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Some Notes on Applied Mathematics for Machine Learning

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Advanced Lectures on Machine Learning (ML 2003)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3176))

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Abstract

This chapter describes Lagrange multipliers and some selected subtopics from matrix analysis from a machine learning perspective. The goal is to give a detailed description of a number of mathematical constructions that are widely used in applied machine learning.

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References

  1. Rouse Ball, W.W.: A Short Account of the History of Mathematics, 4th edn. Dover, Mineola (1908)

    MATH  Google Scholar 

  2. Belkin, M., Niyogi, P.: Laplacian eigenmaps for dimensionality reduction and data representation. In: Advances in Neural Information Processing Systems, vol. 14. MIT Press, Cambridge (2002)

    Google Scholar 

  3. Bell, E.T.: Men of Mathematics. Simon and Schuster. Touchstone edition (1986) (first published 1937)

    Google Scholar 

  4. Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)

    Book  MATH  Google Scholar 

  5. Buck, B., Macaualay, V. (eds.): Maximum Entropy in Action. Clarendon Press, Oxford (1991)

    Google Scholar 

  6. Burges, C.J.C.: A tutorial on support vector machines for pattern recognition. Data Mining and Knowledge Discovery 2(2), 121–167 (1998)

    Article  Google Scholar 

  7. Burges, C.J.C.: Geometric Methods for Feature Extraction and Dimensional Reduction. In: Rokach, L., Maimon, O. (eds.) Data Mining and Knowledge Discovery Handbook: A Complete Guide for Practitioners and Researchers. Kluwer Academic, Dordrecht (to appear, 2004)

    Google Scholar 

  8. Cox, T.F., Cox, M.A.A.: Multidimensional Scaling. Chapman and Hall, Sydney (2001)

    MATH  Google Scholar 

  9. Cressie, N.A.C.: Statistics for spatial data. Wiley, Chichester (1993) (revised edition)

    Google Scholar 

  10. Deerwester, S., Dumais, S.T., Landauer, T.K., Furnas, G.W., Harshman, R.A.: Indexing by Latent Semantic Analysis. Journal of the Society for Information Science 41(6), 391–407 (1990)

    Article  Google Scholar 

  11. Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. Johns Hopkins, Baltimore (1996)

    MATH  Google Scholar 

  12. Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, Cambridge (1985)

    Book  MATH  Google Scholar 

  13. Jaynes, E.T.: Bayesian methods: General background. In: Justice, J.H. (ed.) Maximum Entropy and Bayesian Methods in Applied Statistics, pp. 1–25. Cambridge University Press, Cambridge (1985)

    Google Scholar 

  14. Kline, M.: Mathematical Thought from Ancient to Modern Times, vol. 1,2,3. Oxford University Press, Oxford (1972)

    MATH  Google Scholar 

  15. Mangasarian, O.L.: Nonlinear Programming. McGraw Hill, New York (1969)

    MATH  Google Scholar 

  16. Nigam, K., Lafferty, J., McCallum, A.: Using maximum entropy for text classification. In: IJCAI 1999 Workshop on Machine Learning for Information Filtering, pp. 61–67 (1999)

    Google Scholar 

  17. Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290(22), 2323–2326 (2000)

    Article  Google Scholar 

  18. Schoenberg, I.J.: Remarks to maurice frechet’s article sur la d’efinition axiomatique d’une classe d’espace distanci’es vectoriellement applicable sur l’espace de Hilbert. Annals of Mathematics 36, 724–732 (1935)

    Article  MathSciNet  MATH  Google Scholar 

  19. Tipping, M.E., Bishop, C.M.: Probabilistic principal component analysis. Journal of the Royal Statistical Society 61(3), 611 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  20. Williams, C.K.I.: Prediction with gaussian processes: from linear regression to linear prediction and beyond. In: Jordan, M.I. (ed.) Learning in Graphical Models, pp. 599–621. MIT Press, Cambridge (1999)

    Google Scholar 

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Burges, C.J.C. (2004). Some Notes on Applied Mathematics for Machine Learning. In: Bousquet, O., von Luxburg, U., Rätsch, G. (eds) Advanced Lectures on Machine Learning. ML 2003. Lecture Notes in Computer Science(), vol 3176. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28650-9_2

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  • DOI: https://doi.org/10.1007/978-3-540-28650-9_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23122-6

  • Online ISBN: 978-3-540-28650-9

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