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Transitive State Alignment for the Quantum Jensen-Shannon Kernel

  • Andrea Torsello
  • Andrea Gasparetto
  • Luca Rossi
  • Lu Bai
  • Edwin R. Hancock
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8621)

Abstract

Kernel methods provide a convenient way to apply a wide range of learning techniques to complex and structured data by shifting the representational problem from one of finding an embedding of the data to that of defining a positive semidefinite kernel. One problem with the most widely used kernels is that they neglect the locational information within the structures, resulting in less discrimination. Correspondence-based kernels, on the other hand, are in general more discriminating, at the cost of sacrificing positive-definiteness due to their inability to guarantee transitivity of the correspondences between multiple graphs. In this paper we generalize a recent structural kernel based on the Jensen-Shannon divergence between quantum walks over the structures by introducing a novel alignment step which rather than permuting the nodes of the structures, aligns the quantum states of their walks. This results in a novel kernel that maintains localization within the structures, but still guarantees positive definiteness. Experimental evaluation validates the effectiveness of the kernel for several structural classification tasks.

Keywords

Density Operator Quantum Walk State Alignment Graph Kernel Alignment Step 
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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Andrea Torsello
    • 1
  • Andrea Gasparetto
    • 1
  • Luca Rossi
    • 2
  • Lu Bai
    • 3
  • Edwin R. Hancock
    • 3
  1. 1.Università Ca’ Foscari VeneziaItaly
  2. 2.University of BirminghamUK
  3. 3.University of YorkUK

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