TIEOF: Algorithm for Recovery of Missing Multidimensional Satellite Data on Water Bodies Based on HigherOrder Tensor Decompositions
Abstract
:1. Introduction
2. Materials and Methods
2.1. MultiWay Tensor Decompositions
2.2. Interpolation on a Static Rectangular Grid
2.3. Data Thresholding
2.4. Validation Dataset
2.5. Missing Data Reconstruction
Algorithm 1 TIEOF 

2.6. The Lake Baikal Dataset
3. Results
3.1. Interpolation on a Rectangular Grid
3.2. Effect of Early Stopping
3.3. Data Thresholding Reduces Reconstruction Errors
3.4. Comparison of the Tensor Decomposition Methods
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
ALS  Alternating Least Squares 
DINEOF  Data Interpolating Empirical Orthogonal Functions 
EOF  Empirical Orthogonal Functions 
HOOI  Higher Order Orthogonal Iteration 
HOSVD  Truncated Higher Order Singular Value Decomposition 
MODIS  Moderate Resolution Imaging Spectroradiometer 
NRMSE  Normalized Root Mean Squared Error 
PARAFAC  Parallel Factors 
PCA  Principal component analysis 
SeaWiFS  SeaViewing Wide FieldofView Sensor 
SVD  Singular Value Decomposition [NI](SVD) 
TIEOF  Tensor Interpolating Empirical Orthogonal Functions 
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Method  Improvement Factor 

DINEOF  1.24 
TIEOF: HOSVD  1.56 
TIEOF: PARAFAC  1.56 
TIEOF: HOOI  1.57 
Data  Method  Mean NRMSE 

AQUA  DINEOF  0.68 
TIEOF: HOSVD  0.48  
TIEOF: PARAFAC  0.48  
TIEOF: HOOI  0.47  
TERRA  DINEOF  0.74 
TIEOF: HOSVD  0.51  
TIEOF: PARAFAC  0.51  
TIEOF: HOOI  0.50  
SEAWIFS  DINEOF  1.93 
TIEOF: HOSVD  0.90  
TIEOF: PARAFAC  0.90  
TIEOF: HOOI  0.90 
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Kulikov, L.; Inkova, N.; Cherniuk, D.; Teslyuk, A.; Namsaraev, Z. TIEOF: Algorithm for Recovery of Missing Multidimensional Satellite Data on Water Bodies Based on HigherOrder Tensor Decompositions. Water 2021, 13, 2578. https://doi.org/10.3390/w13182578
Kulikov L, Inkova N, Cherniuk D, Teslyuk A, Namsaraev Z. TIEOF: Algorithm for Recovery of Missing Multidimensional Satellite Data on Water Bodies Based on HigherOrder Tensor Decompositions. Water. 2021; 13(18):2578. https://doi.org/10.3390/w13182578
Chicago/Turabian StyleKulikov, Leonid, Natalia Inkova, Daria Cherniuk, Anton Teslyuk, and Zorigto Namsaraev. 2021. "TIEOF: Algorithm for Recovery of Missing Multidimensional Satellite Data on Water Bodies Based on HigherOrder Tensor Decompositions" Water 13, no. 18: 2578. https://doi.org/10.3390/w13182578