Nearest q-Flat to m Points

Journal of Optimization Theory and Applications - Tập 105 - Trang 249-252 - 2000
P. Tseng1
1Department of Mathematics, University of Washington, Seattle

Tóm tắt

Recently, Bradley and Mangasarian studied the problem of finding the nearest plane to m given points in ℝn in the least square sense. They showed that the problem reduces to finding the least eigenvalue and associated eigenvector of a certain n×n symmetric positive-semidefinite matrix. We extend this result to the general problem of finding the nearest q-flat to m points, with 0≤q≤n−1.

Tài liệu tham khảo

Bradley, P. S., and Mangasarian, O. L., k-Plane Clustering, Computer Sciences Report 9808, University of Wisconsin, Madison, Wisconsin, 1998; Journal of Global Optimization (to appear). Jain, A. K., and Dubes, R. C., Algorithms for Clustering Data, Prentice-Hall, Englewood Cliffs, New Jersey, 1988. Selim, S. Z., and Ismail, M. A., K-Means-Type Algorithms: A Generalized Convergence Theorem and Characterization of Local Optimality, IEEE Transactions on Pattern Analysis and Machine Intellience, Vol. 6, pp. 81–87, 1984. Rockafellar, R. T., Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970. Horn, R. A., and Johnson, C. R., Matrix Analysis, Cambridge University Press, Cambridge, United Kingdom, 1985.