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