In this paper, we study linear filters to process signals defined on simplicial complexes, i.e., signals defined on nodes, edges, triangles, etc. of a simplicial complex, thereby generalizing filtering operations for graph signals. We propose a finite impulse response filter based on the Hodge Laplacian, and demonstrate how this filter can be designed to amplify or attenuate certain spectral components of simplicial signals. Specifically, we discuss how, unlike in the case of node signals, the Fourier transform in the context of edge signals can be understood in terms of two orthogonal subspaces corresponding to the gradient-flow signals and curl-flow signals arising from the Hodge decomposition. By assigning different filter coefficients to the associated terms of the Hodge Laplacian, we develop a subspace-varying filter which enables more nuanced control over these signal types. Numerical experiments are conducted to show the potential of simplicial filters for sub-component extraction, denoising and model approximation.

Qualitative research method was used to explore the formation and development of the attachment relationship between users and social media in the process of using social media. Based on the attachment theory, this study selected three representative social media platforms, namely, TikTok, WeChat, and MicroBlog, as theoretical samples, and this study adopted NVivo12.0 to root, theorize, and construct the original data. Research shows that users are stimulated by co-creation value to stimulate changes in their psychological needs and self-expression, leading to the formation of social attachment. Among them, user participation is a prerequisite for driving the occurrence of co-creation value, creating a continuous-use scenario for the attachment relationship between individuals and social media. Further, psychological needs and self-expression play mediating roles between co-creation of value and social attachment and promote the occurrence of personal belonging to software platforms. The findings of this research better our understandings about the mechanism of developing social attachment from continuous use of social media and offer practical implications for commercial uses of social media platforms.

BACKGROUND: Social attachment has been identified as a key antecedent motivating users’ social media involvement. However, there is a scarcity of research investigating whether and how three dimensions of social attachment exert impacts on users’ continuous usage intention of social media. OBJECTIVE: Based on structural equation model analysis, the current research clarifies the relationships between social attachment, affective commitment and social media continuous usage intention, which unveils the underlying mechanism through which three dimensions of social attachment influence users’ continuous usage intention of social media. METHODS: A survey was conducted with 536 informative responses obtained from TikTok public users for hypothesis testing analysis. RESULTS: Results indicate that three dimensions of social attachment (social connections, social dependence and social identity) are all positively related to users’ continuous usage intention of social media. Affective commitment partially mediates the relationship between social attachment and users’ continuous usage intention of social media. CONCLUSIONS: The current research makes an in-depth study about the underlying mechanism whereby social attachment exerts impacts on social media continuous usage intentionand provides several managerial and theoretical implications. Future research directions are discussed as well.

Perceived value has a positive impact on users’ social attachment in social media usage contexts and is a topic at the forefront of current research in consumer behavior. Although studies have begun to investigate the factors influencing social attachment, there is a lack of research on how perceived value affects social attachment. Therefore, this study uses privacy concern theory, to build a theoretical model with moderated and mediation roles, using Chinese Tik Tok users as data and survey sample, and applying Mplus7.0 to analyze the mediation mechanism and boundary conditions of the relationship between perceived value and social attachment through the structural equation model. In Study 1, data were collected from 600 Tik Tok users to verify the mediating role of the sense of belonging in perceived value and social attachment relationship. The users participating in the questionnaire survey were mainly from mainland China. In Study 2, two waves of data were collected from 500 Tik Tok users to verify the mediating role of the sense of belonging, and support part of the moderating role of privacy concern. However, except that the relationship between information value and social attachment is inhibited by privacy concern, the relationship between entertainment and social value and social attachment is not regulated by privacy concern. This research examines the practical effects of perceived value in the context of social media use, reveals the internal mechanism of the impact of perceived value on social attachment, and provides a reference for the innovative management and commercial practice of social media.

Graphs can model networked data by representing them as nodes and their pairwise relationships as edges. Recently, signal processing and neural networks have been extended to process and learn from data on graphs, with achievements in tasks like graph signal reconstruction, graph or node classifications, and link prediction. However, these methods are only suitable for data defined on the nodes of a graph. In this paper, we propose a simplicial convolutional neural network (SCNN) architecture to learn from data defined on simplices, e.g., nodes, edges, triangles, etc. We study the SCNN permutation and orientation equivariance, complexity, and spectral analysis. Finally, we test the SCNN performance for imputing citations on a coauthorship complex.