Joint Characterization of Sentinel-2 Reflectance: Insights from Manifold Learning
Abstract
:1. Introduction
- Geophysical
- What is the overall S,V,D fraction distribution of globally diverse representatives of significant land cover categories?
- How well does the global S,V,D model fit each land cover category, as measured by root mean square misfit?
- Topological
- How clustered or continuous are the manifolds for each land cover category found by UMAP?
- Joint
- To what extent can S,V,D fractions and UMAP clusters be used together to yield useful information? Specifically,
- i.
- To what extent are UMAP clusters geographically contiguous?
- ii.
- To what extent do disparate UMAP clusters at similar S,V,D fraction values represent physically plausible and/or spectroscopically interpretable spectral variability?
- iii.
- Are some S,V,D fractions, or land cover classes, better suited to JC than others? If so, why? If not, why not?
2. Materials and Methods
2.1. Data
2.2. Methods
- Use a linear spectral mixture model to characterize the overall S,V,D distribution of each land cover class (variance-based, physical, linear).
- Use Uniform Manifold Approximation and Projection (UMAP; [33]) to characterize interdimensional topology & clustering (topology-based, statistical, nonlinear)
- Synthesize Steps A and B into a set of 1 or more bivariate distributions which use the physical meaning of the Step A fraction distributions to differentiate among purely topological relations identified from Step B (joint characterization).
2.2.1. Step A: Linear Characterization and Modeling: Spectral Mixture Analysis
2.2.2. Step B: Nonlinear Characterization and Modeling: Manifold Learning
- -
- n_components: The number of dimensions of the low-D embedding space.
- -
- n_neighbors: The size of the local neighborhood used when learning the manifold structure of the data.
- -
- min_dist: The limit on how closely points may be spaced in the output space.
- -
- metric: The distance metric in the input space.
- -
- n_components = 2
- -
- n_neighbors = 30
- -
- min_dist = 0.1
- -
- metric = Euclidean
2.2.3. Step C: Joint Characterization: Bivariate Distributions and Cluster Identification
3. Results
3.1. Agriculture
3.2. Sands
3.3. Lava and Ash
3.4. Urban
3.5. Forests
3.6. Senescent Vegetation
3.7. Tundra
3.8. Mangroves and Wetlands
3.9. Rocks and Alluvium
4. Discussion
4.1. Revisiting the Motivating Questions
4.1.1. Question 1: Variance-Based Characterization & Modeling
4.1.2. Question 2: Topology-Based Characterization & Modeling
4.1.3. Question 3: Leveraging Variance & Topology with Joint Characterization
4.2. Why JC Works: A Convergence of Visions
4.2.1. The Geophysical Vision: Projecting Each Pixel Spectrum Independently onto the Global Mixing Space
4.2.2. The Statistical Vision: Learning High-Dimensional Structure within and among Clusters of Similar Pixel Spectra
4.2.3. Fusing These Two Visions: Joint Characterization
4.3. Limitations and Future Work
4.3.1. Limitations
4.3.2. Future Work
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Agriculture | |||
---|---|---|---|
TileID | UTM Zone | Easting | Northing |
S2A_MSIL1C_20170205T210921_N0204_R057_T04QHH | 4N | 868610 | 2223190 |
S2A_MSIL1C_20170315T101021_N0204_R022_T32TPP | 32N | 623950 | 4864330 |
S2A_MSIL1C_20170508T012701_N0205_R074_T54STE | 54N | 269220 | 3988590 |
S2A_MSIL1C_20170723T064631_N0205_R020_T41TKG | 41N | 266210 | 4645260 |
S2A_MSIL1C_20170917T190351_N0205_R113_T10SFG | 10N | 688930 | 4167330 |
S2A_OPER_PRD_MSIL1C_PDMC_20161017T044357 | 45N | 723470 | 2625060 |
S2B_MSIL1C_20170730T040549_N0205_R047_T47SND | 47N | 554190 | 4363690 |
S2B_MSIL1C_20170918T054629_N0205_R048_T43SDT | 43N | 459570 | 3800040 |
S2B_MSIL1C_20171008T105009_N0205_R051_T30TYN | 30N | 702100 | 4787760 |
S2B_MSIL1C_20171013T081959_N0205_R121_T36SYF | 36N | 778000 | 4095680 |
Sand | |||
TileID | UTM Zone | Easting | Northing |
S2A_MSIL1C_20170628T173901_N0205_R098_T13SCS | 13N | 372290 | 3654900 |
S2A_MSIL1C_20170908T063621_N0205_R120_T40QFK | 40N | 653400 | 2447190 |
S2A_MSIL1C_20171119T040041_N0206_R004_T48TUK | 48N | 305540 | 4438710 |
S2A_MSIL1C_20171208T111441_N0206_R137_T29QKD | 29N | 291550 | 2399280 |
S2A_MSIL1C_20171209T072301_N0206_R006_T38QND | 38N | 527910 | 1890720 |
S2B_MSIL1C_20171207T105419_N0206_R051_T30RVT | 30N | 481880 | 3290910 |
S2B_MSIL1C_20171208T084329_N0206_R064_T33JWN | 33S | 541880 | 7265640 |
S2B_MSIL1C_20171212T100359_N0206_R122_T32RLQ | 32N | 339750 | 2966720 |
S2B_MSIL1C_20171212T100359_N0206_R122_T32RLR | 32N | 331950 | 3100020 |
Lava & Ash | |||
TileID | UTM Zone | Easting | Northing |
S2A_MSIL1C_20170205T210921_N0204_R057_T04QHH | 4N | 861160 | 2206290 |
S2A_MSIL1C_20171016T073911_N0205_R092_T36MZC | 36S | 819250 | 9703580 |
S2A_MSIL1C_20171016T073911_N0205_R092_T36MZC | 36S | 834220 | 9768640 |
S2A_OPER_PRD_MSIL1C_PDMC_20161014T163303 | 15S | 652170 | 9967520 |
S2B_MSIL1C_20170723T124309_N0205_R095_T28WDT | 28N | 399960 | 7200220 |
Urban | |||
TileID | UTM Zone | Easting | Northing |
S2A_MSIL1C_20170508T012701_N0205_R074_T54STE | 54N | 269890 | 3950620 |
S2A_MSIL1C_20170830T131241_N0205_R138_T23KLP | 23S | 328970 | 7398470 |
S2A_MSIL1C_20170916T055631_N0205_R091_T42RUN | 42N | 300000 | 2758120 |
S2A_MSIL1C_20171017T103021_N0205_R108_T32TLQ | 32N | 390060 | 4999690 |
S2B_MSIL1C_20170912T170949_N0205_R112_T14RLP | 14N | 364980 | 2848280 |
Forest—1 | |||
TileID | UTM Zone | Easting | Northing |
S2A_MSIL1C_20170118T081241_N0204_R078_T35MRV | 35S | 831290 | 9963030 |
S2A_MSIL1C_20170119T074231_N0204_R092_T36JTT | 36S | 284150 | 7247210 |
S2A_MSIL1C_20170205T210921_N0204_R057_T04QHH | 4N | 847400 | 2230620 |
S2A_MSIL1C_20170427T021921_N0205_R060_T50HLH | 50S | 355240 | 6230970 |
S2A_MSIL1C_20170508T012701_N0205_R074_T54STE | 54N | 257880 | 3907290 |
S2A_MSIL1C_20170604T043701_N0205_R033_T45RYL | 45N | 794940 | 3088140 |
S2A_MSIL1C_20170705T022551_N0205_R046_T50NMN | 50N | 450950 | 704020 |
S2A_MSIL1C_20170724T145731_N0205_R039_T18LZL | 18S | 875170 | 8546360 |
S2A_MSIL1C_20170724T145731_N0205_R039_T19LBF | 19S | 215640 | 8582190 |
S2A_MSIL1C_20170830T131241_N0205_R138_T23KLP | 23S | 321220 | 7348390 |
Forest—2 | |||
TileID | UTM Zone | Easting | Northing |
S2A_MSIL1C_20170917T190351_N0205_R113_T10SFG | 10N | 607440 | 4106660 |
S2A_OPER_PRD_MSIL1C_PDMC_20151206T145051 | 20N | 469370 | 431170 |
S2B_MSIL1C_20170713T023549_N0205_R089_T51RTN | 51N | 231700 | 3257530 |
S2B_MSIL1C_20170718T101029_N0205_R022_T32TQS | 32N | 773730 | 5121020 |
S2B_MSIL1C_20170906T002659_N0205_R016_T55KCA | 55S | 353630 | 8006280 |
S2B_MSIL1C_20170912T084549_N0205_R107_T36TUL | 36N | 335150 | 4512660 |
S2B_MSIL1C_20171009T003649_N0205_R059_T55MDP | 55S | 469610 | 9317570 |
S2B_MSIL1C_20171013T081959_N0205_R121_T36SYF | 36N | 791100 | 4092030 |
S2B_MSIL1C_20171116T132219_N0206_R038_T23KKP | 23S | 215910 | 7344400 |
S2B_MSIL1C_20171215T152629_N0206_R025_T18NUF | 18N | 381240 | 26200 |
Senescent Vegetation | |||
TileID | UTM Zone | Easting | Northing |
S2A_MSIL1C_20170119T074231_N0204_R092_T36JUT | 36S | 387540 | 7237130 |
S2A_MSIL1C_20170119T074231_N0204_R092_T36JUT | 36S | 381920 | 7259800 |
S2A_MSIL1C_20170119T074231_N0204_R092_T36JUT | 36S | 375110 | 7261040 |
S2A_MSIL1C_20170119T074231_N0204_R092_T36JUT | 36S | 379990 | 7209420 |
S2A_MSIL1C_20170516T154911_N0205_R054_T18TWQ | 18N | 563770 | 4938390 |
Tundra & Wetlands | |||
TileID | UTM Zone | Easting | Northing |
S2A_MSIL1C_20170718T210021_N0205_R100_T08WNB | 8N | 508380 | 7654750 |
S2A_MSIL1C_20170718T210021_N0205_R100_T08WNB | 8N | 540940 | 7608620 |
S2A_OPER_PRD_MSIL1C_PDMC_20160318T145513 | 19S | 495986 | 7997974 |
S2B_MSIL1C_20170916T215519_N0205_R029_T06WVB | 6N | 442210 | 7700040 |
S2B_MSIL1C_20170916T215519_N0205_R029_T06WVB | 6N | 458950 | 7676830 |
Mangroves | |||
TileID | UTM Zone | Easting | Northing |
S2A_MSIL1C_20170427T153621_N0205_R068_T18NTP | 18N | 258620 | 824760 |
S2A_MSIL1C_20170704T013711_N0205_R031_T52MHD | 52S | 814620 | 9839210 |
S2A_MSIL1C_20170705T022551_N0205_R046_T50NMN | 50N | 498390 | 752360 |
S2A_MSIL1C_20170705T022551_N0205_R046_T50NMN | 50N | 423780 | 704730 |
S2A_MSIL1C_20170916T055631_N0205_R091_T42RUN | 42N | 319520 | 2736030 |
S2A_OPER_PRD_MSIL1C_PDMC_20161018T073751 | 38N | 655730 | 3419140 |
S2B_MSIL1C_20170826T155519_N0205_R011_T17NMJ | 17N | 472220 | 875270 |
S2B_MSIL1C_20170919T140039_N0205_R067_T21KVA | 21S | 445610 | 8017250 |
S2B_MSIL1C_20171123T043059_N0206_R133_T45QYE | 45N | 756960 | 2481220 |
S2B_MSIL1C_20171123T043059_N0206_R133_T45QYE | 45N | 763390 | 2429410 |
Rock & Alluvium—1 | |||
TileID | UTM Zone | Easting | Northing |
S2A_MSIL1C_20160723T143750_T19KER | 19S | 506000 | 7534310 |
S2A_MSIL1C_20170124T051101_N0204_R019_T44RQV | 44N | 781870 | 3417600 |
S2A_MSIL1C_20170412T074611_N0204_R135_T37PDQ | 37N | 467190 | 1496550 |
S2A_MSIL1C_20170412T074611_N0204_R135_T37PDQ | 37N | 415880 | 1480390 |
S2A_MSIL1C_20170613T182921_N0205_R027_T11SMB | 11N | 478340 | 4162580 |
S2A_MSIL1C_20170613T182921_N0205_R027_T11SMB | 11N | 441920 | 4110190 |
S2A_MSIL1C_20170613T182921_N0205_R027_T11SMB | 11N | 424630 | 4194020 |
S2A_MSIL1C_20170613T182921_N0205_R027_T11SMB | 11N | 429810 | 4180830 |
S2A_MSIL1C_20170627T180911_N0205_R084_T12SUF | 12N | 310360 | 4011400 |
S2A_MSIL1C_20170627T180911_N0205_R084_T12SUF | 12N | 304930 | 4096250 |
Rock & Alluvium—2 | |||
TileID | UTM Zone | Easting | Northing |
S2A_MSIL1C_20170627T180911_N0205_R084_T12SUG | 12N | 393280 | 4169500 |
S2A_MSIL1C_20170908T063621_N0205_R120_T40QFK | 40N | 664760 | 2494790 |
S2A_MSIL1C_20171201T150711_N0206_R039_T18LZH | 18S | 866060 | 8213050 |
S2A_MSIL1C_20171207T082321_N0206_R121_T34HCH | 34S | 395100 | 6286480 |
S2A_OPER_PRD_MSIL1C_PDMC_20151022T184002 | 11N | 516790 | 4027140 |
S2A_OPER_PRD_MSIL1C_PDMC_20160318T145513 | 19S | 486817 | 8008443 |
S2B_MSIL1C_20171103T061009_N0206_R134_T42SWC | 42N | 576560 | 3774420 |
S2B_MSIL1C_20171103T061009_N0206_R134_T42SWD | 42N | 544220 | 3856340 |
S2B_MSIL1C_20171202T064229_N0206_R120_T40RGU | 40N | 768340 | 3304040 |
S2B_MSIL1C_20171212T064249_N0206_R120_T40QEL | 40N | 520620 | 2570980 |
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Sousa, D.; Small, C. Joint Characterization of Sentinel-2 Reflectance: Insights from Manifold Learning. Remote Sens. 2022, 14, 5688. https://doi.org/10.3390/rs14225688
Sousa D, Small C. Joint Characterization of Sentinel-2 Reflectance: Insights from Manifold Learning. Remote Sensing. 2022; 14(22):5688. https://doi.org/10.3390/rs14225688
Chicago/Turabian StyleSousa, Daniel, and Christopher Small. 2022. "Joint Characterization of Sentinel-2 Reflectance: Insights from Manifold Learning" Remote Sensing 14, no. 22: 5688. https://doi.org/10.3390/rs14225688