Pattern recognition by homomorphic graph matching using Hopfield neural networks

Suganthan, Ponnuthurai Nagaratnam; Teoh, Eam Khwang; Mital, Dinesh P.

doi:10.1016/0262-8856(95)91467-r

Cited by 53 publications

(26 citation statements)

References 36 publications

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“…In our previous paper [2], the analog network and programming of the network for homomorphic graph matching were explained in detail. In this section, we briefly review the energy function and compatibility functions for graph homomorphism.…”

Section: Programming the Network For Homomorphismmentioning

confidence: 99%

“…Due to its robustness, it has been employed frequently in object recognition [5,6] and other correspondence applications [2]. An improved form of the ARG referred to as the augmented WARG is used in our study to represent models.…”

Section: Graph Representation and Matchingmentioning

confidence: 99%

“…In this representation, each attribute is weighted according to the criteria set out in Section 4. The scenes are represented by ARG [2]. The augmented model WARG representation is defined below.…”

Section: Graph Representation and Matchingmentioning

confidence: 99%

“…In the past, parameters used in the compatibility measure function have been specified by trial-and-error [2,3]. In this paper, parameter learning schemes are proposed.…”

Section: Introductionmentioning

confidence: 99%

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Learning parameters for object recognition by the self-organizing Hopfield network

Mital

Teoh

Suganthan

1996

Journal of Network and Computer Applications

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Section: Programming the Network For Homomorphismmentioning

confidence: 99%

Section: Graph Representation and Matchingmentioning

confidence: 99%

Section: Graph Representation and Matchingmentioning

confidence: 99%

“…In the past, parameters used in the compatibility measure function have been specified by trial-and-error [2,3]. In this paper, parameter learning schemes are proposed.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Learning parameters for object recognition by the self-organizing Hopfield network

Mital

Teoh

Suganthan

1996

Journal of Network and Computer Applications

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“…The comparison process, known as graph matching in Other forms of graph matching (e.g. error-tolerant subgraph isomorphism [5], homomorphism [6,7], monomorphism and various kinds of inexact matching [8]) also play an important role in pattern recognition, but will not be addressed in this work.defined as follows: given two graphs, determine if a one-to-one mapping exists from the nodes of the first graph to the nodes of the second such that if two nodes in the first graph are connected by an edge, then their corresponding mapped nodes in the second graph must also be connected by an edge.…”

Section: ! Introductionmentioning

confidence: 99%

A graph isomorphism algorithm for object recognition

Abdulrahim

Misra

1998

Pattern Analysis & Applic

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: We present an algorithm to solve the graph isomorphism problem for the purpose of object recognition. Objects, such as those which exist in a robot workspace, may be represented by labelled graphs (graphs with attributes on their nodes and/or edges). Thereafter, object recognition is achieved by matching pairs of these graphs. Assuming that all objects are sufficiently different so that their corresponding representative graphs are distinct, then given a new graph, the algorithm efficiently finds the isomorphic stored graph (if it exists). The algorithm consists of three phases: preprocessing, link construction, and ambiguity resolution. Results from experiments on a wide variety and sizes of graphs are reported. Results are also reported for experiments on recognising graphs that represent protein molecules. The algorithm works for all types of graphs except for a class of highly ambiguous graphs which includes strongly regular graphs. However, members of this class are detected in polynomial time, which leaves the option of switching to a higher complexity algorithm if desired.

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A polynomial‐time algorithm for simple undirected graph isomorphism

Chen

Huang

et al. 2019

Concurrency and Computation

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The graph isomorphism problem is to determine two finite graphs that are isomorphic which is not known with a polynomial-time solution. This paper solves the simple undirected graph isomorphism problem with an algorithmic approach as NP=P and proposes a polynomial-time solution to check if two simple undirected graphs are isomorphic or not. Three new representation methods of a graph as vertex/edge adjacency matrix and triple tuple are proposed. A duality of edge and vertex and a reflexivity between vertex adjacency matrix and edge adjacency matrix were first introduced to present the core idea. Beyond this, the mathematical approval is based on an equivalence between permutation and bijection. Because only addition and multiplication operations satisfy the commutative law, we propose a permutation theorem to check fast whether one of two sets of arrays is a permutation of another or not. The permutation theorem was mathematically approved by Integer Factorization Theory, Pythagorean Triples Theorem, and Fundamental Theorem of Arithmetic. For each of two n-ary arrays, the linear and squared sums of elements were respectively calculated to produce the results.

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Pattern recognition by homomorphic graph matching using Hopfield neural networks

Cited by 53 publications

References 36 publications

Learning parameters for object recognition by the self-organizing Hopfield network

Learning parameters for object recognition by the self-organizing Hopfield network

A graph isomorphism algorithm for object recognition

A polynomial‐time algorithm for simple undirected graph isomorphism

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