WHY CLASSICAL MODELS FOR PATTERN RECOGNITION ARE NOT PATTERN RECOGNITION MODELS

Lev Goldfarb and Jaroslav Hook

Faculty of Computer Science

(International Conference on Advances in Pattern Recognition, ed. Sameer Singh, Springer, pp.405–414, 1998)

**ABSTRACT**. In this paper we outline a simple explanation
of why, we think, the classical, or vector-space-based (including the
artificial neural net) models for pattern recognition are *fundamentally *inadequate
as such. The present simple explanation
of this inadequacy is based on a radically new understanding of the nature of
inductive learning processes. The latter
became possible only after a careful analysis of the axiomatic foundations of a
new inductive learning model proposed by the first author in 1990 which
overcomes the above limitations. The new
model¾evolving
transformations system¾has emerged as a result of a 13-year long attempt to
find a mathematical framework that would unify two main and structurally
different approaches to pattern recognition: the vector-space-based and the
syntactic approaches. The decisive
deficiency of the classical vector-space-based pattern recognition model, as it
turns out, relates to the intrinsic inability of the underlying mathematical
model, i.e. the normed vector space, to accommodate,
during the learning process in a realistic environment, the discovery of the
corresponding *class distance function* under more general than numeric,
symbolic, pattern representation. Typically, such *symbolic *distance
functions have very little to do with a very restricted, *“Euclidean”, class of distance functions*, which due to the underlying
algebraic structure of the vector space are *unavoidably associated with this
form of pattern representation.* In
other words, the more general class of *symbolic *distance functions is
incomparably larger than that consistent with the vector space structure, and
so the discovery and construction of the appropriate class distance function
during the learning process simply cannot proceed in the vector space setting.