Riemannian metric and geometric mean for positive semidefinite matrices of fixed rank

This paper introduces a new metric and mean on the set of positive semidefinite matrices of fixed-rank. The proposed metric is derived from a well-chosen Riemannian quotient geometry that generalizes the reductive geometry of the positive cone and the associated natural metric. The resulting Riemannian space has strong geometrical properties: it is geodesically complete, and the metric is invariant with respect to all transformations that preserve angles (orthogonal transformations, scalings, and pseudoinversion). A meaningful approximation of the associated Riemannian distance is proposed, that can be efficiently numerically computed via a simple algorithm based on SVD. The induced mean preserves the rank, possesses the most desirable characteristics of a geometric mean, and is easy to compute. © 2009 Society for Industrial and Applied Mathematics.

the trustworthiness metric model of software process quality based-on life circle

Communication University of China; Wuhan University; James Madison University; Institute of Policy and Management, Chinese Academy of Sciences; IEEE Wuhan Section

A Video Quality Assessment Metric Based on Human Visual System

It is important for practical application to design an effective and efficient metric for video quality. The most reliable way is by subjective evaluation. Thus, to design an objective metric by simulating human visual system (HVS) is quite reasonable and available. In this paper, the video quality assessment metric based on visual perception is proposed. Three-dimensional wavelet is utilized to decompose video and then extract features to mimic the multichannel structure of HVS. Spatio-temporal contrast sensitivity function (S-T CSF) is employed to weight coefficient obtained by three-dimensional wavelet to simulate nonlinearity feature of the human eyes. Perceptual threshold is exploited to obtain visual sensitive coefficients after S-T CSF filtered. Visual sensitive coefficients are normalized representation and then visual sensitive errors are calculated between reference and distorted video. Finally, temporal perceptual mechanism is applied to count values of video quality for reducing computational cost. Experimental results prove the proposed method outperforms the most existing methods and is comparable to LHS and PVQM.

Distance Metric Between 3D Models and 3D Images for Recognition and Classification

Similarity measurements between 3D objects and 2D images are useful for the tasks of object recognition and classification. We distinguish between two types of similarity metrics: metrics computed in image-space (image metrics) and metrics computed in transformation-space (transformation metrics). Existing methods typically use image and the nearest view of the object. Example for such a measure is the Euclidean distance between feature points in the image and corresponding points in the nearest view. (Computing this measure is equivalent to solving the exterior orientation calibration problem.) In this paper we introduce a different type of metrics: transformation metrics. These metrics penalize for the deformatoins applied to the object to produce the observed image. We present a transformation metric that optimally penalizes for "affine deformations" under weak-perspective. A closed-form solution, together with the nearest view according to this metric, are derived. The metric is shown to be equivalent to the Euclidean image metric, in the sense that they bound each other from both above and below. For Euclidean image metric we offier a sub-optimal closed-form solution and an iterative scheme to compute the exact solution.

Trajectory Mapping ("TM''): A New Non-Metric Scaling Technique

Trajectory Mapping "TM'' is a new scaling technique designed to recover the parameterizations, axes, and paths used to traverse a feature space. Unlike Multidimensional Scaling (MDS), there is no assumption that the space is homogenous or metric. Although some metric ordering information is obtained with TM, the main output is the feature parameterizations that partition the given domain of object samples into different categories. Following an introductory example, the technique is further illustrated using first a set of colors and then a collection of textures taken from Brodatz (1966).

Inference and Labeling of Metric-Induced Network Topologies

The development and deployment of distributed network-aware applications and services over the Internet require the ability to compile and maintain a model of the underlying network resources with respect to (one or more) characteristic properties of interest. To be manageable, such models must be compact, and must enable a representation of properties along temporal, spatial, and measurement resolution dimensions. In this paper, we propose a general framework for the construction of such metric-induced models using end-to-end measurements. We instantiate our approach using one such property, packet loss rates, and present an analytical framework for the characterization of Internet loss topologies. From the perspective of a server the loss topology is a logical tree rooted at the server with clients at its leaves, in which edges represent lossy paths between a pair of internal network nodes. We show how end-to-end unicast packet probing techniques could b e used to (1) infer a loss topology and (2) identify the loss rates of links in an existing loss topology. Correct, efficient inference of loss topology information enables new techniques for aggregate congestion control, QoS admission control, connection scheduling and mirror site selection. We report on simulation, implementation, and Internet deployment results that show the effectiveness of our approach and its robustness in terms of its accuracy and convergence over a wide range of network conditions.

Dense spectrum of resonances and particle capture in a near-black-hole metric

We show that a quantum scalar particle in the gravitational field of a massive body of radius R which slightly exceeds the Schwarzschild radius rs, possesses a dense spectrum of narrow resonances. Their lifetimes and density tend to infinity in the limit R?rs. We determine the cross section of the particle capture into these resonances and show that it is equal to the absorption cross section for a Schwarzschild black hole. Thus, a nonsingular static metric acquires black-hole properties before the actual formation of a black hole.

Impact of Metric Selection on Wireless DeAuthentication DoS Attack Performance

DeAuthentication Denial of Service attacks in Public Access WiFi operate by exploiting the lack of authentication of management frames in the 802.11 protocol. Detection of these attacks rely almost exclusively on the selection of appropriate thresholds. In this work the authors demonstrate that there are additional, previously unconsidered, metrics which also influence DoS detection performance. A method of systematically tuning these metrics to optimal values is proposed which ensures that parameter choices are repeatable and verifiable.