Self-Organizing Recognition and Classification of Relational Structures

Self-Organizing Recognition and Classiﬁcation of Relational Structures Brijnesh J. Jain (bjj@cs.tu-ber1in.de) Department of Computer Science; Technical University Berlin Germany Fritz Wysotzki (wysotzki@cs.tu-berlin.de) Department of Computer Science; Technical University Berlin Germany Abstract We present a novel self-organizing structure recog- nition (SOSR) network for classiﬁcation and recog- nition of relational structures represented by graphs. The system consists of several subnets each comparing an input structure with a given model structure. The subnets are indirectly coupled via a winner-take-all (WTA) classiﬁer. During classiﬁca- tion the SOSR system deactivates subnets which in- dicate large dissimilarities between the input struc- ture and the corresponding models. First exper- iments show that this mechanism signiﬁcantly re- duces the oomputational effort in comparison to tra- ditional classiﬁcation systems using a comparative maximum selector as a classiﬁer. Introduction We describe a hierarchical neural net for the recog- nition and classiﬁcation of relational structures by matching with class prototypes which was primarily developed from a theoretical point of view and for practical applications in Artiﬁcial Intelligence. Clas- siﬁcation by means of prototypes is well known in the psychological literature (e.g. Bosch, 1975; Bosch and Lloyd, 1978) but usually is modeled using fea- ture vectors as description of objects and prototypes, respectively. In the context of modeling semantic memory and discussion of the binding problem in Cognitive Neuroscience relational descriptions and representations of structured objects play nowadays a major role (e.g. Hinton, 1994; Taylor, 1993; Tay- lor, 1996; Singer, 2000). Seen from the point of view of modeling the dynamics of neural structures in connection with psychologically observed behav- ior we are not primarily interested in the neural (population or assembly) code of representing rela- tions (e.g. Singer, 2000) but in studying the pro- cessing strategies using symbolic descriptions of ob- jects and prototypes by graphs and a hierarchical organized winner-takes-all (WTA) net. This net will classify objects by competitive matching with a set of predeﬁned prototypes in a self-organizing manner, i.e. without a homunculus acting as a su- pervisor. The investigation of the WTA—processing strategies might also shed light on principles of func- tioning of the Short-Term-Memory (e.g. Grossberg, 1987a; Grossberg, 1987b), on the role of attention (Lee et al., 1999), and on a trade-off between ac- curacy vs. speed of recognition depending on the strength of inhibition as shown in our ﬁrst exper- imental results given below. In Artiﬁcial Intelligence and Image Recognition graphs are a well suited representation of relational structures like molecular structures, data structures, or semantic networks. In any case, a relational struc- ture consists of elementary objects and binary rela- tions between these objects. In a graph of a rela- tional structure the elementary objects are repre- sented by vertices and their relations by directed or undirected edges. For example, in chemistry, graphs model molecular structures where the vertices repre- sent atoms and the edges represent bonds. In Com- puter Vision vertices of a graph are objects within a scene and edges are structural relationships between those objects. A fundamental problem in many application do- mains of processing relational structures is the iden- tiﬁcation and recognition of common structural parts between two relational structures. For exam- ple in classiﬁcation, recognition or clustering tasks, information about structural overlaps between two structures is required in order to determine a simi- larity or distance of these structures. Here we call the computation of a similarity or distance between two relational structures graph matching. In general graph matching problems are well- known NP—complete problems (Garey & Johnson, 1979). Due to the high computational complexity much effort has been directed toward devising effi- cient heuristics to ﬁnd optimal or approximate so- lutions for graph matching problems. Among other heuristics artiﬁcial neural networks have been pro- posed as a promising model of computation for solv- ing graph matching problems (Schadler & Wysotzki, 1999). The high computational complexity is even more inconvenient if the solution of a problem requires several graph matching procedures. In distance- based classiﬁcation using neural networks an input graph G is matched against a given set of N model graphs M1, . . . , M N representing prototypes of cate- gory C1, . . . , CN, respectively. The matching is per- formed by recurrent neural networks 51, . . . ,SN. In