### U.W. Bangor - School of Informatics - Mathematics Preprints 1996

# Pattern Recognition and Fuzzy Systems

#### 96.20 : KUNCHEVA, L.I.

### On the equivalence between fuzzy and statistical classifiers

#### Abstract:

We show the equivalence between fuzzy systems for classification and two nonparametric techniques for pattern recognition: Parzen's classifier and the nearest neighbor rule. This equivalence has been vastly implied without being precisely proved. We define a fuzzy if-then system for classification and derive the conditions under which it coincides with the above techniques. The equivalence is based on the following correspondence: (1) Every reference vector in the data set corresponds to a fuzzy rule, e.g., the premise part of RULE_k means "is_like_Xk", where Xk is the k-th element of the reference set (set of prototypes). The firing strength of RULE_k for an unlabeled vector x (viz. R_k(x)) is interpreted as a measure of how similar x is to Xk. (2) Instead of the usual clauses for the features, e.g.,

#### Published in:

International Journal of Uncertainty, Fuzziness, and Knowledge- Based Systems 4.3 (1996) 245-253#### 96.21 : KUNCHEVA, L.I.

### Fuzzy aggregation of multiple classification decisions

#### Abstract:

We study some aggregation techniques for multiple classifier systems. Given an unlabeled object, the first-level classifiers yield fuzzy decisions in the form of degrees of support for each class to be the true one for that object. These values are not necessarily interpreted as posterior probabilities. We use an aggregation operator based on degree of consensus between the classifiers. The higher the consensus, the stronger the committee decision (for or against) given class. Using an acceptance-rejection plot and a small real data set from neonatal medicine we compared the performance of the aggregation operator with that of the following aggregation operators:- minimum
- maximum
- second minimum
- second maximum
- competition jury
- simple average
- geometric mean

In general, the consensus based fuzzy aggregation operator led to better results.

#### Published in:

*Control and Cybernetics*25 (1996) 337-352

#### 96.22 : KUNCHEVA, L.I. and KRISHNAPURAM, R.

### A fuzzy consensus aggregation operator

#### Abstract:

We propose an aggregation operator for expert opinions expressed as real numbers in the unit interval. These can be interpreted as the expert confidence in a certain hypothesis. An example is a pool of classifiers that produce estimates of the posterior probability of an unlabeled object coming from a certain class. The idea of the operator is to strengthen the support (for or against the hypothesis) if the experts agree. We define an axiomatic framework for the aggregation operator based on this rationale, and suggest several aggregation formulas. The proposed operator can be used in systems with a refuse-to-decide option. We illustrate this on an acceptance-rejection plot with a small data set from neonatology.

#### Published in:

*Fuzzy Sets and Systems*79 (1996) 347-356

#### 96.23 : KUNCHEVA, L.I.

### Prototype knowledge extraction from data using RBF networks

#### Abstract:

In this paper knowledge-based pattern classification is considered. Instead of classical fuzzy if-then rules we suggest using a small reference set of prototypes. The classifier is a radial-basis-function (RBF) network using the prototype set as centers. A comparison is drawn with a fuzzy if-then system of the same size: ANFIS configuration with the same number of rules as the number of prototypes. Experiments with the two-spirals data show that RBF classifier makes better use of data than the fuzzy system, i.e. higher classification accuracy has been achieved with the RBF classifier. Along with this, keeping the number of prototypes small, we preserve a certain level of transparency of the RBF classifier, which has been the most admired feature of fuzzy systems.

#### Published in:

*Proc. FUBEST'96, Sofia, Bulgaria*(1996) 66-70

#### 96.24 : KUNCHEVA, L.I. and ATANASSOV, K.

### An intuitionistic fuzzy RBF network

#### Abstract:

A radial basis function (RBF) network is considered with activation functions taking highly nonsymmetric form, specific for each kernel. The representation of the function is inspired by ntuitionistic fuzzy set theory: every hidden node has a specific function for activation and another one for restraining. This flexibility aims at representation of complex classification boundaries with fewer hidden nodes. The "price" of this is the need for a special training algorithm. We use simulated annealing. An illustration example with the two-spirals data is presented.#### Published in:

*Proc. EUFIT'96, Aachen, Germany*(1996) 777-781

#### 96.25 : KUNCHEVA, L.I. and HADJITODOROV, S.

### An RBF network with tunable function shape

#### Abstract:

We propose a radial basis function network with tunable function shape. Instead of the squared Euclidean distance in the power of the exponent of the basis function, we suggest to use an L_p norm with tunable p. We use simulated annealing for training the network. Some results with the two-spirals data are presented.#### Published in:

*Proc. International Conference on Pattern Recognition, ICPR'96, Vienna*(1996) 645-649

#### 96.26 : KUNCHEVA, L.I. and TODOROVA, L.

### Prototype selection for an RBF network by a genetic algorithm

#### Abstract:

#### Published in:

*Proc. International Symposium on Soft Computing, SOCO'96, Reading, UK*(1996) B100-B106