## Similarity-based methods: A general framework for classification, approximation and association.(English)Zbl 0999.68198

Summary: Similarity-Based-Methods (SBM) are a generalization of the minimal distance methods which form a basis of several machine learning and pattern recognition methods. Investigation of similarity leads to a fruitful framework in which many classification, approximation and association methods are accommodated. Probability $$p(C|{\mathbf X}; M)$$ of assigning class $$C$$ to a vector $$\mathbf X$$, given a classification model $$M$$, depends on adaptive parameters and procedures used in construction of the model. Systematic overview of choices available for model building is presented and numerous improvements suggested. Similarity-Based Methods have natural neural-network type realizations. Such neural network models as the radial basis functions and the multilayer perceptrons are included in this framework as special cases. SBM may also include several different submodels and a procedure to combine their results. Many new versions of similarity-based methods are derived from this framework. A search in the space of all methods belonging to the SBM framework finds a particular combination of parameterizations and procedures that is most appropriate for a given data. No single classification method can beat this approach. Preliminary implementation of SBM elements tested on a real-world datasets gave very good results.

### MSC:

 68T10 Pattern recognition, speech recognition 68T05 Learning and adaptive systems in artificial intelligence

### Keywords:

Similarity-Based-Methods

### Software:

ASA; DistAl; SBL-PM