Audit Analysis of Abnormal Behavior of Social Security Fund Based on Adaptive Spectral Clustering Algorithm

Abnormal behavior detection of social security funds is a method to analyze large-scale data and find abnormal behavior. Although many methods based on spectral clustering have achieved many good results in the practical application of clustering, the research on the spectral clustering algorithm is still in the early stage of development. Many existing algorithms are very sensitive to clustering parameters, especially scale parameters, and need to manually input the number of clustering. Therefore, a density-sensitive similarity measure is introduced in this paper, which is obtained by introducing new parameters to transform the Gaussian function. Under this metric, the distance between data points belonging to different classes will be effectively amplified, while the distance between data points belonging to the same class will be reduced, and finally, the distribution of data will be effectively clustered. At the same time, the idea of Eigen gap is introduced into the spectral clustering algorithm, and the verified gap sequence is constructed on the basis of Laplace matrix, so as to solve the problem of the number of initial clustering. The strong global search ability of artificial bee colony algorithm is used to make up for the shortcoming of spectral clustering algorithm that is easy to fall into local optimal. The experimental results show that the adaptive spectral clustering algorithm can better identify the initial clustering center, perform more effective clustering, and detect abnormal behavior more accurately.

Generalized solution to the problem of reconstructing the graph structure based on the transfer function matr ix

This study presents a generalized solution to the problem of restoring the structure of a graph based on the method of minimizing the transfer matrix norm, consistent with the Euclidean vector norms, with a minimum and extended set of constraints. The problem of complete reconstruction of the adjacency matrix, in the presence of pairs of vectors of exogenous and endogenous influences, expressing the intrinsic resonance properties of the network, and positive semidefinite constraints on the matrix of variables, is a generalization of the problem of reconstructing the structure of a graph from the eigenvalues of the Laplace matrix.

Determination of features based on the formation of persistent spectra of eigenvalues of Laplace matrices

An algorithm for determining the spectrum of eigenvalues of the Laplace matrix for simplicial complexes has been developed in the paper. The spectrum of eigenvalues of the Laplace matrix is used as features in the data structure for image analysis. Similarly to the method of persistent homology, the filtering of embedded simplicial complexes is formed, approximating the image of the object, but the topological features at each stage of filtration is the spectrum of eigenvalues of the Laplace matrix of simplicial complexes. The spectrum of eigenvalues of the Laplace matrix allows to determine the Betti numbers and Euler characteristics of the image. Based on the method of finding the spectrum of eigenvalues of the Laplace matrix, an algorithm is formed that allows you to obtain topological features of images of objects and quantitative estimates of the results of image comparison. Software has been developed that implements this algorithm on computer hardware. The method of determining the spectrum of eigenvalues of the Laplace matrix has the following advantages: the method does not require a bijective correspondence between the elements of the structures of objects; the method is invariant with respect to the Euclidean transformations of the forms of objects. Determining the spectrum of eigenvalues of the Laplace matrix for simplicial complexes allows you to expand the number of features for machine learning, which allows you to increase the diversity of information obtained by the methods of computational topology, while maintaining topological invariants. When comparing the shapes of objects, a modified Wasserstein distance can be constructed based on the eigenvalues of the Laplace matrix of the compared shapes. Using the definition of the spectrum of eigenvalues of the Laplace matrix to compare the shapes of objects can improve the accuracy of determining the distance between images.

Global Robust Exponential Synchronization of Multiple Uncertain Neural Networks Subject to Event-Triggered Strategy

This paper proposes the event-triggered strategy (ETS) for multiple neural networks (NNs) with parameter uncertainty and time delay. By establishing event-triggered mechanism and using matrix inequality techniques, several sufficient criteria are obtained to ensure global robust exponential synchronization of coupling NNs. In particular, the coupling matrix need not be the Laplace matrix in this paper. In addition, the lower bounds of sampling time intervals are also found by the established event-triggered mechanism. Eventually, three numerical examples are offered to illustrate the obtained results.

Spectral conditions of existence of the graph circumference

A graph parameter – a circumference of a graph – and its relationship with the algebraic parameters of a graph – eigenvalues of the adjacency matrix and the unsigned Laplace matrix of a graph – are considered in this article. Earlier we have obtained the lower estimates of the spectral radius of an arbitrary graph and a bipartitebalanced graph for existence of the Hamiltonian cycle in it. Recently the problem of existence of a cycle of length n – 1 in a graph depending on the values of its above-mentioned spectral radii has been investigated. This article studies the problem of existence of a cycle of length n – 2 in a graph depending on the lower estimates of the values of its spectral radius and the spectral radius of its unsigned Laplacian and the spectral conditions of existence of the circumference of a graph (2-connected graph) are obtained.

An integer sequence and standard monomials

For an (oriented) graph [Formula: see text] on the vertex set [Formula: see text] (rooted at [Formula: see text]), Postnikov and Shapiro (Trans. Amer. Math. Soc. 356 (2004) 3109–3142) associated a monomial ideal [Formula: see text] in the polynomial ring [Formula: see text] over a field [Formula: see text] such that the number of standard monomials of [Formula: see text] equals the number of (oriented) spanning trees of [Formula: see text] and hence, [Formula: see text], where [Formula: see text] is the truncated Laplace matrix of [Formula: see text]. The standard monomials of [Formula: see text] correspond bijectively to the [Formula: see text]-parking functions. In this paper, we study a monomial ideal [Formula: see text] in [Formula: see text] having rich combinatorial properties. We show that the minimal free resolution of the monomial ideal [Formula: see text] is the cellular resolution supported on a subcomplex of the first barycentric subdivision [Formula: see text] of an [Formula: see text] simplex [Formula: see text]. The integer sequence [Formula: see text] has many interesting properties. In particular, we obtain a formula, [Formula: see text], with [Formula: see text] for [Formula: see text], [Formula: see text] and [Formula: see text] for [Formula: see text], similar to [Formula: see text].