We consider feature selection and weighting for nearest neighbor classifiers. Atechnical challenge in this scenario is how to cope with discrete update of nearestneighbors when the feature space metric is changed during the learning process.This issue, called the target neighbor change, was not properly addressed in theexisting feature weighting and metric learning literature. I...

This paper develops information geometric representations for nonlinear filters in continuous time. The posterior distribution associated with an abstract nonlinear filtering problem is shown to satisfy a stochastic differential equation on a Hilbert information manifold. This supports the Fisher metric as a pseudo-Riemannian metric. Flows of Shannon information are shown to be connected with t...

Optical aberrations have detrimental effects in multiphoton microscopy. These effects can be curtailed by implementing model-based wavefront sensorless adaptive optics, which only requires the addition of a wavefront shaping device, such as a deformable mirror (DM) to an existing microscope. The aberration correction is achieved by maximizing a suitable image quality metric. We implement a mode...

Much natural language processing still depends on the Euclidean (cosine) distance function between two feature vectors, but this has severe problems with regard to feature weightings and feature correlations. To answer these problems, we propose an optimal metric distance that can be used as an alternative to the cosine distance, thus accommodating the two problems at the same time. This metric...

A gauge theory of quantum gravity is formulated, in which an internal, field dependent metric is introduced which non-linearly realizes the gauge fields on the non-compact group SL(2, C), while linearly realizing them on SU (2). Einstein's SL(2, C) invariant theory of gravity emerges at low energies, since the extra degrees of freedom associated with the quadratic curvature and the internal met...

Similarity retrieval is an important paradigm for searching in environments where exact match has little meaning. Moreover, in order to enlarge the set of data types for which the similarity search can efficiently be performed, the notion of mathematical metric space provides a useful abstraction for similarity. In this paper we consider the problem of organizing and searching large data-sets f...

Conformal invariant new forms of p-brane and Dp-brane actions are proposed. These are quadratic in ∂X for the p-brane case and for Dp-branes in the Abelian field strength. The fields content of these actions are: an induced metric, gauge fields, an auxiliary metric and an auxiliary scalar field. The proposed actions are Weyl invariant in any dimension and the elimination of the auxiliary metric...

Support Vector Machines, SVMs, and the Large Margin Nearest Neighbor algorithm, LMNN, are two very popular learning algorithms with quite different learning biases. In this paper we bring them into a unified view and show that they have a much stronger relation than what is commonly thought. We analyze SVMs from a metric learning perspective and cast them as a metric learning problem, a view wh...

Linear subspace has many important applications in computer vision, such as structure from motion, motion estimation, layer extraction, object recognition, and object tracking. Singular Value Decomposition (SVD) algorithm is a standard technique to compute the subspace from the input data. The SVD algorithm, however, is sensitive to outliers as it uses L2 norm metric, and it can not handle miss...

The integrability of the geodesic flow for the multi-centre metrics began with the discovery of the generalized Runge–Lenz vector for the Taub–NUT metric [1] and the derivation of its Killing–Stäckel tensor in [2]. It was generalized to the Eguchi–Hanson metric in [3] where the Hamilton–Jacobi equation was separated. A further progress led to the integrability proof of the full 2-centre metric ...