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Advanced Algorithms for Influential Data Point Selection in Optical Flow Time Series Analysis

This study explores the optimization of data analysis techniques using a cross-validation approach with simulated data. Focusing on the enhancement of the PMOA algorithm, we develop a new methodology to identify Influential Data Points (IDP) in local polar coordinates, reducing bias in Optical Flow calculations. By implementing bi-cubic smoothing splines, we mitigate effects of large data gaps, improving estimation accuracy. The results indicate a significant enhancement in data processing, achieving RMS error reductions while optimizing parameters for future research.

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Advanced Algorithms for Influential Data Point Selection in Optical Flow Time Series Analysis

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Presentation Transcript

  1. Text

  2. Data • Simulated data • AMSREA, MODIS A-T • Cross-validation approach • Full fields as input data and truth • 15 day sliding data window • Remove 3 or 5 days of data • Calculate error for middle day

  3. 2-D Bi-cubic Smoothing Spline • Inoue (1986): tension parameter, roughness parameter • Tense splines (> 0.9) because of extrapolation • Very smooth splines can’t interpolate over large gaps • Interpolating splines whiten residuals & overfitting • .1 < rho (roughness parameter) < 1.0

  4. Objective Analysis

  5. Influential Data Points (IDP): • O(1,000,000) data pts to O(10) IDP at each OA location • Computationally intensive part of OA code • IDP should be the data most correlated with OA location • PMOA algorithm was designed to efficiently find IDP • New algorithm is finding IDP in local polar coordinates • Goal: Find IDP most correlated that surround OA location •  reduce bias

  6. Optical flow method • DT/dt=0  δT/δt=-(uδT/δx + vδT/δy) • Trend Field is used for input • Moore-Penrose Inverse Solution • Time derivative calculated with δt=2 days • Spatial derivatives weighted (1/4,1/2,1/4) • FDVs outliers are removed (large & near-zero) • Spline smoothing of FDV estimates

  7. Cross-validation error estimates:Remove 3 input days of data insliding 15 day data windowCalculate estimation error for the middle day for 3 months FDV-based estimates were 10%better, RMS of .51 vs .56

  8. Input test Data

  9. OA with FDV & zero FDV

  10. 3 days removed

  11. 5 days of data removed

  12. Future Work • Tune some parameters • Influential Data Point Selection • Estimation variance vs resolution/bias • Merge FDV with MUR: FDV(scale)

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