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• The added earth logo is from the website: http://rst.gsfc.nasa.gov/Sect19/Sect19_2a.html
• PREVIOUS WORK TO SOLVE THE DIFFICULTIES: Semi-supervised approach requires the assumption of smooth changes. However, sometimes the assumption maybe not true for multitemporal data sets.It is also commonly seen that adaptive schemes are used to redefine decision boundaries. Statistically speaking, class distributions will alter due to environments. Mean or variances will be different from a scene to a scene. Decision boundaries therefore are needed to adjust according to samples from new scene. DIFFERENT POINT OF VIEW: in geometric learning point of view, since we are talking about a geometric learning methodology, we assume two data sets are similar in some sense, and we need to find a mapping between two similar structures.
• WHY DOES MA WORK FOR CLASSIFICATION: Our main interest is to classify. Aligning similar underlying manifolds is beneficial to classification work when at least one image contains label information. A joint manifold can characterize geometric structures of both data sets.
• First term: preserving given featuresSecond term: clustering conditions on local properties\\mu: tuning the relative weights of two terms in the cost function
• First term: pairwise alignment constraintsSecond and third terms: Local properties\\mu: tuning the relative weights of two terms in the cost function
• Font in equation description
• BASELINE: Demonstrate how pooled data can fail a proper joint manifoldUse other colors, not gray
• Change color MA space using lower cases
• Bold: class accuracy May, June pair
• [WK] Slide 5 introduced the abbreviations for the local methods.
• [WK] Slide 5 introduced the abbreviations for the local methods.
• Compare to previous results?
• ### Transcript

• 1. Manifold Alignment for MultitemporalHyperspectral Image Classification<br />H. Lexie Yang1, Dr. Melba M. Crawford2<br />School of Civil Engineering, Purdue University<br />and<br />Laboratory for Applications of Remote Sensing<br />Email: {hhyang1, mcrawford2}@purdue.edu<br />July 29, 2011<br />IEEE International Geoscience and Remote Sensing Symposium<br />
• 2. Outline<br />Introduction<br />Research Motivation<br />Effective exploitation of information for multitemporal classification in nonstationary environments<br />Goal: Learn “representative” data manifold<br />Proposed Approach<br />Manifold alignment via given features<br />Manifold alignment via correspondences<br />Manifold alignment with spectral and spatial information<br />Experimental Results<br />Summary and Future Directions<br />
• 3. Introduction<br />N&gt;&gt;30<br />3<br />2<br />1<br />2001<br />2003<br />2004<br />2005<br />2006<br />2002<br />2001<br /> N narrow spectral bands<br />June<br />July<br />May<br />May<br />May<br />May<br />June<br />Challenges for classification of hyperspectral data<br />temporally nonstationary spectra<br />high dimensionality<br />
• 4. Research Motivation<br />Nonstationarities in sequence of images <br />Spectra of same class <br /> may evolve or drift<br />over time<br />Potential approaches<br />Semi-supervised methods<br />Adaptive schemes<br />Exploit similar data geometries<br />Explore data manifolds<br />Good initial conditions required<br />
• 5. Manifold Learning for Hyperspectral Data<br />Characterize data geometry with manifold learning <br />To capture nonlinear structures <br />To recover intrinsic space (preserve spectral neighbors) <br />To reduce data dimensionality<br />Classification performed in low dimensional space<br />Original space<br />Manifold space<br />3rd dim<br />Spectral bands<br />n<br />Spatial dimension<br />6<br />5<br />4<br />3<br />2<br />1<br />Spatial dimension<br />1st dim<br />2nd dim<br />
• 6. Challenges: Modeling Multitemporal Data<br /><ul><li>Unfaithful joint manifold</li></ul> due to spectra shift<br /><ul><li>Often difficult to model the inter-image correspondences</li></ul>Data manifold at T2<br />Data manifolds at T1 and T2 <br />Data manifold at T1<br />
• 7. Proposed Approach: Exploit Local Structure<br /><ul><li> Assumption: local geometric structures are similar
• 8. Approach: Extract and optimally align local geometry to minimize overall differences</li></ul>Locality<br />Spectral space at T2<br />Spectral space at T1<br />
• 9. Proposed Approach: Conceptual Idea<br />(Ham, 2005)<br />
• 10. Proposed Approach: Manifold Alignment<br /><ul><li>Exploit labeled data for classification of multitemporal data sets</li></ul>Samples with class labels<br />Samples with no class labels<br />Joint manifold<br />
• 11. Manifold Alignment: Introduction<br />and are 2 multitemporalhyperspectral images<br /> Predict labels of using labeled <br />Explore local geometries using graph Laplacian and some form of prior information<br />Define Graph Laplacian<br />Twopotential forms of prior information: given features and pairwise correspondences [Ham et al. 2005]<br />
• 12. Manifold Alignment via Given Features<br />Minimize <br />Joint Manifold<br />Given Features <br />
• 13. Manifold Alignment via Pairwise Correspondences<br />Minimize <br />Correspondences between and <br />Joint Manifold <br />
• 14. MA with spectral and spatial information<br />Combine spatial locations with spectral signatures<br />To improve local geometries (spectral) quality<br />Idea: Increase similarity measure when two samples are close together<br />Weight matrix for graph Laplacian:<br />where spatial location of each pixel is represented as <br />
• 15. Experimental Results: Data<br /><ul><li>Three Hyperion images collected in May, June and July 2001
• 16. May, June pair: Adjacent geographical area
• 17. June, July pair: Targeted the same area</li></ul>May June July<br />
• 18. Experimental Results: Framework<br />L<br />L<br />L<br />I1, I2<br />I1<br />I2<br />Graph Laplacian<br />Prior information<br />Joint manifold<br />Given features <br />Classification<br />with KNN<br />Correspondences<br />Develop Data Manifold of Pooled Data <br />
• 19. Manifold Learning for Feature Extraction<br />Global methods consider geodesic distance <br /> Isometric feature mapping (ISOMAP)<br />Local methods consider pairwise Euclidian distance<br />Locally Linear Embedding (LLE): (Saul and Roweis, 2000)<br />Local Tangent Space Alignment (LTSA): (Zhang and Zha, 2004)<br />LaplacianEigenmaps (LE): (Belkin and Niyogi, 2004)<br />(Tenenbaum, 2000)<br />
• 20. MA with Given Features<br />Baseline: Joint manifold developed by pooled data<br />79.21<br />77.29<br />77.88<br />76.31<br />(May, June pair)<br />
• 21. MA Results – Classification Accuracy<br /><ul><li>Evaluate results by overall accuracies</li></li></ul><li>Results – Class Accuracy<br />May, June pair<br />Typical class<br />Critical class<br />(Island Interior)<br />Critical class<br />(Riparian)<br />(Woodlands)<br />
• 22. Summary and Future Directions<br />Multitemporal spectral changes result in failure to provide a faithful data manifold <br />Manifold alignment framework demonstrates potential for nonstationary environment by utilizing similar local geometries and prior information<br />Spatial proximity contributes to stabilization of local geometries for manifold alignment approaches<br />Future directions<br />Investigate alternative spatial and spectral integration strategy<br />Address issue of longer sequences of images<br />
• 23. Thank you.<br />Questions?<br />
• 24. References<br />J. Ham, D. D. Lee, and L. K. Saul, “Semisupervised alignment of manifolds,” in International Workshop on Artificial Intelligence and Statistics, August 2005.<br />
• 25. Backup Slides<br />
• 26. Local Manifold Learning for Feature Extraction (s,f)<br />Local geometry preserved via various strategies for embedding<br />Popular local manifold learning methods<br />Locally Linear Embedding (LLE): (Saul and Roweis, 2000)<br />Local Tangent Space Alignment (LTSA): (Zhang and Zha, 2004)<br />LaplacianEigenmaps (LE): (Belkin and Niyogi, 2004)<br />Pairwise distance between neighbors computed using Gaussian kernel function - O(pN2) method<br />Embedding computed to minimize the total distance between neighbors<br />
• 27. LE: Impact of Parameter Values <br />Parameter values for local embedding<br />s obtained via grid search<br />k, p obtained empirically<br />BOT Class 3, 6<br />BOT Classes 1-9<br />
• 28. <ul><li>Island Interior</li></ul>Alignment Results: Typical Class<br />
• 29. <ul><li>Critical class: Riparian</li></ul>Alignment Results: Critical Class<br />
• 30. Alignment Results: Critical Class<br />Critical class: Woodlands<br />
• 31. MA Results – Classification Accuracy<br /><ul><li>Evaluate results by overall accuracies</li></ul>Labeled Class<br />(Subset Data)<br />Classified via<br />Given Features <br />Classified via Correspondences<br />Classified via <br />Pooled Data<br />May, June pair<br />
• 32. MA Results – Classification Accuracy<br />Classified via<br />Given Features<br />(Spectral + spatial) <br />Classified via Correspondences<br />(Spectral + spatial)<br />Labeled Class<br />(Subset Data)<br />Classified via <br />Given Features<br />(Spectral) <br />Classified via Correspondences<br />(Spectral)<br />May, June pair<br />