A Note on the Locally Linear Embedding Algorithm

نویسندگان

  • Wojciech Chojnacki
  • Michael J. Brooks
چکیده

The paper presents mathematical underpinnings of the locally linear embedding technique for data dimensionality reduction. It is shown that a cogent framework for describing the method is that of optimisation on a Grassmann manifold. The solution delivered by the algorithm is characterised as a constrained minimiser for a problem in which the cost function and all the constraints are defined on such a manifold. The role of the internal gauge symmetry in solving the underlying optimisation problem is illuminated.

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عنوان ژورنال:
  • IJPRAI

دوره 23  شماره 

صفحات  -

تاریخ انتشار 2009