Learning from patches by efficient spectral decomposition of a structured kernel

Moshe Salhov*, Amit Bermanis, Guy Wolf, Amir Averbuch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We present a kernel based method that learns from a small neighborhoods (patches) of multidimensional data points. This method is based on spectral decomposition of a large structured kernel accompanied by an out-of-sample extension method. In many cases, the performance of a spectral based learning mechanism is limited due to the use of a distance metric among the multidimensional data points in the kernel construction. Recently, different distance metrics have been proposed that are based on a spectral decomposition of an appropriate kernel prior to the application of learning mechanisms. The diffusion distance metric is a typical example where a distance metric is computed by incorporating the relation of a single measurement to the entire input dataset. A method, which is called patch-to-tensor embedding (PTE), generalizes the diffusion distance metric that incorporates matrix similarity relations into the kernel construction that replaces its scalar entries with matrices. The use of multidimensional similarities in PTE based spectral decomposition results in a bigger kernel that significantly increases its computational complexity. In this paper, we propose an efficient dictionary construction that approximates the oversized PTE kernel and its associated spectral decomposition. It is supplemented by providing an out-of-sample extension for vector fields. Furthermore, the approximation error is analyzed and the advantages of the proposed dictionary construction are demonstrated on several image processing tasks.

Original languageEnglish
Pages (from-to)81-102
Number of pages22
JournalMachine Learning
Issue number1
StatePublished - 1 Apr 2016


  • Diffusion maps
  • High-dimensional data analysis
  • Kernel method
  • Manifold learning
  • Non-scalar similarity
  • Out of sample extension
  • Vector field interpolation


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