Classification with Positive and Negative Equivalence Constraints: Theory, Computation and Human Experiments
We tested the efficiency of category learning when participants are provided only with pairs of objects, known to belong either to the same class (Positive Equivalence Constraints or PECs) or to different classes (Negative Equivalence Constraints or NECs). Our results in a series of cognitive experiments show dramatic differences in the usability of these two information building blocks, even when they are chosen to contain the same amount of information. Specifically, PECs seem to be used intuitively and quite efficiently, while people are rarely able to gain much information from NECs (unless they are specifically directed for the best way of using them). Tests with a constrained EM clustering algorithm under similar conditions also show superior performance with PECs. We conclude with a theoretical analysis, showing (by analogy to graph cut problems) that the satisfaction of NECs is computationally intractable, whereas the satisfaction of PECs is straightforward. Furthermore, we show that PECs convey more information than NECs by relating their information content to the number of different graph colorings. These inherent differences between PECs and NECs may explain why people readily use PECs, while many of them need specific directions to be able to use NECs effectively.
KeywordsCategorization Similarity Rule learning Expectation Maximization
Unable to display preview. Download preview PDF.
- 2.Bar-Hilel, A., Hertz, T., Shental, N., Weinshall, D.: Learning distance functions using equivalence relations. In: The 20th International Conference on Machine Learning (2003)Google Scholar
- 3.Bilenko, M., Basu, S., Mooney, R.J.: Integrating constraints and metric learning in semi-supervised clustering. In: Banff Canada, AAAI press, Stanford, California, USA (2004)Google Scholar
- 4.Bishop, C.M.: Neural Networks for Pattern Recognition. Oxford press, Oxford (1995)Google Scholar
- 9.Hammer, R., Hertz, T., Hochstein, S., Weinshall, D.: Category learning from equivalence constraints. Cognitive Processing (in press)Google Scholar
- 10.Hertz, T., Bar-Hillel, A., Weinshall, D.: Boosting margin based distance functions for clustering. In: ICML (2004)Google Scholar
- 12.Klein, D., Kamvar, S., Manning, C.: From instance-level constraints to space-level constraints: Making the most of prior knowledge in data clustering. In: Proceedings of the Nineteenth International Conference on Machine Learning (2002)Google Scholar
- 13.Krivelevich, M.: Sparse graphs usually have exponentially many optimal colorings. Electronic Journal of Combinatorics 9 (2002)Google Scholar
- 14.Shental, N., Bar-Hilel, A., Hertz, T., Weinshall, D.: Computing Gaussian mixture models with EM using equivalence constraints. In: Advances in Neural Information Processing Systems, vol. 16, MIT Press, Cambridge (2004)Google Scholar
- 15.Stanislaw, H., Todorov, N.: Calculating signal detection theory measures. Behavior Research Methods, Instruments, & Computers 31(1), 137–149 (1999)Google Scholar
- 16.Wagstaff, K., Cardie, C., Rogers, S., Schroedl, S.: Constrained K-means clustering with background knowledge. In: Proc. 18th International Conf. on Machine Learning, pp. 577–584. Morgan Kaufmann, San Francisco, CA (2001)Google Scholar
- 17.Xing, E.P., Ng, A.Y., Jordan, M.I., Russell, S.: Distance metric learnign with application to clustering with side-information. In: Advances in Neural Information Processing Systems, vol. 15, MIT Press, Cambridge (2002)Google Scholar