ABSTRACT
Two aspects are crucial when constructing any real world supervised classification task: the set of classes whose distinction might be useful for the domain expert, and the set of classifications that can actually be distinguished by the data. Often a set of labels is defined with some initial intuition but these are not the best match for the task. For example, labels have been assigned for land cover classification of the Earth but it has been suspected that these labels are not ideal and some classes may be best split into subclasses whereas others should be merged. This paper formalizes this problem using three ingredients: the existing class labels, the underlying separability in the data, and a special type of input from the domain expert. We require a domain expert to specify an L × L matrix of pairwise probabilistic constraints expressing their beliefs as to whether the L classes should be kept separate, merged, or split. This type of input is intuitive and easy for experts to supply. We then show that the problem can be solved by casting it as an instance of penalized probabilistic clustering (PPC). Our method, Class-Level PPC (CPPC) extends PPC showing how its time complexity can be reduced from O(N2) to O(NL) for the problem of class re-definition. We further extend the algorithm by presenting a heuristic to measure adherence to constraints, and providing a criterion for determining the model complexity (number of classes) for constraint-based clustering. We demonstrate and evaluate CPPC on artificial data and on our motivating domain of land cover classification. For the latter, an evaluation by domain experts shows that the algorithm discovers novel class definitions that are better suited to land cover classification than the original set of labels.
Supplemental Material
- A. M. Aisen et al. Automated storage and retrieval of medical images to assist diagnosis: Implementation and preliminary assessment. Radiology, 228:265--270, July 2003.Google ScholarCross Ref
- H. Akaike. A new look at the statistical identification model. IEEE Trans. Auto Control, AC-19:716--723, 1974.Google ScholarCross Ref
- S. Basu, A. Banerjee, and R. J. Mooney. Semi-supervised clustering by seeding. In ICML, pages 27--34, 2002. Google ScholarDigital Library
- S. Basu, I. Davidson, and K. Wagstaff. Constrained Clustering: Advances in Algorithms, Theory, and Applications. Chapman & Hall/CRC, 2008. Google ScholarDigital Library
- C.-C. Chen and D. Landgrebe. A spectral feature design system for the hiris/modis era. Geoscience and Remote Sensing, IEEE Transactions on, 27(6):681--686, Nov 1989.Google Scholar
- U. M. Fayyad, G. Piatetsky-Shapiro, and P. Smyth. From data-mining to knowledge discovery: An overview. In U. M. Fayyad, G. Piatetsky-Shapiro, P. Smyth, and R. Uthurasamy, editors, Advances in Knowledge Discovery and Data Mining. AAAI/MIT Press, 1996. Google ScholarDigital Library
- M. Friedl et al. Global land cover mapping from MODIS: Algorithms and early results. Remote Sensing of Environment, 83:287--302, 2002.Google ScholarCross Ref
- H. Ghassemian and D. Landgrebe. Object-oriented feature extraction method for image data compaction. Control Systems Magazine, IEEE, 8(3):42--48, Jun 1988.Google ScholarCross Ref
- E. J. Hannan and B. G. Quinn. The determination of the order of an autoregression. Journal of the Royal Statistical Society, Series B, 41(2):190--195, 1979.Google Scholar
- T. S. Jaakkola. Tutorial on variational approximation methods. In Advanced Mean Field Methods: Theory and Practice, pages 129--159. MIT Press, 2000.Google Scholar
- I. T. Jolliffe. Principal component analysis. Springer Series in Statistics, 1986.Google Scholar
- B. Kulis, S. Basu, I. S. Dhillon, and R. J. Mooney. Semi-supervised graph clustering: a kernel approach. Machine Learning, 74(1):1--22, 2009. Google ScholarDigital Library
- M. H. C. Law, E. Topchy, and A. K. Jain. Clustering with soft and group constraints. Proc. Joint IAPR International Workshops on Structural, Syntactic, And Statistical Pattern Recognition, pages 662--670, 2004.Google ScholarCross Ref
- T. Loveland et al. Development of a global land cover characteristics database and IGBP DISCover from 1-km AVHRR data. Remote Sensing of Environment, 83:287--302, 2002.Google Scholar
- Z. Lu and T. K. Leen. Penalized probabilistic clustering. Neural Comput., 19(6):1528--1567, 2007. Google ScholarDigital Library
- J. B. MacQueen. Some methods for classification and analysis of multivariate observations. In Proc. of the Fifth Sym. on Math, Statistics, and Probability, pages 281--297, 1967.Google Scholar
- G. J. McLachlan and K. E. Basford. Mixture models. Inference and applications to clustering. Statistics: Textbooks and Monographs, 1988.Google Scholar
- M. Pugh and A. Waxman. Classification of spectrally-similar land cover using multi-spectral neural image fusion and the fuzzy artmap neural classifier. In IGARSS 2006, pages 1808--1811, 31 2006-Aug. 4 2006.Google ScholarCross Ref
- G. Schwartz. Estimating the dimension of a model. The Annals of Statistics, 5(2):461--464, 1978.Google ScholarCross Ref
- N. Shental, A. Bar-hillel, and D. Weinshall. Computing gaussian mixture models with EM using equivalence constraints. In In Advances in Neural Information Processing Systems 16. MIT Press, 2003.Google Scholar
- S. D. Spiegelhalter et al. Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society: Series B, 64(4):583--639, 2002.Google ScholarCross Ref
- N. Ueda, R. Nakano, Z. Ghahramani, and G. E. Hinton. Split and merge EM algorithm for improving gaussian mixture density estimates. J. VLSI Signal Process. Syst., 26(1-2):133--140, 2000. Google ScholarDigital Library
- U. von Luxburg. A tutorial on spectral clustering. Statistics and Computing, 17(4):395--416, 2007. Google ScholarDigital Library
- K. Wagstaff, C. Cardie, and S. Schroedl. Constrained k-means clustering with background knowledge. In ICML, pages 577--584, 2001. Google ScholarDigital Library
- Q. Zhao and D. J. Miller. Mixture modeling with pairwise, instance-level class constraints. Neural Computation, 17(11):2482--2507, 2005. Google ScholarDigital Library
Index Terms
- Redefining class definitions using constraint-based clustering: an application to remote sensing of the earth's surface
Recommendations
A Mixture Model and EM-Based Algorithm for Class Discovery, Robust Classification, and Outlier Rejection in Mixed Labeled/Unlabeled Data Sets
Several authors have shown that, when labeled data are scarce, improved classifiers can be built by augmenting the training set with a large set of unlabeled examples and then performing suitable learning. These works assume each unlabeled sample ...
Semisupervised Clustering with Metric Learning using Relative Comparisons
Semi-supervised clustering algorithms partition a given data set using limited supervision from the user. The success of these algorithms depend on the type of supervision and also on the kind of dissimilarity measure used while creating partitions of ...
Semi-supervised learning using multiple clusterings with limited labeled data
Supervised classification consists in learning a predictive model using a set of labeled samples. It is accepted that predictive models accuracy usually increases as more labeled samples are available. Labeled samples are generally difficult to obtain ...
Comments