Random walk-based similarity measure method for patterns in complex object

Abstract

This paper discusses the similarity of the patterns in complex objects. The complex object is composed both of the attribute information of patterns and the relational information between patterns. Bearing in mind the speci city of complex object, a random walk-based similarity measurement method for patterns is constructed. In this method, the reachability of any two patterns with respect to the relational information is fully studied, and in the case of similarity of patterns with respect to the relational information can be calculated. On this bases, an integrated similarity measurement method is proposed, and algorithms 1 and 2 show the performed calculation procedure. One can nd that this method makes full use of the attribute information and relational information. Finally, a synthetic example shows that our proposed similarity measurement method is validated. Introductory comments and Problem statementSimilarity measurement, as a tool to determine the similar between two patterns, is given special attention from its wide application in many elds, such as pattern recog [24]. Besides these, many similarity measure methods are applied, such as the cosine method, correlation coe cient method and the max-min method, amongst others.No matter which representation the data has or what similarity measurement method is used, all the data are vector-based attribute information, to some extent. But, in practical problem solving, this is not enough. For example, if we want to detect the community structure, the research should be aimed at network data [25]. Therefore, the data takes not only the attribute information of patterns but also the relational information between patterns.In view of the similarity problem of such data, a lot of studies have been done. For example, Rossi et al. [26] proposed a quantum algorithm to measure the similarity between a pair of unattributed graphs, and in which the theory of quantum Jensen-Shannon divergence constitutes the basis of theoretical analysis. Moreover, Rossi et al. [27] discussed the similarity between attributed graphs by means of the evolution of a continuous-time quantum walk. In [28], Cason et al. computed the low approximation of the graph similarity matrix. Brandes and Lerner [29] introduced the concept of structural similarity by relaxation of equitable partitions. Kpodjedo et al.[30] investigated heuristics for approximate graph matching. Maggini et al. [2] presented a neural networks model that could be used to learn a similarity measure for pairs of patterns. Grewenig, Zimmer and Weickert [31] studied the rotationally invariant similarity measures for non-local image denoising. Besides these studies, many other similarity measuring approaches are proposed in references [32][33][34][35][36][37][38][39], in this paper's.Taking the relational information of directly-linked patterns and indirectly-linked patterns into account, here we propose a random walk-based similarity measure method for patterns in complex object. Here, the "random walk" refers to ...

Relative Entropy-Based Similarity for Patterns in Graph Data

“…In this section, we propose some basic concepts used in this paper, such as graph data [26], relative entropy [32], and pattern's neighbor [23].…”

“…That is to say, it is hard to distinguish differences between patterns with similar degree. In addition, there are many other ways to calculate pattern similarity, see [25][26][27][28] for details.…”