Simpliied Art: a New Class of Art Algorithms

The Simpliied Adaptive Resonance Theory (SART) class of networks is proposed to handle problems encountered in Adaptive Resonance Theory 1 (ART 1)-based algorithms when detection of binary and analog patterns is performed. The basic idea of SART is to substitute ART 1-based \unidirectional" (asymmetric) activation and match functions with \bidirectional" (symmetric) function pairs. This substitution makes the class of SART algorithms potentially more robust and less time-consuming than ART 1-based systems. One SART algorithm, termed Fuzzy SART, is discussed. Fuzzy SART employs probabilistic and possibilistic fuzzy membership functions to combine soft competitive learning with outlier detection. Its soft competitive strategy relates Fuzzy SART to the well-known Self-Organizing Map and Neural Gas clustering algorithm. A new Normalized Vector Distance, which can be employed by Fuzzy SART, is also presented. Fuzzy SART performs better than ART 1-based Carpenter-Grossberg-Rosen Fuzzy ART in the clustering of a simple two-dimensional data set and the standard four-dimensional IRIS data set. As expected, Fuzzy SART is less sensitive than Fuzzy ART to small changes in input parameters and in the order of the presentation sequence. In the clustering of the IRIS data set, performances of Fuzzy SART are analogous to or better than those of several clustering models found in the literature. Nomenclature W template vector X input vector FS feature space d dimensionality of the input space (d 2 I +) t index of time (t 2 I +) c current number of output categories (processing elements) (c 2 I +) n number of input patterns (n 2 I +) j index of template vector or output category (j 2 f1; cg) k index of input vector component (k 2 f1; dg) i index of input vector (i 2 f1; ng) E j jth output processing element F k kth input unit W (t) j jth bottom-up template vector, equivalent to weights of input-to-output connections converging on processing element E j at time t X (t) input vector at time t W (t) k;j connection weight from the kth input unit to the jth output processing element X (t) k kth scalar component of X (t) (t) j activation value of unit E j at time t arg max j=1;:::;c n (t) j o picks index j for which (t) j is maximum vigilance threshold (2 0; 1]) Fuzzy ART choice parameter kX (t) k norm of X (t) j X (t) j length (modulus) of …