The choice of transfer functions may strongly influence complexity and performance of neural networks. Although sigmoidal transfer functions are the most common there is no apriorireason why models based on such functions should always provide optimal decision borders. A large number of alternative transfer functions has been described in the literature. A taxonomy of activation and output functions is proposed, and advantages of various non-local and local neural transfer functions are discussed. Several less-known types of transfer functions and new combinations of activation/output functions are described. Universal transfer functions, parametrized to change from localized to delocalized type, are of greatest interest. Other types of neural transfer functions discussed here include functions with activations based on nonEuclidean distance measures, bicentral functions, formed from products or linear combinations of pairs of sigmoids, and extensions of such functions making rotations...

A framework for Similarity-Based Methods (SBMs) includes many classification models as special cases: neural network of the Radial Basis Function Networks type, Feature Space Mapping neurofuzzy networks based on separable transfer functions, Learning Vector Quantization, variants of the k nearest neighbor methods and several new models that may be presented in a network form. Multilayer Perceptrons (MLPs) use scalar products to compute weighted activation of neurons, combining soft hyperplanes to provide decision borders. Distance-based multilayer perceptrons (D-MLPs) evaluate similarity of inputs to weights offering a natural generalization of standard MLPs. Cluster-based initialization procedure determining architecture and values of all adaptive parameters is described. Networks

Abstract. Although computational intelligence (CI) covers a vast variety of different methods it still lacks an integrative theory. Several proposals for CI foundations are discussed: computing and cognition as compression, meta-learning as search in the space of data models, (dis)similarity based methods providing a framework for such meta-learning, and a more general approach based on chains of transformations. Many useful transformations that extract information from features are discussed. Heterogeneous adaptive systems are presented as particular example of transformation-based systems, and the goal of learning is redefined to facilitate creation of simpler data models. The need to understand data structures leads to techniques for logical and prototype-based rule extraction, and to generation of multiple alternative models, while the need to increase predictive power of adaptive models leads to committees of competent models. Learning from partial observations is a natural extension towards reasoning based on perceptions, and an approach to intuitive solving of such problems is presented. Throughout the paper neurocognitive inspirations are frequently used and are especially important in modeling of the higher cognitive functions. Promising directions such as liquid and laminar computing are identified and many open problems presented. 1

Abstract. A general framework for similarity-based (SB) classification methods is presented. Neural networks, such as the Radial Basis Function (RBF) and the Multilayer Perceptrons (MLPs) models, are special cases of SB methods. Many new versions of minimal distance methods are derived from this framework.

. The class of similarity based methods (SBM) covers most neural models and many other classifiers. Performance of such methods is significantly improved if irrelevant features are removed and feature weights introduced, scaling their influence on calculation of similarity. Several methods for feature selection and weighting are described. As an alternative to the global minimization procedures computationally efficient best--first search methods are advocated. Although these methods can be used with any SBM classifier they have been tested using the k-NN method, since it is relatively fast and for some databases gives excellent results. A few illustrative examples show significant improvements due to the feature weighting and selection. Introduction. M ANY neural, pattern recognition and machine learning methods developed in the past use explicitly or implicitly similarity measures during the training and classification process (although our focus here is on classification the sam...

A general framework for minimal distance methods is presented. Radial Basis Functions (RBFs) and Multilayer Perceptrons (MLPs) neural networks are included in this framework as special cases. New versions of minimal distance methods are formulated. A few of them have been tested on a real-world datasets obtaining very encouraging results.

Neural network models are presented as special cases of a framework for general Similarity-Based Methods (SBMs). Distance-based multilayer perceptrons (D-MLPs) with non-Euclidean metric functions are described. D-MLPs evaluate similarity to prototypes making the interpretation of the results easier. Renormalization of the input data in the extended feature space brings dramatic changes in the shapes of decision borders. An illustrative example showing these changes is provided.

A framework for Similarity-Based Methods (SBMs) includes many neural network models as special cases. Multilayer Perceptrons (MLPs) use scalar products to compute weighted activation of neurons, combining soft hyperplanes to provide decision borders. Scalar product is replaced by a distance function between the inputs and the weights, offering a natural generalization of the standard MLP model to the distance-based multilayer perceptron (D-MLP) model. D-MLPs evaluate similarity of inputs to weights making the interpretation of their mappings easier. Cluster-based initialization procedure determining architecture and values of all adaptive parameters is described. D-MLP networks are useful not only for classification and approximation, but also as associative memories, in problems requiring pattern completion, offering an efficient way to deal with missing values. Non-Euclidean distance functions may also be introduced by normalization of the input vectors in an extended fe...

Multilayer Perceptrons (MLPs) use scalar products to compute weighted activation of neurons providing decision borders using combinations of soft hyperplanes. The weighted fun-in activation function corresponds to Euclidean distance functions used to compute similarities between input and weight vector. Replacing the fan-in activation function by non-Euclidean distance function offers a natural generalization of the standard MLP model, providing more flexible decision borders. An alternative way leading to similar results is based on renormalization of the input vectors using non-Euclidean norms in extended feature spaces. Both approaches influence the shapes of decision borders dramatically, allowing to reduce the complexity of MLP networks.

Abstract. Multilayer Perceptrons (MLPs) use scalar products to compute weighted activation of neurons providing decision borders using combinations of soft hyperplanes. The weighted fun-in activation function may be replaced by a distance function between the inputs and the weights, offering a natural generalization of the standard MLP model. Non-Euclidean distance functions may also be introduced by normalization of the input vectors into an extended feature space. Both approaches influence the shapes of decision borders dramatically. An illustrative example showing these changes is provided.