Metric (mathematics)

About: Metric (mathematics) is a research topic. Over the lifetime, 42617 publications have been published within this topic receiving 836571 citations. The topic is also known as: distance function & metric.

Multiple single objective Pareto sampling

Abstract: We detail a new nonPareto evolutionary multiobjective algorithm, multiple single objective Pareto sampling (MSOPS), that performs a parallel search of multiple conventional target vector based optimisations, e.g. weighted min-max. The method can be used to generate the Pareto set and analyse problems with large numbers of objectives. The method allows bounds and discontinuities of the Pareto set to be identified and the shape of the surface to be analysed, despite not being able to visualise the surface easily. A new combination metric is also introduced that allows the shape of the objective surface that gives rise to discontinuities in the Pareto surface to be analysed easily.

Cyclomatic complexity density and software maintenance productivity

Abstract: A study of the relationship between the cyclomatic complexity metric (T. McCabe, 1976) and software maintenance productivity, given that a metric that measures complexity should prove to be a useful predictor of maintenance costs, is reported. The cyclomatic complexity metric is a measure of the maximum number of linearly independent circuits in a program control graph. The current research validates previously raised concerns about the metric on a new data set. However, a simple transformation of the metric is investigated whereby the cyclomatic complexity is divided by the size of the system in source statements. thereby determining a complexity density ratio. This complexity density ratio is demonstrated to be a useful predictor of software maintenance productivity on a small pilot sample of maintenance projects. >

The Hidden Geometry of Deformed Grids: Or, Why Space Syntax Works, When it Looks as Though it Shouldn't:

Abstract: A common objection to the space syntax analysis of cities is that even in its own terms the technique of using a nonuniform line representation of space and analysing it by measures that are essentially topological ignores too much geometric and metric detail to be credible. In this paper it is argued that far from ignoring geometric and metric properties the 'line graph' internalises them into its structure of the graph and in doing so allows the graph analysis to pick up the nonlocal, or extrinsic, properties of spaces that are critical to the movement dynamics through which a city evolves its essential structures. Nonlocal properties are those which are defined by the relation of elements to all others in the system, rather than those which are intrinsic to the element itself. The method also leads to a powerful anslysis of urban stuctures because cities are essentially nonlocal systems.

A new image quality metric for image fusion: The sum of the correlations of differences

Abstract: Measuring the quality of fused images is a very important stage for image fusion applications. The fused image must comprise maximum information from each of source images of the same scene taken by different sensors. Therefore, the amount of the information gathered in the fused images reflects the quality of them. This paper proposes a new quality metric by making use of this knowledge. The metric employed to compare the performance of different image fusion algorithms. In the experiments, subjective correspondence of the proposed metric and several well-known metrics are compared. Experimental results show the feasibility of the developed metric.

Local Multidimensional Scaling for Nonlinear Dimension Reduction, Graph Drawing, and Proximity Analysis

Abstract: In the past decade there has been a resurgence of interest in nonlinear dimension reduction. Among new proposals are “Local Linear Embedding,” “Isomap,” and Kernel Principal Components Analysis which all construct global low-dimensional embeddings from local affine or metric information. We introduce a competing method called “Local Multidimensional Scaling” (LMDS). Like LLE, Isomap, and KPCA, LMDS constructs its global embedding from local information, but it uses instead a combination of MDS and “force-directed” graph drawing. We apply the force paradigm to create localized versions of MDS stress functions with a tuning parameter to adjust the strength of nonlocal repulsive forces. We solve the problem of tuning parameter selection with a meta-criterion that measures how well the sets of K-nearest neighbors agree between the data and the embedding. Tuned LMDS seems to be able to outperform MDS, PCA, LLE, Isomap, and KPCA, as illustrated with two well-known image datasets. The meta-criterion can also be ...