Temporal Multiresolution Graph Learning

Koki Yamada,Yuichi Tanaka

doi:10.1109/access.2021.3120994

Koki Yamada, Yuichi Tanaka

Open Access

https://doi.org/10.1109/access.2021.3120994

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Journal: IEEE Access	Publication Date: Jan 1, 2021
Citations: 2	License type: CC BY 4.0

Affiliation: Tokyo University of Agriculture and Technology

Abstract

Estimating time-varying graphs, i.e., a set of graphs in which one graph represents the relationship among nodes in a certain time slot, from observed data is a crucial problem in signal processing, machine learning, and data mining. Although many existing methods only estimate graphs with a single temporal resolution, the actual graphs often demonstrate different relationships in different temporal resolutions. In this study, we propose an approach for time-varying graph learning by leveraging a multiresolution property. The proposed method assumes that time-varying graphs can be decomposed by a linear combination of graphs localized at different temporal resolutions. We formulate a convex optimization problem for temporal multiresolution graph learning. In experiments using synthetic and real data, the proposed method demonstrates the promising objective performances for synthetic data, and obtains reasonable temporal multiresolution graphs from real data.

Highlights

M ANY applications of signal processing, machine learning, and data mining require the handling of sensor data, where the sensors are often distributed nonuniformly in a physical space
static graph learning (SGL) based on smoothness criterion (SGL-S) [21]
time-varying graph learning (TVGL) based on smoothness with temporal variation constraint (TVGL-S) [12], [16], [17]

Summary

Introduction

M ANY applications of signal processing, machine learning, and data mining require the handling of sensor data, where the sensors are often distributed nonuniformly in a physical space. Analyzing such data by considering their underlying spatial structure, i.e., network, can significantly improve the quality of data analysis. GSP has found many applications such as brain signal analysis [5], [6], image processing [7]– [9], and sensor networks [10]. Graph learning [11]–[14], techniques and algorithms for estimating a graph from observed data and/or feature values, are required in various GSP applications, for sensor measurements

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Conclusion