An hacking day of Mathematics for Data Science at the Department of Mathematics

Alessandra Bernardi

Alessandra Bernardi

(Università di Trento)
Personal website

Syllabus

In this series of lectures we will focus on High Order Singular Value Decomposition (HOSVD). We will briefly recall the classical SVD for matrices, we will go through some applications (image and signal processing, pattern recognition, data miming and machine learning, chemometrics …), and we will present various tensor decompositions (like Tucker decomposition, HOSVD and approximation by low multilinear rank). Algorithms can be implemented in Matlab.

References

  • Hitchcock, F.L. (1928). Multiple Invariants and Generalized Rank of a P-Way Matrix or Tensor. Journal of Mathematics and Physics. 7(1–4): 39–79. doi:10.1002/sapm19287139.
  • Tucker, L.R. (1966). Some mathematical notes on three-mode factor analysis. Psychometrika, 31(3), 279–311. doi:10.1007/bf02289464.
  • Tucker, L.R. (1963). Implications of factor analysis of three-way matrices for measurement of change. In C. W. Harris (Ed.), Problems in measuring change. Madison, Wis.: Univ. Wis. Press.: 122–137.
  • Tucker, L.R. (1964). The extension of factor analysis to three-dimensional matrices. In N. Frederiksen and H. Gulliksen (Eds.), Contributions to mathematical psychology. New York: Holt, Rinehart and Winston: 109–127.
  • De Lathauwer, L., De Moor, B. and Vandewalle, J. (2000). A Multilinear Singular Value Decomposition. SIAM Journal on Matrix Analysis and Applications. 21(4), 1253-1278. doi:10.1137/s0895479896305696.
  • Carlini, E. and Kleppe, J. (2011). Ranks derived from multilinear maps. Journal of Pure and Applied Algebra. 215(8), 1999-2004. doi:10.1016/j.jpaa.2010.11.010.
  • Vannieuwenhoven, N., Vandebril, R. and Meerbergen, K. (2012). A New Truncation Strategy for the Higher-Order Singular Value Decomposition. SIAM Journal on Scientific Computing. 34(2), A1027-A1052. doi:10.1137/110836067.

Schedule

  • Friday 2018/12/07 14.15-18.00 Room A210

Details

  • The participation is free. Please send an email to Prof. Claudio Agostinelli by November 30, 2018.
  • For further information, please contact Prof. Claudio Agostinelli
  • Poster: PDF
  • Venue: Polo Scientifico e Tecnologico F. Ferrari – Room A210
  • Language: English

Videos (Restricted access, user: HOSVD2018)

Material (Restricted access, user: HOSVD2018)