Research And Application Of Affinity Model Construction In Spectral Clustering

With the development of artificial intelligence,data processing and analysis as a key step has become more and more important.Clustering analysis technology is an important direction in the field of data processing and analysis,and has been widely applied to many fields such as image processing,speech recognition,and information retrieval.As an important clustering algorithm,spectral clustering algorithm has also received extensive attention.In spectral clustering,it is first necessary to construct an affinity model,and use the similarity between data to cluster the data.Constructing a suitable affinity model based on input data has a critical impact on the performance of the spectral clustering algorithm.Constructing different affinity models enable the spectral clustering algorithm to accurately mine the knowledge contained in the data when processing different data.This provides reliable pre-information for subsequent artificial intelligence technologies making different decisions for different applications.The paper starts from two aspects and studies the construction of affinity models in the spectral clustering algorithm.First,low-order affinity model: how to construct affinity models by using multi-scale features,and study the construction of multi-scale affinity models from two perspectives: input data and original affinity model;second,high-order similarity model: how to construct a higher-order affinity model in the spectral clustering algorithm,and study the higherorder extension of normalized cut algorithm and the full higher-order affinity model,and the higher-order affinity model with multi-level features.(1)In order to solve the problem that the research focus on parameter optimization and multiscale feature is not considered when constructing affinity models in existing algorithms.Based on(a)the image segmentation,(b)the input image data,a waveletbased kernel similarity measurement function is designed to construct an affinity model.This function inherits the multi-resolution analysis of wavelet analysis and can extract the required feature information from the input image at a given scale.This paper proves that the function satisfies the allowable conditions of the Mercer kernel and satisfies the general conditions of the similarity measure function.Based on this,the corresponding spectral clustering algorithm is designed,and the performance of the proposed affinity model is analyzed and verified.(2)In order to solve the problem that the existing algorithm only constructs the multiscale affinity model from the image,and needs to preprocessing the image.Based on image segmentation,based on the original affinity model constructed by spectral clustering algorithm,based on the spectral wavelet theory,two methods for constructing affinity models are designed under two different ideas.First,the spectral clustering algorithm exhibits the filtering characteristics when selecting the eigenvectors.Inspired by this,and taking into account the filtering characteristics of the spectral wavelet basis function,the spectral wavelet basis function is used to process the weighting graph,and the spectral domain is processed.Then a new multi-scale affinity model is constructed.Second,using the multi-resolution characteristics of the wavelet coefficients of the spectral wavelet,A pointwise multi-resolution feature descriptor is designed.An affinity model is constructed at the appropriate scale,and the relevant cosine distance and affinity model construction methods are defined.Aiming at the affinity model constructed by the two ideas,the paper designs the spectral clustering algorithms and designs the experiment to verify the performance of the proposed affinity model.(3)The affinity model for the normalized cut algorithm is limited by the binary similarity relationship between data.This paper studies how to extend the normalized cut algorithm into a higher-order algorithm,that is,how to use the higher-order affinity model constructed by multivariate similarity in the algorithm? Based on the relaxation objective function of the normalized cut algorithm,this paper analyzes the idea of extending the algorithm to higher order based on the higher-order singular value decomposition theory,and designs the flow of the high-order normal cutting algorithm.An improved sampling algorithm is proposed to construct a sparse higher-order affinity model,which makes the higher-order algorithm practical.(4)Two problems in the construction of affinity models for existing higher-order spectral clustering algorithms are studied.First,how to use a full higher-order affinity model in higher-order spectral clustering algorithms;Second,how to use higher-order affinity models that fuse multi-order similarity relationships in higher-order spectral clustering algorithms.Based on the higher-order singular value decomposition theory,transductive inference technique and higher-order normalized cut algorithm,two different higher-order affinity models are proposed to solve these two problems,namely the full higher-order affinity model.And the full multi-order affinity model,and analyze the form when using non-normalized Laplacian matrix and using normalized Laplacian matrix for each model.Since the two models are defined in the form of dense matrix,this paper analyzes how the two models can be applied efficiently under the spectral clustering framework,so that the two models can be embedded into the spectral clustering by using the advantages of sparse matrix eigen-decomposition.Based on this,two higher-order algorithms are designed in this paper: full higher-order normalized cut algorithm and full multi-level normalized cut algorithm.