Practical content-based image retrieval systems require efficient relevance feedback techniques. Researchers have proposed many relevance feedback methods using quadratic-form distance metric as similarity measure and learning similarity matrix from feedback samples by linear transform. Existing linear approaches do not deal with data distribution in real image database very well. In this paper...

A. In this article we exhibit the optimal (i.e. largest) constants for the quadratic isoperimetric and the linear filling radius inequality which ensure that a geodesic metric space X is Gromov hyperbolic. Our results show that the Euclidean plane is a borderline case for the isoperimetric inequality. Furthermore, by only requiring the existence of isoperimetric fillings in L∞(X) satisfy...

Similarity join is an interesting complement of the wellestablished similarity range and nearest neighbors search primitives in metric spaces. However, the quadratic computational complexity of similarity join prevents from applications on large data collections. We present MCAN, an extension of MCAN (a Content-Addressable Network for metric objects) to support similarity self join queries. The...

The close relationship between the theory of quadratic forms and distance analysis has been known for centuries, and the theory of metric spaces that formalizes distance analysis and was developed over the last century, has obvious strong relations to quadraticform theory. In contrast, the first paper that studied metric spaces as such – without trying to study their embeddability into any one ...

We consider perturbative solutions to the classical field equations coming from a quadratic gravitational lagrangian in four dimensions. We study the charged, spherically symmetric black hole and explicitly give corrections up to third order (in the coupling constant β multiplying the RμνR μν term) to the Reissner–Nordström hole metric. We consider the thermodynamics of such black holes, in par...

In order to effectively visualize the results of huge numerical simulations it is critical that the size of datasets be efficiently reduced to a manageable size. Various methods have been developed to address this problem by constructing sequences of tetrahedral meshes approximating scalar-valued functions. Several methods rely on iterative vertex insertion. For example, methods described by Ha...

We consider a modified form of gravity, which has an extra term quadratic in the Riemann tensor. This term mimics a Yang-Mills theory. The other defining characteristic of this gravity is having the affine connection independent of the metric. (The metricity of the metric is rejected, too, since it implies a Levi-Civita connection.) It is then shown that, in the low density limit, this modified...

In this paper, we address the metric learning problem utilizing a margin-based approach. Our metric learning problem is formulated as a quadratic semi-definite programming problem (QSDP) with local neighborhood constraints, which is based on the Support Vector Machine (SVM) framework. The local neighborhood constraints ensure that examples of the same class are separated from examples of differ...

The Newtonian limit of fourth-order gravity is worked out discussing its viability with respect to the standard results of General Relativity. We investigate the limit in the metric approach which, with respect to the Palatini formulation, has been much less studied in the recent literature, due to the higherorder of the field equations. In addition, we refrain from exploiting the formal equiva...

Introduction. In the present paper a new invariant quadratic differential form Û is geometrically defined for a general pair of surfaces S> S' whose corresponding points x, x' determine the metric normal to S a t x. The ratio of the form Q to the first fundamental form ds of 5, in which Î2 and ds are defined for a common arc element of S at x, is found to be independent of the direction of the ...