An overview of the self-organizing map algorithm, on which the papers in this issue are based, is presented in this article.

The Self-Organizing Map

Wave digital filters (WDFs) are modeled after classical filters, preferably in lattice or ladder configurations or generalizations thereof. They have very good properties concerning coefficient accuracy requirements, dynamic range, and especially all aspects of stability under finite-arithmetic conditions. A detailed review of WDF theory is given. For this several goals are set: to offer an introduction for those not familiar with the subject, to stress practical aspects in order to serve as a guide for those wanting to design or apply WDFs, and to give insight into the broad range of aspects of WDF theory and its many relationships with other areas, especially in the signal-processing field. Correspondingly, mathematical analyses are included only if necessary for gaining essential insight, while for all details of more special nature reference is made to existing literature.

Wave digital filters: Theory and practice

Fuzzy Rule-Based Systems Evolutionary Computation Introduction to Genetic Fuzzy Systems Genetic Tuning Processes Learning with Genetic Algorithms Genetic Fuzzy Rule-Based Systems Based on the Michigan Approach Genetic Fuzzy Rule-Based Systems Based on the Pittsburgh Approach Genetic Fuzzy Rule-Based Systems Based on the lterative Rule Learning Approach Other Genetic Fuzzy Rule-Based System Other Kinds of Evolutionary Fuzzy Systems Applications.

Genetic Fuzzy Systems: Evolutionary Tuning And Learning Of Fuzzy Knowledge Bases

The present article is a novel attempt in providing an exhaustive survey of neuro-fuzzy rule generation algorithms. Rule generation from artificial neural networks is gaining in popularity in recent times due to its capability of providing some insight to the user about the symbolic knowledge embedded within the network. Fuzzy sets are an aid in providing this information in a more human comprehensible or natural form, and can handle uncertainties at various levels. The neuro-fuzzy approach, symbiotically combining the merits of connectionist and fuzzy approaches, constitutes a key component of soft computing at this stage. To date, there has been no detailed and integrated categorization of the various neuro-fuzzy models used for rule generation. We propose to bring these together under a unified soft computing framework. Moreover, we include both rule extraction and rule refinement in the broader perspective of rule generation. Rules learned and generated for fuzzy reasoning and fuzzy control are also considered from this wider viewpoint. Models are grouped on the basis of their level of neuro-fuzzy synthesis. Use of other soft computing tools like genetic algorithms and rough sets are emphasized. Rule generation from fuzzy knowledge-based networks, which initially encode some crude domain knowledge, are found to result in more refined rules. Finally, real-life application to medical diagnosis is provided.

Neuro-fuzzy rule generation: survey in soft computing framework

Hybrid Systems I

Defines four types of fuzzy neurons and proposes the structure of a four-layer feedforward fuzzy neural network (FNN) and its associated learning algorithm. The proposed four-layer FNN performs well when used to recognize shifted and distorted training patterns. When an input pattern is provided, the network first fuzzifies this pattern and then computes the similarities of this pattern to all of the learned patterns. The network then reaches a conclusion by selecting the learned pattern with the highest similarity and gives a nonfuzzy output. The 26 English alphabets and the 10 Arabic numerals, each represented by 16/spl times/16 pixels, were used as original training patterns. In the simulation experiments, the original 36 exemplar patterns were shifted in eight directions by 1 pixel (6.25% to 8.84%) and 2 pixels (12.5% to 17.68%). After the FNN has been trained by the 36 exemplar patterns, the FNN can recall all of the learned patterns with 100% recognition rate. It can also recognize patterns shifted by 1 pixel in eight directions with 100% recognition rate and patterns shifted by 2 pixels in eight directions with an average recognition rate of 92.01%. After the FNN has been trained by the 36 exemplar patterns and 72 shifted patterns, it can recognize patterns shifted by 1 pixel with 100% recognition rate and patterns shifted by 2 pixels with an average recognition rate of 98.61%. The authors have also tested the FNN with 10 kinds of distorted patterns for each of the 36 exemplars. The FNN can recognize all of the distorted patterns with 100% recognition rate. The proposed FNN can also be adapted for applications in some other pattern recognition problems. >

A fuzzy neural network and its application to pattern recognition

A simple sigmoid-like second-order piecewise activation function suitable for direct digital hardware implementation is presented. Simulation results on the uses of the second-order function and the bipolar sigmoid function for training multilayer feedforward networks using the backpropagation algorithm show that they have similar generalisation properties while the second-order function has a slight advantage in convergence speed.<
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Simple sigmoid-like activation function suitable for digital hardware implementation

DNA sequence analysis using digital signal processing requires conversion of a base sequence to a numerical sequence. The choice of the numerical representation of a DNA sequence affects how well its biological properties can be reflected in the numerical domain for the detection and identification of the characteristics of special regions of interest. This paper presents some selected methods of DNA numerical representation for DNA sequence analysis, discusses their relative merits and demerits, and includes some concluding remarks.

Numerical representation of DNA sequences

A new algorithm for designing multilayer feedforward neural networks with single powers-of-two weights is presented. By applying this algorithm, the digital hardware implementation of such networks becomes easier as a result of the elimination of multipliers. This proposed algorithm consists of two stages. First, the network is trained by using the standard backpropagation algorithm. Weights are then quantized to single powers-of-two values, and weights and slopes of activation functions are adjusted adaptively to reduce the sum of squared output errors to a specified level. Simulation results indicate that the multilayer feedforward neural networks with single powers-of-two weights obtained using the proposed algorithm have generalization performance similar to that of the original networks with continuous weights. >

Multilayer feedforward neural networks with single powers-of-two weights

A multilayer feedforward neural network is applied to pulse compression. The 13-element Barker code and the maximum-length sequences (m-sequences) with lengths 15, 31, and 63 b were used as the signal codes, and four networks were implemented, respectively. In each of these networks, the number of input units was the same as the signal length while the number of hidden units was three and the number of output units was one. In training each of these networks, backpropagation learning was used and the number of training epochs was 500. Using this approach, a more than 40 dB output peak signal-to-sidelobe ratio can be achieved. These fault-tolerant neural networks can provide a robust means for pulse radar detection. >

Hon Keung Kwan

Papers

A fuzzy neural network and its application to pattern recognition

Simple sigmoid-like activation function suitable for digital hardware implementation

Numerical representation of DNA sequences

Multilayer feedforward neural networks with single powers-of-two weights

A neural network approach to pulse radar detection