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Manifold models provide low-dimensional representations that are useful for analyzing and classifying data in a transformation-invariant way. In this paper we study the problem of jointly building multiple pattern transformation manifolds from a collection ...
Many applications in machine learning require optimizing unknown functions defined over a high-dimensional space from noisy samples that are expensive to obtain. We address this notoriously hard challenge, under the assumptions that the function varies onl ...
We propose a compressive sensing algorithm that exploits geometric properties of images to recover images of high quality from few measurements. The image reconstruction is done by iterating the two following steps: 1) estimation of normal vectors of the i ...
Recovering the 3D shape of deformable surfaces from single images is known to be a highly ambiguous problem because many different shapes may have very similar projections. This is commonly addressed by restricting the set of possible shapes to linear comb ...
Institute of Electrical and Electronics Engineers2013
We study spectral properties of generalized weighted Hilbert matrices. In particular, we establish results on the spectral norm, the determinant, and various relations between the eigenvalues and eigenvectors of such matrices. We also study the asymptotic ...
Machine learning is most often cast as an optimization problem. Ideally, one expects a convex objective function to rely on efficient convex optimizers with nice guarantees such as no local optima. Yet, non-convexity is very frequent in practice and it may ...
Let X be a (not-necessarily homotopy-associative) H-space. We show that TCn+1(X) = cat(X-n), for n >= 1, where TCn+1(-) denotes the so-called higher topological complexity introduced by Rudyak, and cat(-) denotes the Lusternik-Schnirelmann category. We als ...
In this paper we consider the problem of recovering a high dimensional data matrix from a set of incomplete and noisy linear measurements. We introduce a new model that can efficiently restrict the degrees of freedom of the problem and is generic enough to ...
Institute of Electrical and Electronics Engineers2012
The set of solutions of a parameter-dependent linear partial differential equation with smooth coefficients typically forms a compact manifold in a Hilbert space. In this paper we review the generalized reduced basis method as a fast computational tool for ...
In this paper we consider recovery of a high dimensional data matrix from a set of incomplete and noisy linear measurements. We introduce a new model which can efficiently restricts the degrees of freedom of data and, at the same time, is generic so that f ...
