1. A New Subspace Approach for Supervised Hyperspectral Image Classification Jun Li 1,2, José M. Bioucas-Dias 2 and Antonio Plaza 1 1 Hyperspectral Computing Laboratory University of Extremadura, Cáceres, Spain 2 Instituto de Telecomunicaçoes, Instituto Superior Técnico, TULisbon, Portugal Contact e-mails: {junli, aplaza}@unex.es, bioucas@lx.it.pt

2. Talk Outline: 1. Challenges in hyperspectral image classification 2. Subspace projection 2.1. Subspace projection-based framework 2.2. Considered subspace projection techniques: PCA versus HySime 2.3. Integration with different classifiers (LDA, SVM, MLR) 3. Experimental results 3.1. Experiments with AVIRIS Indian Pines hyperspectral data 3.2. Experiments with ROSIS Pavia University hyperspectral 4. Conclusions and future research lines 1. Challenges in hyperspectral image classification 2. Subspace projection 2.1. Subspace projection-based framework 2.2. Considered subspace projection techniques: PCA versus HySime 2.3. Integration with different classifiers (LDA, SVM, MLR) 3. Experimental results 3.1. Experiments with AVIRIS Indian Pines hyperspectral data 3.2. Experiments with ROSIS Pavia University hyperspectral 4. Conclusions and future research lines A New Subspace Approach for Hyperspectral Classification IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2011), Vancouver, Canada, July 24 – 29, 2011

3. Concept of hyperspectral imaging using NASA Jet Propulsion Laboratory’s Airborne Visible Infra-Red Imaging Spectrometer 1 IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2011), Vancouver, Canada, July 24 – 29, 2011 Challenges in Hyperspectral Image Classification

4. Panchromatic Hyperspectral (100’s of bands) Hyperspectral (100’s of bands) Multispectral (10’s of bands) Multispectral (10’s of bands) Challenges in Hyperspectral Image Classification Ultraspectral (1000’s of bands) Ultraspectral (1000’s of bands) 2 IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2011), Vancouver, Canada, July 24 – 29, 2011 Challenges in hyperspectral image classification Imbalance between dimensionality and training samples, presence of mixed pixels

5. Challenges in hyperspectral image classification The special characteristics of hyperspectral data pose several processing problems: 1.The high-dimensional nature of hyperspectral data introduces important limitations in supervised classifiers, such as the limited availability of training samples or the inherently complex structure of the data 2.There is a need to address the presence of mixed pixels resulting from insufficient spatial resolution and other phenomena in order to properly model the hyperspectral data 3.There is a need to develop computationally efficient algorithms, able to provide a response in a reasonable time and thus address the computational requirements of time-critical remote sensing applications In this work, we evaluate the impact of using subspace projection techniques prior to supervised classification of hyperspectral image data while analyzing each of the aforementioned items Challenges in Hyperspectral Image Classification 3 IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2011), Vancouver, Canada, July 24 – 29, 2011

6. Talk Outline: 1. Challenges in hyperspectral image classification 2. Subspace projection 2.1. Subspace projection-based framework 2.2. Considered subspace projection techniques: PCA versus HySime 2.3. Integration with different classifiers (LDA, SVM, MLR) 3. Experimental results 3.1. Experiments with AVIRIS Indian Pines hyperspectral data 3.2. Experiments with ROSIS Pavia University hyperspectral 4. Conclusions and future research lines 1. Challenges in hyperspectral image classification 2. Subspace projection 2.1. Subspace projection-based framework 2.2. Considered subspace projection techniques: PCA versus HySime 2.3. Integration with different classifiers (LDA, SVM, MLR) 3. Experimental results 3.1. Experiments with AVIRIS Indian Pines hyperspectral data 3.2. Experiments with ROSIS Pavia University hyperspectral 4. Conclusions and future research lines A New Subspace Approach for Hyperspectral Classification IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2011), Vancouver, Canada, July 24 – 29, 2011

7. Subspace Projection-Based Framework 4 IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2011), Vancouver, Canada, July 24 – 29, 2011 Subspace projection-based framework.- Hyperspectral image data generally lives in a lower-dimensional subspace compared with the input feature dimensionality This can be exploited to address ill-posed problems given by limited training samples The projection into such subspaces allows us to specifically avoid spectral confusion due to mixed pixels, thus reducing their impact in the subsequent classification process J. Li, J. M. Bioucas-Dias and A. Plaza, “Spectral-spatial hyperspectral image segmentation using sub- space multinomial logistic regression and Markov random fields,” IEEE Transactions on Geoscience and Remote Sensing, in press, 2011.

8. Considered Subspace Projection Techniques: PCA versus HySime 5 IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2011), Vancouver, Canada, July 24 – 29, 2011 Principal Component Analysis (PCA).- High-dimensional data can be transformed effectively according to its distribution in feature space (e.g. by finding the most important directions or axes, establishing those axes as the references of a new coordinate system which takes into account data distribution) Orders the resulting components in decreasing order of variance

9. 6 IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2011), Vancouver, Canada, July 24 – 29, 2011 Principal Component Analysis (PCA).- High-dimensional data can be transformed effectively according to its distribution in feature space (e.g. by finding the most important directions or axes, establishing those axes as the references of a new coordinate system which takes into account data distribution) Orders the resulting components in decreasing order of variance Considered Subspace Projection Techniques: PCA versus HySime

10. 7 IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2011), Vancouver, Canada, July 24 – 29, 2011 Hyperspectral Signal Identification by Minimum Error (HySime).- A recently developed method for subspace identification in remotely sensed hyperspectral data, which offers several additional features with regards to principal component analysis and other subspace projection techniques J. M. Bioucas-Dias and J. M. P Nascimento, “Hyperspectral subspace identification,” IEEE Transactions on Geoscience and Remote Sensing, vol. 46, no. 8, pp. 2435-2445, 2008. Principal Component Analysis Seeks for the projection that best represents the original hyperspectral data in least square sense Reduces the original signal into subset of eigenvectors without computing any noise statistics The difficulty in getting reliable noise estimates from the resulting eigenvalues is that these eigenvalues still represent mixtures of signal sources and noise HySime HySime finds the subset of eigenvectors and the correspondent eigenvalues by minimizing the mean square error between the original signal and its projection onto the eigenvector subspace Uses multiple regressions for the estimation of the noise and signal covariance matrices Optimally represents the original signal with minimum error Considered Subspace Projection Techniques: PCA versus HySime

11. Supervised Classification Framework Tested in this Work 8 IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2011), Vancouver, Canada, July 24 – 29, 2011 Test classification accuracy PCA, HySime Supervised Classification Framework.- Includes subspace projection and supervised classification based on training samples: Subspace projection Supervised classifier Training Samples Test Samples Randomly selected

12. 9 IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2011), Vancouver, Canada, July 24 – 29, 2011 Integration of subspace-based framework with different classifiers.- Three different supervised classifiers tested in this work: 1.Linear discriminant analysis (LDA): find a linear combination of features which separate two or more classes; the resulting combination may be used as a linear classifier (only linearly separable classes will remain separable after applying LDA) 2.Support vector machine (SVM): constructs a set of hyperplanes in high-dimensional space; a good separation is achieved by the hyperplane that has the largest distance to the nearest training data points of any class 3.Multinomial logistic regression (MLR): models the posterior class distributions in a Bayesian framework, thus supplying (in addition to the boundaries between the classes) a degree of plausibility for such classes Integration with different classifiers (LDA, SVM, MLR)

13. Talk Outline: 1. Challenges in hyperspectral image classification 2. Subspace projection 2.1. Classic techniques for subspace projection: PCA versus HySime 2.2. Subspace projection-based framework 2.3. Integration with different classifiers (LDA, SVM, MLR) 3. Experimental results 3.1. Experiments with AVIRIS Indian Pines hyperspectral data 3.2. Experiments with ROSIS Pavia University hyperspectral 4. Conclusions and future research lines 1. Challenges in hyperspectral image classification 2. Subspace projection 2.1. Classic techniques for subspace projection: PCA versus HySime 2.2. Subspace projection-based framework 2.3. Integration with different classifiers (LDA, SVM, MLR) 3. Experimental results 3.1. Experiments with AVIRIS Indian Pines hyperspectral data 3.2. Experiments with ROSIS Pavia University hyperspectral 4. Conclusions and future research lines A New Subspace Approach for Hyperspectral Classification IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2011), Vancouver, Canada, July 24 – 29, 2011

14. AVIRIS Indian Pines data set.- Challenging classification scenario due to spectrally similar classes Early growth stage of the agricultural features (only around 5% coverage of soil) 145x145 pixels, 202 spectral bands, 16 ground-truth classes 10366 labeled pixels (random training subsets evenly distributed among classes) Experimental Results Using Real Hyperspectral Data Sets 10 IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2011), Vancouver, Canada, July 24 – 29, 2011 False color compositionGround-truth

15. AVIRIS Indian Pines data set.- Classification results using 160 training samples (10 training samples per class) For the SVM classifier we used the Gaussian RBF kernel after testing other kernels The mean accuracies (after 10 Monte Carlo runs) and processing times are reported 11 IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2011), Vancouver, Canada, July 24 – 29, 2011 Experimental Results Using Real Hyperspectral Data Sets

16. AVIRIS Indian Pines data set.- Classification results using 240 training samples (15 training samples per class) For the SVM classifier we used the Gaussian RBF kernel after testing other kernels The mean accuracies (after 10 Monte Carlo runs) and processing times are reported 12 IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2011), Vancouver, Canada, July 24 – 29, 2011 Experimental Results Using Real Hyperspectral Data Sets

17. AVIRIS Indian Pines data set.- Classification results using 320 training samples (20 training samples per class) For the SVM classifier we used the Gaussian RBF kernel after testing other kernels The mean accuracies (after 10 Monte Carlo runs) and processing times are reported 13 IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2011), Vancouver, Canada, July 24 – 29, 2011 Experimental Results Using Real Hyperspectral Data Sets

18. 14 IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2011), Vancouver, Canada, July 24 – 29, 2011 AVIRIS Indian Pines data set.- Classification results using 320 training samples (20 training samples per class) SVM (OA=65.36%) Subspace SVM (OA=70.33%) LDA (OA=50.74%) Subspace LDA (OA=54.90%) Linear MLR (OA=60.38%) Subspace MLR (OA=67.53%) Ground-truth Experimental Results Using Real Hyperspectral Data Sets

19. ROSIS Pavia University data set.- 15 IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2011), Vancouver, Canada, July 24 – 29, 2011 Experimental Results Using Real Hyperspectral Data Sets Overall classification accuracies and kappa coefficient (in the parentheses) using different training sets for the ROSIS Pavia University

20. Conclusions and Future Lines.- We have evaluated the impact of subspace projection on supervised classification of remotely sensed hyperspectral image data sets Two dimensionality reduction methods have been used: PCA and HySime, although many others are available and could be used: MNF, OSP, VD Three different supervised classifiers considered: LDA, SVM, MLR Experimental results indicate that different approaches for hyperspectral image classification approaches can benefit from subspace projection, particularly when very limited training samples are available Subspace projection can be naturally integrated with multinomial logistic regression (MLR) classifiers, which greatly benefit from dimensionality reduction Future work will focus on the evaluation of other subspace projection approaches and hyperspectral data sets Conclusions and Hints at Plausible Future Research 16 IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2011), Vancouver, Canada, July 24 – 29, 2011

21. IEEE J-STARS Special Issue on Hyperspectral Image and Signal Processing 17 IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2011), Vancouver, Canada, July 24 – 29, 2011

22. A New Subspace Approach for Supervised Hyperspectral Image Classification Jun Li 1,2, José M. Bioucas-Dias 2 and Antonio Plaza 1 1 Hyperspectral Computing Laboratory University of Extremadura, Cáceres, Spain 2 Instituto de Telecomunicaçoes, Instituto Superior Técnico, TULisbon, Portugal Contact e-mails: {junli, aplaza}@unex.es, bioucas@lx.it.pt