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Using Lowly Correlated Time Series to Recover Missing Values in Time Series: A Comparison Between SVD and CD

  • Mourad KhayatiEmail author
  • Michael H. Böhlen
  • Philippe Cudré Mauroux
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9239)

Abstract

The Singular Value Decomposition (SVD) is a matrix decomposition technique that has been successfully applied for the recovery of blocks of missing values in time series. In order to perform an accurate block recovery, SVD requires the use of highly correlated time series. However, using lowly correlated time series that exhibit shape and/or trend similarities could increase the recovery accuracy. Thus, the latter time series could also be exploited by including them in the recovery process.

In this paper, we compare the accuracy of the Centroid Decomposition (CD) against SVD for the recovery of blocks of missing values using highly and lowly correlated time series. We show that the CD technique better exploits the trend and shape similarity to lowly correlated time series and yields a better recovery accuracy. We run experiments on real world hydrological and synthetic time series to validate our results.

Keywords

Time Series Mean Square Error Singular Value Decomposition Input Matrix Stochastic Gradient Descent 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Khayati, M., Böhlen, M.: Rebom: Recovery of blocks of missing values in time series. In: Proceedings of the 2012 ACM International Conference on Management of Data. COMAD 2012, pp. 44–55. Computer Society of India (2012)Google Scholar
  2. 2.
    Li, M., Bi, W., Kwok, J.T., Lu, B.: Large-scale nyström kernel matrix approximation using randomized SVD. IEEE Trans. Neural Netw. Learn. Syst. 26, 152–164 (2015)CrossRefGoogle Scholar
  3. 3.
    Halko, N., Martinsson, P.G., Tropp, J.A.: Finding structure with randomness: probabilistic algorithms for constructing approximate matrix decompositions. SIAM Rev. 53, 217–288 (2011)zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Achlioptas, D., McSherry, F.: Fast computation of low-rank matrix approximations. J. ACM 54 (2007)Google Scholar
  5. 5.
    Li, L., McCann, J., Pollard, N.S., Faloutsos, C.: Dynammo: mining and summarization of coevolving sequences with missing values. In: Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 507–516. Paris, France, 28 June–1 July 2009Google Scholar
  6. 6.
    Chu, M., Funderlic, R.: The centroid decomposition: relationships between discrete variational decompositions and svds. SIAM J. Matrix Anal. Appl. 23, 1025–1044 (2001)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Khayati, M., Böhlen, M., Gamper, J.: Memory-efficient centroid decomposition for long time series. In: ICDE. pp. 100–111 (2014)Google Scholar
  8. 8.
    Kolda, T.G., O’Leary, D.P.: A semidiscrete matrix decomposition for latent semantic indexing information retrieval. ACM Trans. Inf. Syst. 16, 322–346 (1998)CrossRefGoogle Scholar
  9. 9.
    Kolda, T.G., O’Leary, D.P.: Algorithm 805: computation and uses of the semidiscretematrix decomposition. ACM Trans. Math. Softw. 26, 415–435 (2000)CrossRefGoogle Scholar
  10. 10.
    Yu, H., Hsieh, C., Si, S., Dhillon, I.S.: Scalable coordinate descent approaches to parallel matrix factorization for recommender systems. In: 12th IEEE International Conference on Data Mining, ICDM 2012, pp. 765–774. Brussels, Belgium, 10–13 December 2012Google Scholar
  11. 11.
    Gemulla, R., Nijkamp, E., Haas, P.J., Sismanis, Y.: Large-scale matrix factorization with distributed stochastic gradient descent. In: KDD, pp. 69–77 (2011)Google Scholar
  12. 12.
    Koren, Y., Bell, R.M., Volinsky, C.: Matrix factorization techniques for recommender systems. IEEE Comput. 42, 30–37 (2009)CrossRefGoogle Scholar
  13. 13.
    Balzano, L., Nowak, R., Recht, B.: Online identification and tracking of subspaces from highly incomplete information. CoRR abs/1006.4046 (2010)Google Scholar
  14. 14.
    Golub, G.H., van Loan, C.F.: Matrix computations, 3rd edn. Johns Hopkins University Press, Baltimore (1996)zbMATHGoogle Scholar
  15. 15.
    Björck, A.: Numerical methods for least squares problems. SIAM (1996)Google Scholar
  16. 16.
    Griffiths, D.V., Smith, I.M.: Numerical Methods for Engineers. CRC Press, Boca Raton (2006)zbMATHGoogle Scholar
  17. 17.
    Jain, A., Nandakumar, K., Ross, A.: Score normalization in multimodal biometric systems. Pattern Recogn. 38, 2270–2285 (2005)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Mourad Khayati
    • 1
    • 2
    Email author
  • Michael H. Böhlen
    • 1
  • Philippe Cudré Mauroux
    • 2
  1. 1.Department of Computer ScienceUniversity of ZurichZurichSwitzerland
  2. 2.EXascale InfolabUniversity of FribourgFribourgSwitzerland

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