Research And Application Of Hypergraph Membrane Algorithm

Membrane computing(also known as membrane systems or P systems)is a highly parallel computing model emerging in recent years.It was abstracted from working mechanism and principle of cooperation within a living organism.Recently the construction of new membrane computing models has become a research hotspot in the field of membrane computing Researchers expect to develop more flexible,efficient,and easily expandable new membrane computing models to solve complex practical applications.Hypergraph is an extension of simple graph,and it has been applied to many fields such as image processing,clustering and spatial data mining.In hypergraph theory,a hyperedge can contain multiple vertices,and a vertex can exist in multiple different hyperedges.Hypergraph can represent multi-terminal elements and multi-level network structures that cannot be represented in ordinary graphs.It overcomes the defects of ordinary graphs in the representation of complex logical relationships so that it can describe higher-order relationships.Therefore,using hypergraph theory to build models guarantees the accuracy of describing complex relationships between objects in the real world to some extentThis paper attempts to combine membrane systems with hypergraph theory by establishing hypergraph membrane computing models,and then proposes three hypergraph membrane algorithms.It mainly studies the hypergraph membrane algorithms and their applications in clustering tasks and fundus image segmentation tasks based on deep learning.The main works are as follows(1)This paper establishes a new membrane computing model based on the multivariate relationship between hyperedge and hypervertex in hypergraph theory,which is called hypergraph P systems(HPS).In HPS,one hypervertex membrane can exist in multiple different hyperedge membranes.Then,three extensions of hypergraph P systems are proposed,namely dynamic hypergraph hybrid P systems(HDHPS),chain hypergraph hybrid P systems(HCHPS),and grid hypergraph P systems(GHPS).The three extension models have more flexible and complex structures.The definition,membrane structure and objects of the three extension models are introduced to deal with complex practical applications(2)This paper combines the hypergraph P systems and deep learning models by proposing a multi-task deep membrane segmentation algorithm based on dynamic hypergraph hybrid membrane systems(HDHPS-MDPS).Membrane system,objects and rules for the algorithm are introduced.HDHPS-MDPS performs calculation operations by evolving objects according to rules in graph-based units,and executes multiple convolutional neural networks called Mask R-CNN in tree-based units in parallel.In this way,it can take advantage of the excellent parallelism of membrane structure and the excellent performance of CNN in image segmentation tasks.Multi-task segmentation experiments of microaneurysm,hard exudate,and optic disc are performed on three diabetic retina public datasets using HDHPS-MDPS.The experimental results and comparative analysis prove that HDHPS-MDPS has achieved the best segmentation performance than other state-of-the-art methods(3)This paper improves fuzzy C-means clustering algorithm using hypergraph membrane systems by proposed a multi-objective fuzzy clustering ensemble algorithm based on chain hypergraph hybrid P systems(HCHPS-MOEC).By designing membrane system and membrane structure,Objects,and rules,this paper uses three multi-objective evolutionary algorithms in parallel to optimize the fuzzy C-means clustering in the reaction chain membrane subsystem,and the local non-dominated objects obtained during the evolution process communicate in the local communication membrane subsystem,and finally non-dominated objects from different base clusters are ensembled in the global ensemble membrane subsystem.Comparative experiments on 8 real datasets prove the superiority,stability,and robustness of HCHPS-MOEC(4)This paper improves the CLIQUE algorithm using the hypergraph membrane system by proposing an improved CLIQUE algorithm(ICLIQUE)based on a grid hypergraph P system(GHPS-ICLIQUE).To reduce the noise points of images in segmentation tasks,the efficiency data points are defined and a new search paths are proposed when discerning and grouping dense units in the improved CLIQUE algorithm.Then GHPS-ICLIQUE uses the designed grid hypergraph P system and new rules to execute the improved CLIQUE algorithm to clustering.Comparative experiments on the challenging segmentation task of choroidal neovascularization for Optical Coherence Tomography Angiography proved the superiority of the proposed GHPS-ICLIQUE algorithm in segmentation accuracy and segmentation efficiency.