Image recognition in client server system has a problem of data traffic. However, reducing data traffic gives rise to worsening of performance. Therefore, we represent binary codes as high dimensional local features in client side, and represent real vectors in server side. As a result, we can suppress the worsening of the performance, but it problems of an increase in the computational cost of...

Monge’s problem refers to the classical problem of optimally transporting mass: given Borel probability measures μ = μ− on R, find the measure preserving map s(x) between them which minimizes the average distance transported. Here distance can be induced by the Euclidean norm, or any other uniformly convex and smooth norm d(x, y) = ‖x− y‖ onR. Although the solution is never unique, we give a ge...

For iterative sequences that converge to the solution set of a linear matrix inequality, we show that the distance of the iterates to the solution set is at most O(2 ?d). The nonnegative integer d is the so{called degree of singularity of the linear matrix inequality, and denotes the amount of constraint violation in the iterate. For infeasible linear matrix inequalities, we show that the minim...

A precise positioning of transmitting nodes enhances the performance of Cognitive Radio (CR), by enabling more efficient dynamic allocation of channels and transmit powers for unlicensed users. Most localization techniques rely on random positioning of sensor nodes where, few sensor nodes may have a small separation between adjacent nodes. Closely spaced nodes introduces correlated observations...

A fuzzy classifier using multiple ellipsoids approximating decision regions for classification is to be designed in this paper. An algorithm called Gustafson-Kessel algorithm (GKA) with an adaptive distance norm based on covariance matrices of prototype data points is adopted to learn the ellipsoids. GKA is able to adapt the distance norm to the underlying distribution of the prototype data poi...

High-dimensional vectors are ubiquitous in algorithms and this lecture seeks to introduce some common properties of these vectors. We encounter the so-called curse of dimensionality which refers to the fact that algorithms are simply harder to design in high dimensions and often have a running time exponential in the dimension. We also show that it is possible to reduce the dimension of a datas...

Given a function f and weightsw on the vertices of a directed acyclic graphG, an isotonic regression of (f, w) is an order-preserving real-valued function that minimizes the weighted distance to f among all order-preserving functions. When the distance is given via the supremum norm there may be many isotonic regressions. One of special interest is the strict isotonic regression, which is the l...

introduce a multi-scale metric on a space equipped with a diffusion semigroup. We prove, under some technical conditions, that the norm dual to the space of Lipschitz functions with respect to this metric is equivalent to two other norms, one of which is a weighted sum of the averages at each scale, and one of which is a weighted sum of the difference of averages across scales. The notion of 's...

Let A belong to the Schatten-von Neumann ideal Sp for 0 < p < ∞. We give an upper bound for the operator norm of the resolvent (zI − A)−1 of A in terms of the departure from normality of A and the distance of z to the spectrum of A. As an application we provide an upper bound for the Hausdorff distance of the spectra of two operators belonging to Sp.

The approximation of road distances by the weighted lp distance measure has been studied in a series of papers ([5, 6], etc.) and it is argued with empirical study that lp distances weighted by an inflation factor tailored to given regions can better describe the irregularity in the transportation networks such as hill, bends, and are therefore superior to the weighted rectangular and Euclidean...