Learning a kernel matrix for nonlinear dimensionality reduction

  title={Learning a kernel matrix for nonlinear dimensionality reduction},
  author={Kilian Q. Weinberger and Fei Sha and Lawrence K. Saul},
We investigate how to learn a kernel matrix for high dimensional data that lies on or near a low dimensional manifold. Noting that the kernel matrix implicitly maps the data into a nonlinear feature space, we show how to discover a mapping that "unfolds" the underlying manifold from which the data was sampled. The kernel matrix is constructed by maximizing the variance in feature space subject to local constraints that preserve the angles and distances between nearest neighbors. The main… CONTINUE READING
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