Advertisement

On-line Learning on Temporal Manifolds

  • Marco Maggini
  • Alessandro RossiEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10037)

Abstract

We formulate an online learning algorithm that exploits the temporal smoothness of data evolving on trajectories in a temporal manifold. The learning agent builds an undirected graph whose nodes store the information provided by the data during the input evolution. The agent’s behavior is based on a dynamical system that is derived from the temporal coherence assumption for the prediction function. Moreover, the graph connections are developed in order to implement a regularization process in both the spatial and temporal dimensions. The algorithm is evaluated on a benchmark based on a temporal sequence obtained from the MNIST dataset by generating a video from the original images. The proposed approach is compared with standard methods when the number of supervisions decreases.

Keywords

Graph regularization Temporal manifold Dissipative system 

Notes

Acknowledgements

We wish to thank Fondazione Bruno Kessler, Trento - Italy, (http://www.fbk.eu) research center that partially funded this research. We also thank Marco Gori, Duccio Papini and Paolo Nistri for helpful discussions.

References

  1. 1.
    Poggio, T., Girosi, F.: A theory of networks for approximation and learning. Technical report, MIT (1989)Google Scholar
  2. 2.
    Betti, A., Gori, M.: The principle of least cognitive action. Theor. Comput. Sci. 633, 83–99 (2016). Biologically Inspired Processes in Neural ComputationMathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Herrera, L., Núñez, L., Patiño, A., Rago, H.: A variational principle and the classical and quantum mechanics of the damped harmonic oscillator. Am. J. Phys. 54, 273–277 (1986)CrossRefGoogle Scholar
  4. 4.
    Gnecco, G., Gori, M., Melacci, S., Sanguineti, M.: Foundations of support constraint machines. Neural Comput. 27, 388–480 (2015)CrossRefzbMATHGoogle Scholar
  5. 5.
    Schoelkopf, B., Smola, A.: From regularization operators to support vector kernels. In: Kaufmann, M. (ed.) Advances in Neural Information Processing Systems. MIT Press, Cambridge (1998)Google Scholar
  6. 6.
    Gnecco, G., Gori, M., Sanguineti, M.: Learning with boundary conditions. Neural Comput. 25, 1029–1106 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Frandina, S., Gori, M., Lippi, M., Maggini, M., Melacci, S.: Variational foundations of online backpropagation. In: Mladenov, V., Koprinkova-Hristova, P., Palm, G., Villa, A.E.P., Appollini, B., Kasabov, N. (eds.) ICANN 2013. LNCS, vol. 8131, pp. 82–89. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-40728-4_11 CrossRefGoogle Scholar
  8. 8.
    Frandina, S., Lippi, M., Maggini, M., Melacci, S.: On–line laplacian one–class support vector machines. In: Mladenov, V., Koprinkova-Hristova, P., Palm, G., Villa, A.E.P., Appollini, B., Kasabov, N. (eds.) ICANN 2013. LNCS, vol. 8131, pp. 186–193. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-40728-4_24 CrossRefGoogle Scholar
  9. 9.
    Lecun, Y., Bottou, L., Bengio, Y., Haffner, P.: Gradient-based learning applied to document recognition. Proc. IEEE 86, 2278–2324 (1998)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Department of Information Engineering and Mathematical SciencesUniversity of SienaSienaItaly

Personalised recommendations