RL-HNFB [Figueiredo,2005a], RL-HNFP RL-HNFP [Figueiredo,2005b]). The focus of this paper is on the first sub-set of models, which are described in the following sections.
Key Terms in this Chapter
Machine Learning: Concerned with the design and development of algorithms and techniques that allow computers to “learn”. The major focus of machine learning research is to automatically extract useful information from historical data, by computational and statistical methods
Binary Space Partitioning: The space is successively divided in two regions, in a recursive way. This partitioning can be represented by a binary tree that illustrates the successive n-dimensional space sub-divisions in two convex subspaces. This process results in two new subspaces that can be later partitioned by the same method
Bayesian Neural Networks: Multi-layer neural networks that use training algorithms based on statistical Bayesian inference. BNNs offer a number of important advantages over the standard Backpropagation learning algorithm including confidence intervals can be assigned to the predictions generated by a network they allow the values of regularization coefficients to be selected using only training data similarly, they allow different models to be compared using only the training data dealing with the issue of model complexity without the need to use cross validation
Artificial Neural Networks: Composed of several units called neurons, connected through synaptic weights, which are iteratively adapted to achieve the desired response. Each neuron performs a weighted sum of its inputs, which is then passed through a nonlinear function that yields the output signal. ANNs have the ability to perform a non-linear mapping between their inputs and outputs, which is learned by a training algorithm
Fuzzy Logic: Can be used to translate, in mathematical terms, the imprecise information expressed by a set of linguistic IF-THEN rules. Fuzzy Logic studies the formal principles of approximate reasoning and is based on Fuzzy Set Theory. It deals with intrinsic imprecision, associated with the description of the properties of a phenomenon, and not with the imprecision associated with the measurement of the phenomenon itself. While classical logic is of a bivalent nature (true or false), fuzzy logic admits multivalence
Pattern Recognition: A sub-topic of machine learning, which aims to classify input patterns into a specific class of pre-defined groups. The classification is usually based on the availability of a set of patterns that have already been classified. Therefore, the resulting learning strategy is based on supervised learning
Supervised Learning: A machine learning technique for creating a function from training data, which consist of pairs of input patterns as well as the desired outputs. Therefore, the learning process depends on the existance of a “teacher” that provides, to each input pattern, the real output value. The output of the function can be a continuous value (called regression), or a class label of the input object (called classification)