This document proposes a novel active learning strategy for domain adaptation in the classification of remote sensing images. The strategy uses active learning to iteratively select the most informative unlabeled samples from the target domain to label and add to the training set, while also removing less relevant samples from the source domain training set. This allows a classifier trained on one image (source domain) to be adapted for classifying another similar image (target domain). Experimental results on two datasets show the method improves classification accuracy on the target domain with fewer labeled samples needed than other domain adaptation techniques.

1. A NOVEL ACTIVE LEARNING STRATEGY FOR DOMAIN ADAPTATION IN THE CLASSIFICATION OF REMOTE SENSING IMAGES C. Persello L. Bruzzone e-mail: claudio.persello@disi.unitn.it, lorenzo.bruzzone@ing.unitn.it, Web page: http://rslab.disi.unitn.it

2. C. Persello, L. Bruzzone Outline Background on Domain Adaptation and Active Learning 1 Aim of the Work 2 Proposed Approach to Address Domain Adaptation Problems with Active Learning 3 Experimental Results 4 Conclusions 5 2

3. Introduction Scenario: Growing availability of space-borne datathat gives the opportunity to develop several applications related to land-cover mapping andmonitoring. Problem: Common automatic classification techniques are based on supervised learning methods, which require a set of new training samples every time that a new remote sensing image has to be classified Need for the developmentof efficient techniques capable to adapt the supervised classifier trained on a image for the classification of another similar but not identical image acquired either: 1) on a different area,or 2) on the same area at a different time. C. Persello, L. Bruzzone 3

4. Background on Domain Adaptation Domain Adaptation: models the problem of adapting a supervised classifier trained on a given image (source domain) to the classification of another similar but not identical image (target domain) acquired either on a different area, or on the same area at a different time. Assumption: Source and target domainshare the same set of land cover classes. Source Domain Target Domain Semisupervisedtechniques (e.g., [1], [2]) Problem: correct converngence is not always possible Class 𝜔1 Class 𝜔2 Unknown Class Class 𝜔3 [1] L. Bruzzone, D. Fernandez Prieto, “Unsupervised retraining of a maximum-likelihood classifier for the analysis of multitemporal remote-sensing images,” IEEE Trans. Geosci. Remote Sens., Vol. 39, No.2, pp. 456-460, 2001. [2] L. Bruzzone, M. Marconcini, “Domain Adaptation Problems: a DASVM Classification Technique and a Circular Validation Strategy,” IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 32, 2010, No. 5, pp. 770-787, 2010. C. Persello, L. Bruzzone 4

5. Working Assumption Working Assumption: In this work we assume that some samples (as little as possible) from the target domain can be labeled by the user and added to the existing training set. Proposed solution: use of Active Learning [1], [2] procedure for selecting the most informative samples of the target domain. General Active Process U G: Supervisedclassifier; Q: Query function; S: Supervisor; T: Training set; U: Unlabeleddata classification Ti Ti-1 G Update T X S Q [1] S. Rajan, J. Ghosh, and M. M. Crawford, “An active learning approach to hyperspectral data classification,” IEEE Transactions on Geoscience and Remote Sensing, vol. 46, no. 4, pp. 1231-1242, Apr. 2008. [2]B. Demir, C. Persello, and L. Bruzzone, “Batch mode active learning methods for the interactive classification of remote sensing images,” IEEE Transactions on Geoscience and Remote Sensing, vol. 49, no.3, pp. 1014-1031, March 2011. C. Persello, L. Bruzzone 5

6. Aim of the Work Aim of the Work: propose a novel Domain Adaptation technique based on Active Learning, which aims at classifying the target image, while requiring the minimum number of labeled samples from the new image. Basic Idea: iterative process based on labeling and adding to the training set the most informative samples from the target domain (query+), while removingfrom the training set the source-domain samples that do not fit with the distributions of the classes in the target domain (query-). Example: Source Domain Target Domain Query- Query+ Convergence reached! Class 𝜔1 Class 𝜔2 Class 𝜔3 C. Persello, L. Bruzzone 6

7. Proposed Technique Classification technique: Gaussian Maximum Likelihood 𝑦𝑡=argmax𝜔𝑛∈Ω𝑝𝐱𝑡|𝜔𝑛, Ω=𝜔1,𝜔2,…,𝜔𝐶. Query+: selects the batch of the h+ most informative samples from the pool of unlabeled samples, which are taken from the target domain. 𝐱+=argmin𝐱∈𝑈𝑝(𝑖)𝐱|𝜔𝑚𝑎𝑥1−𝑝(𝑖)𝐱|𝜔𝑚𝑎𝑥2, 𝜔𝑚𝑎𝑥1=argmax𝜔𝑛∈Ω𝑝(𝑖)𝐱|𝜔𝑛, 𝜔𝑚𝑎𝑥2=argmax𝜔𝑚∈Ω𝜔𝑚𝑎𝑥1}{𝑝(𝑖)(𝐱|𝜔𝑚)} Second largest class-conditional density Largest class-conditional density 𝑝𝑖𝐱|𝜔2 𝑝𝑖𝐱|𝜔3 𝑝𝑖𝐱|𝜔1 x 𝐱+ C. Persello, L. Bruzzone 7

8. Proposed Technique Query-: removesfrom the source-domain training set the labeled samples that do not fit withthe distribution of the classes in the target domain. 𝐱−=argmax𝐱∈𝑇(0)𝑝0𝐱|𝜔𝑐−𝑝𝑖𝐱|𝜔𝑐 Class-conditional density computed using source-domain samples Class-conditional density computed using samples at iteration i 𝑝𝑖𝐱|𝜔2 𝑝0𝐱|𝜔2 𝑝0𝐱|𝜔1 𝑝𝑖𝐱|𝜔1 𝑝0𝐱−|𝜔1 𝑝𝑖𝐱−|𝜔1 x - x C. Persello, L. Bruzzone 8

10. h− number of samples selected by q-;

11. 𝛼=h+/h−Stop Criterion: we considered the Bhattacharyya distance: The active learning process is stopped when 𝐵𝑖 reaches a stable saturation point. This allows the user to detect the convergence of the algorithm without a test set on the target domain 𝐵𝑖=1𝐶𝑛=1𝐶𝐵𝑛𝑖 𝐵𝑛𝑖=−ln𝒙𝑝0𝐱|𝜔n𝑝𝑖𝐱|𝜔n Class-conditional density computed using source-domain samples Class-conditional density computed using samples at iteration i C. Persello, L. Bruzzone 9

12. Data Set Description: VHR data set Data set: Two Quickbirdimages acquired in 2006 over two rural areas in Trento, Italy. Reference labeled data: Two sets of labeled samples for each image. Land-cover classes: Vineyard, water, agriculture fields, forest, apple tree, urban area. Image QB1 Image QB2 C. Persello, L. Bruzzone 10

13. Data Set Description Distribution of labeled samples on bands 3 and 4 of the two Quickbird images Source Domain Target Domain C. Persello, L. Bruzzone 11

15. Initial training set size: 965 samples

16. For the proposed technique we used:h+=2 h−=10 C. Persello, L. Bruzzone 12

18. a spatially correlated test set TS1

19. a training set T2 spatially disjoint from T1

20. a test set TS2 spatially correlated with T2Area 1 T1 TS1 T2 TS2 Area 2 C. Persello, L. Bruzzone 13

22. Initial training set size: 707 samples

23. For the proposed technique we used:h+=10 h−=30 C. Persello, L. Bruzzone 14

26. Extend the proposed method to kernel-based classifiers.C. Persello, L. Bruzzone 15