Retraining maximum likelihood classifiers using a low-rank model Arnt-Børre Salberg Norwegian Computing Center Oslo, Norwa...
Introduction <ul><li>Challenge:  Dataset shift problem:  </li></ul><ul><ul><li>Training data match the test data poorly du...
Introduction <ul><li>Many surface reflectance algorithms often requires data from external sources </li></ul><ul><ul><li>L...
An existing method… <ul><li>Models the test image as a mixture distribution and estimates all parameters using the EM-algo...
Low-rank parameter modeling <ul><li>Training image  k :  </li></ul><ul><ul><li>Class mean vector and covariance matrix (cl...
Low-rank data modeling <ul><li>The proposed method for modeling the test data is a low-rank approach since the number of p...
Parameter estimation <ul><li>Procedure for estimating    and    </li></ul><ul><ul><li>Select  N  random samples  { y 1,...
Parameter estimation <ul><li>Procedure for estimating    and    </li></ul><ul><ul><li>Select  N  random samples  { y 1,...
Experiment 1: Cloud detection in optical images <ul><li>15 different QuickBird and WorldView-2 images covering 7 different...
Experiment 1: Cloud detection in optical images <ul><li>Model </li></ul><ul><ul><li> i  is the eigenvector corresponding ...
Experiment 1: Cloud detection in optical images <ul><li>Parameter estimation. At iteration  l +1 : </li></ul><ul><li>where...
Results: Cloud detection in optical images Without retraining With retraining
Results: Cloud detection in optical images
Results: Cloud detection in optical images
Experiment 2: Tree cover mapping of tropical forest <ul><li>13 different Landsat TM images covering an area nearby Amani, ...
Experiment 2: Tree cover mapping of tropical forest <ul><li>Model </li></ul><ul><ul><li>   constrained to contain only po...
Experiment 2: Tree cover mapping of tropical forest <ul><li>Parameter estimation: At iteration  l + 1 </li></ul><ul><li>wh...
Results: Tree cover mapping of tropical forest <ul><li>* </li></ul>Without retraining With retraining February 2010 July 2...
Summary and conclusion <ul><li>Proposed a simple method for handling the dataset shift between training and test data </li...
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Retraining maximum likelihood classifiers using low-rank model.ppt

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Retraining maximum likelihood classifiers using low-rank model.ppt

  1. 1. Retraining maximum likelihood classifiers using a low-rank model Arnt-Børre Salberg Norwegian Computing Center Oslo, Norway IGARSS July 25, 2011
  2. 2. Introduction <ul><li>Challenge: Dataset shift problem: </li></ul><ul><ul><li>Training data match the test data poorly due to atmospherical, geographical, botanical and phenological variations in the image data </li></ul></ul><ul><ul><li>-> reduced classification performance </li></ul></ul><ul><ul><li>Class-dependent data distribution varies </li></ul></ul><ul><ul><ul><li>between training images </li></ul></ul></ul><ul><ul><ul><li>between test and training images </li></ul></ul></ul><ul><li>Goal: Develop a method that re-estimates the parameters such that classifier possess a good fit to the test data </li></ul>
  3. 3. Introduction <ul><li>Many surface reflectance algorithms often requires data from external sources </li></ul><ul><ul><li>LEDAPS (Landsat): </li></ul></ul><ul><ul><ul><li>ozone and water vapor measurements </li></ul></ul></ul><ul><li>Phenological, botanical and geographical variation in addition to atmospherical makes the calibration problem even harder </li></ul>
  4. 4. An existing method… <ul><li>Models the test image as a mixture distribution and estimates all parameters using the EM-algorithm, with estimated parameters from training data as initial values </li></ul><ul><li>To many degrees of freedom. Statistic fit is excellent, but class labels get mixed . </li></ul>
  5. 5. Low-rank parameter modeling <ul><li>Training image k : </li></ul><ul><ul><li>Class mean vector and covariance matrix (class i ) </li></ul></ul><ul><li>Class mean vector and covariance matrix model for the test image </li></ul><ul><ul><li> and  are unknown parameter vectors to be estimated from the data </li></ul></ul>
  6. 6. Low-rank data modeling <ul><li>The proposed method for modeling the test data is a low-rank approach since the number of parameters in  is L<D. </li></ul><ul><ul><li>This is much less than estimating all C·D parameters i  i , i=1,…,C </li></ul></ul><ul><li>By using a low-rank estimation of the class mean vectors of the test data, the spectral differences between the classes is in larger degree maintained </li></ul>
  7. 7. Parameter estimation <ul><li>Procedure for estimating  and   </li></ul><ul><ul><li>Select N random samples { y 1, y 2,… y N } from the test image </li></ul></ul>
  8. 8. Parameter estimation <ul><li>Procedure for estimating  and   </li></ul><ul><ul><li>Select N random samples { y 1, y 2,… y N } from the test image </li></ul></ul><ul><ul><li>Model them using a Gaussian mixture distribution </li></ul></ul><ul><li>Estimate the parameters by solving the likelihood </li></ul>
  9. 9. Experiment 1: Cloud detection in optical images <ul><li>15 different QuickBird and WorldView-2 images covering 7 different scenes in Norway </li></ul><ul><li>Features </li></ul><ul><ul><li>Band 2 (green) </li></ul></ul><ul><ul><li>Band 3 (red) </li></ul></ul><ul><li>Classes </li></ul><ul><ul><li>clouds, cloud shadows, vegetation, concrete/asphalt/etc., haze and water </li></ul></ul><ul><li>Resolution down-sampled to 19.2 m (16.0 m) </li></ul><ul><li>4 different training (sub)images </li></ul>
  10. 10. Experiment 1: Cloud detection in optical images <ul><li>Model </li></ul><ul><ul><li> i is the eigenvector corresponding to the largest eigenvalue  i of the matrix </li></ul></ul>average Test eigenvector
  11. 11. Experiment 1: Cloud detection in optical images <ul><li>Parameter estimation. At iteration l +1 : </li></ul><ul><li>where </li></ul>
  12. 12. Results: Cloud detection in optical images Without retraining With retraining
  13. 13. Results: Cloud detection in optical images
  14. 14. Results: Cloud detection in optical images
  15. 15. Experiment 2: Tree cover mapping of tropical forest <ul><li>13 different Landsat TM images covering an area nearby Amani, Tanzania (path/row 166/063) </li></ul><ul><li>Features </li></ul><ul><ul><li>Band 1-5 and 7 </li></ul></ul><ul><li>Classes </li></ul><ul><ul><li>Forest, spares forest, grass and soil </li></ul></ul><ul><li>Two training images (1986-10-06 and 2010-02-10) </li></ul>
  16. 16. Experiment 2: Tree cover mapping of tropical forest <ul><li>Model </li></ul><ul><ul><li> constrained to contain only positive elements </li></ul></ul><ul><li>Solution found using non-negative least-squares in combination with iterative maximum-likelihood estimation </li></ul>
  17. 17. Experiment 2: Tree cover mapping of tropical forest <ul><li>Parameter estimation: At iteration l + 1 </li></ul><ul><li>where </li></ul>
  18. 18. Results: Tree cover mapping of tropical forest <ul><li>* </li></ul>Without retraining With retraining February 2010 July 2009
  19. 19. Summary and conclusion <ul><li>Proposed a simple method for handling the dataset shift between training and test data </li></ul><ul><li>Cloud detection: Evaluated successfully on a many different Quickbird and WorldView-2 images. </li></ul><ul><ul><li>Haze versus clouds </li></ul></ul><ul><ul><li>Confuses snow and clouds </li></ul></ul><ul><li>Guidelines on how to select the low-rank modeling functions is needed </li></ul><ul><li>EM-algorithm and local minima problem </li></ul><ul><li>More testing and evalidation of the method is necessary </li></ul>
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