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The phenomena with within-strata characteristics that are more similar than between-strata characteristics are ubiquitous (e.g., land-use types and image classifications). It can be summarized as spatial stratified heterogeneity (SSH), which is measured and attributed using the geographical detector (Geodetector) q-statistic. SSH is typically calibrated by stratification and hundreds of algorithms have been developed. Little is discussed about the conditions of the methods. In this work, a novel stratification method based on head/tail breaks is introduced for the purpose of better capturing the SSH of geographical variables with a heavy-tailed distribution. Compared to conventional sample-based stratifications, the presented approach is a population-based optimized stratification that indicates an underlying scaling property in geographical spaces. It requires no prior knowledge or auxiliary variables and supports a naturally determined number of strata instead of being subjectively preset. In addition, our approach reveals the inherent hierarchical structure of geographical variables, characterizes its dominant components across all scales, and provides the potential to make the stratification meaningful and interpretable. The advantages were illustrated by several case studies in natural and social sciences. The proposed approach is versatile and flexible so that it can be applied for the stratification of both geographical and nongeographical variables and is conducive to advancing SSH-related studies as well. This study provides a new way of thinking for advocating spatial heterogeneity or scaling law and advances our understanding of geographical phenomena. [ABSTRACT FROM AUTHOR]

Estimation of quality of expert judgements and their suitability for reliable evaluation of decision alternatives is one of key issues for successful decision-making. The notions of strong and weak consistency are used to estimate the contradiction level of expert pairwise comparison matrix (PCM). Several methods are used to find the most inconsistent elements of a PCM. They may lead to different results, and there is a problem to find an element that has to be changed to increase the consistency level of a PCM. To solve this problem, a novel methodology for analysis of efficiency of methods for finding the most inconsistent elements of a PCM is proposed. An improved M_Outflow method for finding the most inconsistent element and a cycle in a PCM is established. Using computer modelling, it is shown that the proposed M_Outflow method is more efficient under accepted conditions in comparison with other considered methods. [ABSTRACT FROM AUTHOR]

SIPRI has collected data on military expenditure almost since its foundation in the 1960s, but various historical difficulties led to breaks in the consistency of the data series, so that until recently SIPRI’s consistent military expenditure database has only provided data from 1988 onwards. This paper describes recent efforts at SIPRI that have succeeded in extending these consistent series for most countries back to at least the 1960s, and in some cases to 1949. It describes the underlying difficulties involved in collecting military expenditure data and ensuring consistent series, the sources used in the reconstruction of the long data-set, the methodological choices made, and the results of the exercise. Overall, consistent constant price data series have been extended back as far as 1957 for half of the countries covered by the SIPRI database that existed at the time. Europe and the Americas generally have the best data coverage. One of the biggest problems with the extended data-set is the extensive use of estimates to splice together overlapping, but disagreeing series for the same country, adjusting the older series upwards or downwards by an appropriate ratio to give greater consistency with the later series. A number of case studies are investigated where parallel series exist for countries, suggesting that this approach may in some cases involve significant margins for error. [ABSTRACT FROM AUTHOR]

In this article, the frequency polygon studied by Scott (1985) is investigated as a nonparametric estimator for negatively associated samples. By the Bernstein type inequality, we give the uniformly strong consistency of the estimator and obtain the corresponding rate under some mild conditions. [ABSTRACT FROM PUBLISHER]

Preference relations are a powerful tool to address decision-making problems. In some situations, because of the complexity of decision-making problems and the inherent uncertainty, the decision makers cannot express their preferences by using numerical values. Interval linguistic preference relations, which are more reliable and informative for the decision-makers' preferences, are a good choice to cope with this issue. Just as with the other types of preference relations, the consistency and consensus analysis is very importance to ensure the reasonable ranking order by using interval linguistic preference relations. Considering this situation, this paper introduces a consistency concept for interval linguistic preference relations. To measure the consistency of interval linguistic preference relations, a consistency measure is defined. Then, a consistency-based programming model is built, by which the consistent linguistic preference relations with respect to each object can be obtained. To cope with the inconsistency case, two models for deriving the adjusted consistent linguistic preference relations are constructed. Then, a consistency-based programming model to estimate the missing values is built. After that, we present a group consensus index and present some of its desirable properties. Furthermore, a group consensus-based model to determine the weights of the decision makers with respect to each object is established. Finally, an approach to group decision making with interval linguistic preference relations is developed, which is based on the consistency and consensus analysis. Meanwhile, the associated numerical examples are offered to illustrate the application of the procedure. [ABSTRACT FROM AUTHOR]

Do truth tables—the ordinary sort that we use in teaching and explaining basic propositional logic—require an assumption ofconsistencyfor their construction? In this essay we show that truth tables can be built in a consistency-independent paraconsistent setting, without any appeal to classical logic. This is evidence for a more general claim—that when we write down the orthodox semantic clauses for a logic, whatever logic we presuppose in the background will be the logic that appears in the foreground. Rather than any one logic being privileged, then, on this count partisans across the logical spectrum are in relatively similar dialectical positions. [ABSTRACT FROM PUBLISHER]

We propose incorporating semantic topic information into a hierarchical conditional random fields (CRFs) framework to promote object recognition and retrieval accuracy. Specially, we devise convenient yet effective methods based on multiple segmentations to perform accurate image retrieval tasks for rigid and amorphous man-made objects. Through a robust topic consistency potential (RTCP) modelling approach, we perform accurate multi-class segmentation on high-resolution remote-sensing images. The generated segments can be readily used for object recognition and discovery. We report satisfactory the performance on two sets of high-resolution remote-sensing images that cover a highly populated urban area and a rural area, respectively. Experimental results demonstrate that our approach outperforms the state-of-the-art CRF models, due to its ability to capture inherent semantic information for efficient object recognition and boundary discovery. [ABSTRACT FROM AUTHOR]

In this paper, we provide some exponential inequalities for extended negatively dependent (END) random variables. By using these exponential inequalities and the truncated method, we investigate the complete consistency for the estimator of nonparametric regression model based on END errors. As an application, the complete consistency for the nearest neighbour estimator is obtained. [ABSTRACT FROM AUTHOR]

In a lot of practical machine learning applications, such as web page classification, protein shape classification, unlabelled instances are easy to obtain, but labelled instances are rather too expensive to get. Thus, recently, semi-supervised learning (SSL) methods including graph-based algorithms have attracted many interests from researchers. However, most of these algorithms used the Gaussian function to calculate weights of the edge of the graph. In this paper, we proposed a novel weight for graph-based semi-supervised algorithms. In this new algorithm, the label information is added from problem into SSL algorithm, and the geodesic distance is utilized instead of Euclidean distance to calculate the distance between two instances. Furthermore, class prior knowledge is also added from problem into the target function. In this paper, we focus on learning with local and global consistency. We found that the effect of class prior knowledge maybe different between under low-label rate and high-label rate. Experiments on two University of California Irvine (UCI) data sets and United States Postal Service handwritten digit recognition show that our proposed algorithm is really effective. [ABSTRACT FROM PUBLISHER]