An insertion heuristic for the traveling salesman problem adds cities iteratively to an existing tour by replacing one edge with a two-edge path through the new city in the cheapest possible way. Rosenkrantz, Stearns, and Lewis asked whether every order of inserting vertices gives a constant-factor approximation algorithm. We answer this question by showing that for some point sets, there is an...

This paper presents an improved version of anchor model applied to solve the two-class classification tasks of the INTERSPEECH 2012 speaker trait Challenge. To build the anchor model space of each task, we include the class models of all tasks. The introduction of within-class covariance normalization (WCCN) applied to the log-likelihood scores of the anchor space not only improves the results ...

Rips complexes are important structures for analyzing topological features of metric spaces. Unfortunately, generating these complexes constitutes an expensive task because of a combinatorial explosion in the complex size. For n points in R, we present a scheme to construct a 3 √ 2approximation of the multi-scale filtration of the L∞-Rips complex, which extends to a O(d0.25)approximation of the...

We consider the problem of embedding a certain finite metric space to the Euclidean space, trying to keep the bi-Lipschitz constant as small as possible. We introduce the notation c2 (X, d) for the least distortion with which the metric space (X, d) may be embedded in a Euclidean space. It is known that if (X,d) is a metric space with n points, then c2(X,d) 0(logn) and the bound is tight. Let T...

We consider approximate nearest neighbor searching in metric spaces of constant doubling dimension. More formally, we are given a set S of n points and an error bound ε > 0. The objective is to build a data structure so that given any query point q in the space, it is possible to efficiently determine a point of S whose distance from q is within a factor of (1 + ε) of the distance between q and...

This paper investigates the problem of image segmentation using superpixels. We propose two approaches to enhance the discriminative ability of the superpixel’s covariance descriptors. In the first one, we employ the Log-Euclidean distance as the metric on the covariance manifolds, and then use the RBF kernel to measure the similarities between covariance descriptors. The second method is focus...

The James-Stein estimator is an of the multivariate normal mean and dominates maximum likelihood (MLE) under squared error loss. original work inspired great interest in developing shrinkage estimators for a variety problems. Nonetheless, research on estimation manifold-valued data scarce. In this paper, we propose parameters Log-Normal distribution defined manifold $N \times N$ symmetric posit...

We study the topology of metric spaces which are definable in o-minimal expansions of ordered fields. We show that a definable metric space either contains an infinite definable discrete set or is definably homeomorphic to a definable set equipped with its euclidean topology. This implies that a separable metric space which is definable in an o-minimal expansion of the real field is definably h...

We provide an efficient reduction from the problem of querying approximate multiplicatively weighted farthest neighbors in a metric space to the unweighted problem. Combining our techniques with core-sets for approximate unweighted farthest neighbors, we show how to find (1+ ε)-approximate farthest neighbors in time O(logn) per query in D-dimensional Euclidean space for any constants D and ε. A...

Objectives. An analysis of the problem evaluating alternatives based on results expert paired comparisons is presented. The importance and relevance this task due to its numerous applications in a variety fields, whether technical natural sciences or humanities, ranging from construction politics. In such contexts, frequently arises concerning how calculate an objective ratings vector evaluatio...