Pattern recognition with weighted complex networks

Abstract

In this paper we introduce a weighted complex networks model to investigate and recognize structures of patterns. The regular treating in pattern recognition models is to describe each pattern as a high-dimensional vector which however is insufficient to express the structural information. Thus, a number of methods are developed to extract the structural information, such as different feature extraction algorithms used in preprocessing steps, or the local receptive fields in convolutional networks. In our model, each pattern is attributed to a weighted complex network, whose topology represents the structure of that pattern. Based upon the training samples, we get several prototypal complex networks which could stand for the general structural characteristics of patterns in different categories. We use these prototypal networks to recognize the unknown patterns. It is an attempt to use complex networks in pattern recognition, and our result shows the potential for real-world pattern recognition. A spatial parameter is introduced to get the optimal recognition accuracy, and it remains constant insensitive to the amount of training samples. We have discussed the interesting properties of the prototypal networks. An approximate linear relation is found between the strength and color of vertexes, in which we could compare the structural difference between each category. We have visualized these prototypal networks to show that their topology indeed represents the common characteristics of patterns. We have also shown that the asymmetric strength distribution in these prototypal networks brings high robustness for recognition. Our study may cast a light on understanding the mechanism of the biologic neuronal systems in object recognition as well. In spatial cognition of biologic neuronal systems, an object possesses many properties, such as color, size, brightness, and structures, etc. The main characteristic of an object is represented by its structures which is the primary reason to classify one object from other objects. The structure of an object is expressed as the description of the spatial arrangements and correlations among its individual parts ͓1-3͔. It has been hypothesized that the aim of cortical information processing is to transform the highly redundant inputs into a higher-order representation which reveals the structure ͓4,5͔.In the usual pattern recognition models, such as artificial neural networks ͓6-8͔, each pattern is attributed to a high dimensional vector which is often constructed by a row-byrow scan in the pixel box. Such expression is insufficient in expressing the structural information of each pattern, since the arrangements and correlations between the pixel points is not manifested in the vector. The synaptic matrix treats the computation of each dimension separately, and the spatial arrangements take no effect in computation. Thus, in order to overcome such shortcoming, a number of different methods are developed to extract the structural information within the raw inputs, such as featu...