Connected Hypergraphs with Small Spectral Radius

In 1970 Smith classified all connected graphs with the spectral radius at most $2$. Here the spectral radius of a graph is the largest eigenvalue of its adjacency matrix. Recently, the definition of spectral radius has been extended to $r$-uniform hypergraphs. In this paper, we generalize the Smith's theorem to $r$-uniform hypergraphs. We show that the smallest limit point of the spectral radii of connected $r$-uniform hypergraphs is $\rho_r=(r-1)!\sqrt[r]{4}$. We discovered a novel method for computing the spectral radius of hypergraphs, and classified all connected $r$-uniform hypergraphs with spectral radius at most $\rho_r$.Comment: 20 pages, fixed a missing class in theorem 2 and other small typo

A novel data analytic model for mining user insurance demands from microblogs

This paper proposes a method based on LDA model and Word2Vec for analyzing Microblog users' insurance demands. First of all, we use LDA model to analyze the text data of Microblog user to get their candidate topic. Secondly, we use CBOW model to implement topic word vectorization and use word similarity calculation to expand it. Then we use K-means model to cluster the expanded words and redefine the topic category. Then we use the LDA model to extract the keywords of various insurance information on the “Pingan Insurance” website and analyze the possibility of users with different demands to purchase various types of insurance with the help of word vector similarity. Finally, the validity of the method in this paper is verified against Microblog user information. The experimental results show that the accuracy, recall rate and F1 value of the LDA-CBOW extending method have been proposed compared with that of the traditional LDA model, respectively, which proves the feasibility of this method. The results of this paper will help insurance companies to accurately grasp the preferences of Microblog users, understand the potential insurance needs of users timely, and lay a foundation for personalized recommendation of insurance products