Abstract
Archetypal analysis represents the members of a set of multivariate data as a convex combination of extremal points of the data. It allows for dimensionality reduction and clustering and is particularly useful whenever the data are superpositions of basic entities. However, since its computation costs grow quadratically with the number of data points, the original algorithm hardly applies to modern pattern recognition or data mining settings. In this paper, we introduce ways of notably accelerating archetypal analysis. Our experiments are the first successful application of the technique to large scale data analysis problems.
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References
Cutler, A., Breiman, L.: Archetypal Analysis. Technometrics 36(4), 338–347 (1994)
Jolliffe, I.: Principal Component Analysis. Springer, Heidelberg (1986)
Schölkopf, B., Smola, A.J., Müller, K.-R.: Nonlinear Component Analysis as a Kernel Eigenvalue Problem. Neural Computation 10(5), 1299–1319 (1998)
Lee, D.D., Seung, S.: Learning the Parts of Objects by Non-Negative Matrix Factorization. Nature 401(6755), 788 (1999)
Finesso, L., Spreij, P.: Approximate Nonnegative Matrix Factorization via Alternating Minimization. In: Proc. 16th Int. Symp. on Mathematical Theory of Networks and Systems, Leuven (July 2004)
Stone, E., Cutler, A.: Archetypal Analysis of Spatio-temporal Dynamics. Physica D 90(3), 209–224 (1996)
Chan, B.H.P.: Archetypal Analysis of Galaxy Spectra. Monthly Notices of the Royal Astronomical Society 338(3), 790–795 (2003)
Huggins, P., Pachter, L., Sturmfels, B.: Toward the Human Genotope. Bulletin of Mathematical Biology 69(8), 2723–2735 (2007)
Joachims, T.: Making Large-Scale Support Vector Machine Learningn Practical. In: Advances in Kernel Methods: Support Vector Learning, MIT Press, Cambridge (1999)
de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry. Springer, Heidelberg (2000)
Ziegler, G.M.: Lectures on Polytopes. Springer, Heidelberg (1995)
Donoho, D.L., Tanner, J.: Neighborliness of Randomly-Projected Simplices in High Dimensions. Proc. of the Nat. Academy of Sciences 102(27), 9452–9457 (2005)
Hall, P., Marron, J., Neeman, A.: Geometric representation of high dimension low sample size data. J. of the Royal Statistical Society B 67(3), 427–444 (2005)
Blank, M., Gorelick, L., Shechtman, E., Irani, M., Basri, R.: Actions as Space-Time Shapes. In: Proc. ICCV (2005)
Torralba, A., Fergus, R., Freeman, W.T.: 80 Million Tiny Images: A Large Dataset for Non-parametric Object and Scene Recognition. IEEE Trans. on Pattern Analalysis and Machine Intelligence 30(11), 1958–1970 (2008)
Heidemann, G.: The principal components of natural images revisited. IEEE Trans. on Pattern Analalysis and Machine Intelligence 28(5), 822–826 (2006)
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Bauckhage, C., Thurau, C. (2009). Making Archetypal Analysis Practical. In: Denzler, J., Notni, G., Süße, H. (eds) Pattern Recognition. DAGM 2009. Lecture Notes in Computer Science, vol 5748. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03798-6_28
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DOI: https://doi.org/10.1007/978-3-642-03798-6_28
Publisher Name: Springer, Berlin, Heidelberg
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