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It is known that for a convex body K in R-d of volume one, the expected volume of random simplices in K is minimized if K is an ellipsoid, and for d = 2, maximized if K is a triangle. Here we provide corresponding stability estimates. ...
We revisit the problem of extending the notion of principal component analysis (PCA) to multivariate datasets that satisfy nonlinear constraints, therefore lying on Riemannian manifolds. Our aim is to determine curves on the manifold that retain their cano ...
We consider total variation (TV) minimization for manifold-valued data. We propose a cyclic proximal point algorithm and a parallel proximal point algorithm to minimize TV functionals with l(p) -type data terms in the manifold case. These algorithms are ba ...
In this paper, we consider the problem of manifold approximation with affine subspaces. Our objective is to discover a set of low dimensional affine subspaces that represent manifold data accurately while preserving the manifold's structure. For this purpo ...
In the context of robotic control, synergies can form an elementary unit of behavior. By specifying task-dependent coordination behaviors at a low control level, one can achieve task-specific disturbance rejection. In this work we present an approach to le ...
This paper presents a new framework for manifold learning based on a sequence of principal polynomials that capture the possibly nonlinear nature of the data. The proposed Principal Polynomial Analysis (PPA) generalizes PCA by modeling the directions of ma ...
With growing concern about process variation in deeply nano-scaled technologies, parameterized device and circuit modeling is becoming very important for design and verification. However, the high dimensionality of parameter space is a serious modeling cha ...
Numerous dimensionality reduction problems in data analysis involve the recovery of low-dimensional models or the learning of manifolds underlying sets of data. Many manifold learning methods require the estimation of the tangent space of the manifold at a ...
In this paper, the differential geometry of the novel hierarchical Tucker format for tensors is derived. The set HT,k of tensors with fixed tree T and hierarchical rank k is shown to be a smooth quotient manifold, namely the set of orbits of a Lie group ac ...