Kronecker Decomposition for Image Classification

  • Sabrina Fontanella
  • Antonio J. Rodríguez-Sánchez
  • Justus Piater
  • Sandor Szedmak
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9822)


We propose an image decomposition technique that captures the structure of a scene. An image is decomposed into a matrix that represents the adjacency between the elements of the image and their distance. Images decomposed this way are then classified using a maximum margin regression (MMR) approach where the normal vector of the separating hyperplane maps the input feature vectors into the outputs vectors. Multiclass and multilabel classification are native to MMR, unlike other more classical maximum margin approaches, like SVM. We have tested our approach with the ImageCLEF 2015 multi-label classification task, Pascal VOC and Flickr dataset.


ImageCLEF Kronecker decomposition Maximum margin MMR SVM Multi-label classification Medical images 



The research leading to these results has received funding from the EU seventh Framework Programme FP7/2007-2013 under grant agreement no. 270273, Xperience.


  1. 1.
    LeCun, Y., Bottou, L., Bengio, Y., Haffner, P.: Gradient-based learning applied to document recognition. Proc. IEEE 86(11), 2278–2324 (1998)CrossRefGoogle Scholar
  2. 2.
    Everingham, M., Eslami, S.A., Van Gool, L., Williams, C.K., Winn, J., Zisserman, A.: The pascal visual object classes challenge: a retrospective. Int. J. Comput. Vision 111(1), 98–136 (2014)CrossRefGoogle Scholar
  3. 3.
    Russakovsky, O., Deng, J., Su, H., Krause, J., Satheesh, S., Ma, S., Huang, Z., Karpathy, A., Khosla, A., Bernstein, M., Berg, A.C., Fei-Fei, L.: ImageNet large scale visual recognition challenge. Int. J. Comput. Vision 115(3), 211–252 (2015)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Villegas, M., et al.: General overview of ImageCLEF at the CLEF 2015 Labs. In: Mothe, J., Savoy, J., Kamps, J., Pinel-Sauvagnat, K., Jones, G., San Juan, E., Capellato, L., Ferro, N. (eds.) CLEF 2015. LNCS, vol. 9283, pp. 444–461. Springer, Heidelberg (2015). doi: 10.1007/978-3-319-24027-5_45 CrossRefGoogle Scholar
  5. 5.
    Seco, G., de Herrera, A., Müller, H., Bromuri, S.: Overview of the ImageCLEF 2015 medical classification task. In: Working Notes of CLEF 2015. CEUR Workshop Proceedings (2015).
  6. 6.
    Taskar, B., Guestrin, C., Koller, D.: Max-margin Markov networks. In: NIPS (2003)Google Scholar
  7. 7.
    Altun, Y., Tsochantaridis, I., Hofmann, T.: Hidden markov support vector machines. In: ICML 2003, pp. 3–10 (2003)Google Scholar
  8. 8.
    Tsochantaridis, I., Joachims, T., Hofmann, T., Altun, Y.: Large margin methods for structured and interdependent output variables. J. Mach. Learn. Res. (JMLR) 6, 1453–1484 (2005)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Rousu, J., Saunders, C., Szedmak, S., Shawe-Taylor, J.: Learning hierarchical multi-category text classification models. In: ICML (2005)Google Scholar
  10. 10.
    Bakir, G.H., Hofmann, T., Scholkopf, B., Smola, A.J., Taskar, B., Vishwanathan, S.V.N. (eds.): Predicting Structured Data. MIT Press, Cambridge (2007)Google Scholar
  11. 11.
    Loan, C.: The ubiquitous kronecker product. J. Comput. Appl. Math. 123, 85–100 (2000). The nearest Kronecker productMathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Everingham, M., Van Gool, L., Williams, C.K.I., Winn, J., Zisserman, A.: The PASCAL Visual Object Classes Challenge 2007 (VOC2007) Results (2007).
  13. 13.
    Huiskes, M.J., Lew, M.S.: The MIR flickr retrieval evaluation. In: MIR 2008: Proceedings of the 2008 ACM International Conference on Multimedia Information Retrieval. ACM, New York (2008)Google Scholar
  14. 14.
    Guillaumin, M., Mensink, T., Verbeek, J., Schmid, C.: Tagprop: Discriminative metric learning in nearest neighbor models for image auto-annotation. In: International Conference on Computer Vision, pp. 309–316, September 2009Google Scholar
  15. 15.
    INRIA: Inria features for image annotation and classification data sets.
  16. 16.
    Xiong, H., Szedmak, S., Piater, J.: Scalable, accurate image annotation with joint SVMs and output kernels. Neurocomputing 169, 205–214 (2015)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Sabrina Fontanella
    • 1
    • 2
  • Antonio J. Rodríguez-Sánchez
    • 1
  • Justus Piater
    • 1
  • Sandor Szedmak
    • 3
  1. 1.Intelligent and Interactive Systems, Department of Computer ScienceUniversity of InnsbruckInnsbruckAustria
  2. 2.Department of Computer ScienceUniversity of SalernoFiscianoItaly
  3. 3.Department of Computer ScienceAalto UniversityEspooFinland

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