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Volume 14
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Article

Interpolating Missing Spatial Data Using Graph Laplacian Eigenbasis

by
Zihan Jin
1 and
Hiroshi Yamada
2,*
1
Graduate School of Humanities and Social Sciences, Hiroshima University, 1-2-1 Kagamiyama, Higashihiroshima 739-8525, Japan
2
Faculty of Economics, Kansai University, 3-3-35 Yamate, Suita 564-8680, Japan
*
Author to whom correspondence should be addressed.
Mathematics 2026, 14(9), 1435; https://doi.org/10.3390/math14091435
Submission received: 3 March 2026 / Revised: 3 April 2026 / Accepted: 19 April 2026 / Published: 24 April 2026
(This article belongs to the Special Issue Graph Theory and Applications, 3rd Edition)
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Abstract

This paper addresses the problem of interpolating missing spatial data at the vertices of a connected undirected simple graph. We show that, by exploiting the eigenbasis of the graph Laplacian, all missing values can be reconstructed even from a single observation. This work establishes a novel connection between spatial statistics and spectral graph theory.
Keywords: spatial statistics; spectral graph theory; interpolation; graph Laplacian; spatial autocorrelation; Geary’s c spatial statistics; spectral graph theory; interpolation; graph Laplacian; spatial autocorrelation; Geary’s c

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MDPI and ACS Style

Jin, Z.; Yamada, H. Interpolating Missing Spatial Data Using Graph Laplacian Eigenbasis. Mathematics 2026, 14, 1435. https://doi.org/10.3390/math14091435

AMA Style

Jin Z, Yamada H. Interpolating Missing Spatial Data Using Graph Laplacian Eigenbasis. Mathematics. 2026; 14(9):1435. https://doi.org/10.3390/math14091435

Chicago/Turabian Style

Jin, Zihan, and Hiroshi Yamada. 2026. "Interpolating Missing Spatial Data Using Graph Laplacian Eigenbasis" Mathematics 14, no. 9: 1435. https://doi.org/10.3390/math14091435

APA Style

Jin, Z., & Yamada, H. (2026). Interpolating Missing Spatial Data Using Graph Laplacian Eigenbasis. Mathematics, 14(9), 1435. https://doi.org/10.3390/math14091435

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