Basic statistics for probabilistic symbolic variables: a novel metric-based approach

In data mining, it is usually to describe a set of individuals using some summaries (means, standard deviations, histograms, confidence intervals) that generalize individual descriptions into a typology description. In this case, data can be described by several values. In this paper, we propose an approach for computing basic statics for such data, and, in particular, for data described by numerical multi-valued variables (interval, histograms, discrete multi-valued descriptions). We propose to treat all numerical multi-valued variables as distributional data, i.e. as individuals described by distributions. To obtain new basic statistics for measuring the variability and the association between such variables, we extend the classic measure of inertia, calculated with the Euclidean distance, using the squared Wasserstein distance defined between probability measures. The distance is a generalization of the Wasserstein distance, that is a distance between quantile functions of two distributions. Some properties of such a distance are shown. Among them, we prove the Huygens theorem of decomposition of the inertia. We show the use of the Wasserstein distance and of the basic statistics presenting a k-means like clustering algorithm, for the clustering of a set of data described by modal numerical variables (distributional variables), on a real data set. Keywords: Wasserstein distance, inertia, dependence, distributional data, modal variables.Comment: 19 pages, 3 figure

Using the Bootstrap Method for a Statistical Significance Test of Differences between Summary Histograms

A new method is proposed to compare statistical differences between summary histograms, which are the histograms summed over a large ensemble of individual histograms. It consists of choosing a distance statistic for measuring the difference between summary histograms and using a bootstrap procedure to calculate the statistical significance level. Bootstrapping is an approach to statistical inference that makes few assumptions about the underlying probability distribution that describes the data. Three distance statistics are compared in this study. They are the Euclidean distance, the Jeffries-Matusita distance and the Kuiper distance. The data used in testing the bootstrap method are satellite measurements of cloud systems called cloud objects. Each cloud object is defined as a contiguous region/patch composed of individual footprints or fields of view. A histogram of measured values over footprints is generated for each parameter of each cloud object and then summary histograms are accumulated over all individual histograms in a given cloud-object size category. The results of statistical hypothesis tests using all three distances as test statistics are generally similar, indicating the validity of the proposed method. The Euclidean distance is determined to be most suitable after comparing the statistical tests of several parameters with distinct probability distributions among three cloud-object size categories. Impacts on the statistical significance levels resulting from differences in the total lengths of satellite footprint data between two size categories are also discussed

Accurate Distances Measures and Machine Learning of the Texture-Property Relation for Crystallographic Textures Represented by One-Point Statistics

The crystallographic texture of metallic materials is a key microstructural feature that is responsible for the anisotropic behavior, e.g., important in forming operations. In materials science, crystallographic texture is commonly described by the orientation distribution function, which is defined as the probability density function of the orientations of the monocrystal grains conforming a polycrystalline material. For representing the orientation distribution function, there are several approaches such as using generalized spherical harmonics, orientation histograms, and pole figure images . Measuring distances between crystallographic textures is essential for any task that requires assessing texture similarities, e.g. to guide forming processes. Therefore, we introduce novel distance measures based on (i) the Earth Movers Distance that takes into account local distance information encoded in histogram-based texture representations and (ii) a distance measure based on pole figure images. For this purpose, we evaluate and compare existing distance measures for selected use-cases. The present study gives insights into advantages and drawbacks of using certain texture representations and distance measures with emphasis on applications in materials design and optimal process control

Transition from tunneling to direct contact in tungsten nanojunctions

We apply the mechanically controllable break junctions technique to investigate the transition from tunneling to direct contact in tungsten. This transition is quite different from that of other metals and is determined by the local electronic properties of the tungsten surface and the relief of the electrodes at the point of their closest proximity. The conductance traces show a rich variety of patterns from the avalanche-like jump to a mesoscopic contact to the completely smooth transition between direct contact and tunneling. Due to the occasional absence of an adhesive jump the conductance of the contact can be continuously monitored at ultra-small electrode separations. The conductance histograms of tungsten are either featureless or show two distinct peaks related to the sequential opening of spatially separated groups of conductance channels. The role of surface states of tungsten and their contribution to the junction conductance at sub-Angstrom electrode separations are discussed.Comment: 6 pages, 6 figure

Formation and properties of metal-oxygen atomic chains

Suspended chains consisting of single noble metal and oxygen atoms have been formed. We provide evidence that oxygen can react with and be incorporated into metallic one-dimensional atomic chains. Oxygen incorporation reinforces the linear bonds in the chain, which facilitates the creation of longer atomic chains. The mechanical and electrical properties of these diatomic chains have been investigated by determining local vibration modes of the chain and by measuring the dependence of the average chain-conductance on the length of the chain. Additionally, we have performed calculations that give insight in the physical mechanism of the oxygen-induced strengthening of the linear bonds and the conductance of the metal-oxygen chains.Comment: 10 pages, 9 fig

Analyzing Citation-Distance Networks for Evaluating Publication Impact

Studying citation patterns of scholarly articles has been of interest to many researchers from various disciplines. While the relationship of citations and scientific impact has been widely studied in the literature, in this paper we develop the idea of analyzing the semantic distance of scholarly articles in a citation network (citation-distance network) to uncover patterns that reflect scientific impact. More specifically, we compare two types of publications in terms of their citation-distance patterns, seminal publications and literature reviews, and focus on their referencing patterns as well as on publications which cite them. We show that seminal publications are associated with a larger semantic distance, measured using the content of the articles, between their references and the citing publications, while literature reviews tend to cite publications from a wider range of topics. Our motivation is to understand and utilize this information to create new research evaluation metrics which would better reflect scientific impact