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This is a tutorial and survey paper on unification of spectral dimensionalityreduction methods, kernel learning by Semidefinite Programming (SDP), MaximumVariance Unfolding (MVU) or Semidefinite Embedding (SDE), and its variants. Wefirst explain how the spectral dimensionality reduction methods can be unifiedas kernel Principal Component Analysis (PCA) with different kernels. Thisunification can be interpreted as eigenfunction learning or representation ofkernel in terms of distance matrix. Then, since the spectral methods areunified as kernel PCA, we say let us learn the best kernel for unfolding themanifold of data to its maximum variance. We first briefly introduce kernellearning by SDP for the transduction task. Then, we explain MVU in detail.Various versions of supervised MVU using nearest neighbors graph, by class-wiseunfolding, by Fisher criterion, and by colored MVU are explained. We alsoexplain out-of-sample extension of MVU using eigenfunctions and kernel mapping.Finally, we introduce other variants of MVU including action respectingembedding, relaxed MVU, and landmark MVU for big data.

Unified Framework for Spectral Dimensionality Reduction, Maximum  Variance Unfolding, and Kernel Learning By Semidefinite Programming: Tutorial  and Survey