A duality view of spectral methods for dimensionality reduction

  title={A duality view of spectral methods for dimensionality reduction},
  author={Lin Xiao and Jun Sun and Stephen P. Boyd},
We present a unified duality view of several recently emerged spectral methods for nonlinear dimensionality reduction, including Isomap, locally linear embedding, Laplacian eigenmaps, and maximum variance unfolding. We discuss the duality theory for the maximum variance unfolding problem, and show that other methods are directly related to either its primal formulation or its dual formulation, or can be interpreted from the optimality conditions. This duality framework reveals close connections… CONTINUE READING
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