In a flurry of articles in the mid to late 1990s, various metrics for the group of rigid-body motions, SE(3), were introduced for measuring distance between any two reference frames or rigid-body motions. During this time, it was shown that one can choose a smooth distance function that is invariant under either all left shifts or all right shifts, but not both. For example, if one defines the ...

Abstract Full waveform inversion is a methodology that determines high-resolution parameters. The widely used L2-norm misfit function has local minima if the low wavenumber components are not accurate. Suffering from cycle skipping problem, solution of will be trapped in minima. Dynamic time warping aims to find an optimal alignment between two signals, which more robust measure avoid cycle-ski...

In this paper, we propose a Lasso based framework to generate the sparse total variability supervectors (s-vectors). Rather than the factor analysis framework, which uses a low dimensional Eigenvoice subspace to represent the mean supervector, the proposed Lasso approach utilizes the l norm regularized least square estimation to project the mean supervector on a pre-defined dictionary. The numb...

We consider two different theoretical approaches for the problem of the perturbation of invariant subspaces. The first approach belongs to the standard theory. In that approach the bounds for the norm of the perturbation of the projector are proportional to the norm of perturbation matrix, and inversely proportional to the distance between the corresponding eigenvalues and the rest of the spect...

We study the asymptotic behavior of the diameter or maximum interpoint distance of a cloud of i.i.d. d-dimensional random vectors when the number of points in the cloud tends to infinity. This is a non standard extreme value problem since the diameter is a max U -statistic, hence the maximum of dependent random variables. Therefore, the limiting distributions may not be extreme value distributi...

This paper addresses the regularization by sparsity constraints by means of weighted lp penalties for 0 ≤ p ≤ 2. For 1 ≤ p ≤ 2 special attention is payed to convergence rates in norm and to source conditions. As main results it is proven that one gets a convergence rate of √ δ in the 2-norm for 1 < p ≤ 2 and in the 1-norm for p = 1 as soon as the unknown solution is sparse. The case p = 1 needs...

The method of stable random projections [39, 41] is popular for data streaming computations, data mining, and machine learning. For example, in data streaming, stable random projections offer a unified, efficient, and elegant methodology for approximating the lα norm of a single data stream, or the lα distance between a pair of streams, for any 0 < α ≤ 2. [18] and [20] applied stable random pro...

There is a natural norm associated with a starting point of the homogeneous selfdual (HSD) embedding model for conic convex optimization. In this norm two measures of the HSD model’s behavior are precisely controlled independent of the problem instance: (i) the sizes of ε-optimal solutions, and (ii) the maximum distance of ε-optimal solutions to the boundary of the cone of the HSD variables. Th...

In this paper, the effects of feature selection and feature normalization to the performance of a local appearance based face recognition scheme are presented. From the local features that are extracted using block-based discrete cosine transform, three feature sets are derived. These local feature vectors are normalized in two different ways; by making them unit norm and by dividing each coeff...

In this paper, we obtain a generalized version of the wellknown distance function family Lp norm. We prove that the new functions satisfy distance function properties. By using these functions, convex symmetric shapes can be described as loci, the set of points which are in equal distance from a given point. We also show that these symmetric convex shapes can be easily parameterized. We also sh...