Functional Tensor Decomposition for Modeling Functional-Edged Networks

Temel Kavramlar

The core message of this article is to propose a novel Functional Edged Network (FEN) model based on functional tensor decomposition, which can effectively model networks with functional edges and capture the underlying community structure.

Özet

The article introduces a Functional Edged Network (FEN) model for network modeling, where the edges are represented as functional data rather than scalar or vector values. The key highlights are:

FEN models the network edges as a functional tensor, where the third dimension represents the continuous functions defined on a specific domain. This allows FEN to directly handle functional edges without the need for discretization or interpolation.

FEN incorporates community structure into the model by assuming the edge functions can be decomposed as a product of node-specific community membership and community-to-community connection strength. This is achieved through a symmetrical Tucker decomposition of the functional tensor.

To handle irregularly observed functional edges, FEN formulates the model estimation as a tensor completion problem, which is optimized using a Riemann conjugate gradient descent method. Theoretical analysis is provided to show the desirable properties of the FEN model.

The efficacy of the FEN model is evaluated using both simulation data and a real-world case study on metro system passenger flow data from Hong Kong and Singapore.

İstatistikler

The article does not provide any specific numerical data or statistics to support the key logics. The focus is on the model formulation and theoretical analysis.

Alıntılar

The article does not contain any striking quotes that support the key logics.

Önemli Bilgiler Şuradan Elde Edildi

Functional-Edged Network Modeling

by Haijie Xu,Ch... : arxiv.org 04-02-2024

https://arxiv.org/pdf/2404.00218.pdf

Daha Derin Sorular

How can the FEN model be extended to handle dynamic networks where the functional edges evolve over time

To extend the FEN model to handle dynamic networks where the functional edges evolve over time, we can introduce a time dimension to the functional adjacency tensor. This would transform the three-dimensional tensor into a four-dimensional tensor, with the fourth dimension representing time. The Tucker decomposition can then be applied to this four-dimensional tensor to capture the evolving relationships between nodes over time. By incorporating the time dimension into the model, we can analyze how the functional edges change and evolve, allowing for a more comprehensive understanding of the dynamic network structure.

What are the potential limitations of the symmetrical Tucker decomposition in capturing complex community structures, and how can the model be further generalized

The symmetrical Tucker decomposition used in the FEN model may have limitations in capturing complex community structures due to its assumption of symmetry in the basis matrices. To address this limitation and generalize the model, we can consider relaxing the symmetry constraint on the basis matrices. By allowing for asymmetry in the basis matrices, the model can better capture the diverse and intricate community structures present in real-world networks. Additionally, incorporating higher-order interactions or non-linear relationships between nodes can enhance the model's ability to represent complex community dynamics.

The article focuses on network modeling, but how can the insights from FEN be applied to other domains involving functional data analysis and tensor decomposition

The insights from the FEN model can be applied to various domains involving functional data analysis and tensor decomposition. In fields such as bioinformatics, neuroscience, finance, and environmental science, where data is represented as functions over continuous domains, the FEN model can be utilized to analyze the interactions and relationships between entities. By adapting the FEN framework to these domains, researchers can gain valuable insights into the underlying structures and patterns present in the data. Furthermore, the tensor decomposition techniques used in FEN can be applied to multidimensional data in diverse fields, enabling efficient data representation, analysis, and modeling.