Zero-flux boundary condition in a two-probability-parameter random walk model

In this paper we consider 2D nonlocal diffusion models with a finite nonlocal horizon parameter δ characterizing the range of nonlocal interactions, and consider the treatment of Neumann-like boundary conditions that have proven challenging for discretizations of nonlocal models. We propose a new generalization of classical local Neumann conditions by converting the local flux to a correction term in the nonlocal model, which provides an estimate for the nonlocal interactions of each point with points outside the domain. While existing 2D nonlocal flux boundary conditions have been shown to exhibit at most first order convergence to the local counter part as δ → 0, the proposed Neumann-type boundary formulation recovers the local case as O(δ2) in the L∞ (Ω) norm, which is optimal considering the O(δ2) convergence of the nonlocal equation to its local limit away from the boundary. We analyze the application of this new boundary treatment to the nonlocal diffusion problem, and present conditions under which the solution of the nonlocal boundary value problem converges to the solution of the corresponding local Neumann problem as the horizon is reduced. To demonstrate the applicability of this nonlocal flux boundary condition to more complicated scenarios, we extend the approach to less regular domains, numerically verifying that we preserve second-order convergence for non-convex domains with corners. Based on the new formulation for nonlocal boundary condition, we develop an asymptotically compatible meshfree discretization, obtaining a solution to the nonlocal diffusion equation with mixed boundary conditions that converges with O(δ2) convergence.

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The prediction model of personality in social networks by using data mining deep learning algorithm and random walk model

International Journal of Electrical Engineering Education ◽

10.1177/0020720920936839 ◽

2020 ◽

pp. 002072092093683

Author(s):

Yu Zhu

Keyword(s):

Data Mining ◽

Deep Learning ◽

Social Network ◽

Random Walk ◽

Prediction Method ◽

Random Walk Model ◽

Personality Characteristics ◽

User Personality ◽

Network Platform ◽

Personality Prediction

The objective is to predict and analyze the behaviors of users in the social network platform by using the personality theory and computational technologies, thereby acquiring the personality characteristics of social network users more effectively. First, social network data are analyzed, which finds that the type of text data marks the majority. By using data mining technology, the raw data of numerous social network users can be obtained. Based on the random walk model, the data information of the text status of social network users is analyzed, and a user personality prediction method integrating multi-label learning is proposed. In addition, the online social network platform Weibo is taken as the research object. The blog information of Weibo users is obtained through crawler technology. Then, the users are labeled in accordance with personality characteristics. The Pearson correlation coefficient is used to evaluate the relation between the user personality characteristics and the user behavior characteristics of the Weibo users. The correlation between the network behaviors and personality characteristics of Weibo users is analyzed, and the scientificity of the prediction method is verified by the Big Five Model of Personality. By applying relevant technologies and algorithms of data mining and deep learning, the learning ability of neural networks on data characteristics can be improved. In terms of performance on analyzing text information of social network users, the user personality prediction method of integrated multi-label learning based on the random walk model has a large advantage. For the problem of personality prediction of social network users, through combining data mining technology and deep neural network technology in deep learning, the data processing results of social network user behaviors are more accurate.

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