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This report concerns the problem of dimensionality reduction through information geometric methods on statistical manifolds. While there has been considerable work recently presented regarding dimensionality reduction for the purposes of learning tasks such as classification, clustering, and visualization, these methods have focused primarily on Riemannian manifolds in Euclidean space. While sufficient for many applications, there are many high-dimensional signals which have no straightforward and meaningful Euclidean representation. In these cases, signals may be more appropriately represented as a realization of some distribution lying on a statistical manifold, or a manifold of probability density functions (PDFs). We present a framework for dimensionality reduction that uses information geometry for both statistical manifold reconstruction as well as dimensionality reduction in the data domain.
Existing dimensionality reduction methods are adept at revealing hidden underlying manifolds arising from high-dimensional data and thereby producing a low-dimensional representation. However, the smoothness of the manifolds produced by classic techn
Molecular dynamics (MD) simulations have been widely applied to study macromolecules including proteins. However, high-dimensionality of the datasets produced by simulations makes it difficult for thorough analysis, and further hinders a deeper under
Spectral dimensionality reduction methods enable linear separations of complex data with high-dimensional features in a reduced space. However, these methods do not always give the desired results due to irregularities or uncertainties of the data. T
Grassmann manifolds have been widely used to represent the geometry of feature spaces in a variety of problems in medical imaging and computer vision including but not limited to shape analysis, action recognition, subspace clustering and motion segm
This is a tutorial and survey paper on unification of spectral dimensionality reduction methods, kernel learning by Semidefinite Programming (SDP), Maximum Variance Unfolding (MVU) or Semidefinite Embedding (SDE), and its variants. We first explain h