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Use of several non-Euclidean metrics to compute distances between every two points in a plane bounded convex set
Get PDFWe consider movements between two chosen points in a plane-bounded set. The length of the movement between two points is measured by the Euclidean metric. We can then obtain the distribution of distances regarding the bounded set by repeatedly measuring the lengths of the movements. When we select two points uniformly in a bounded set, the shape of the bounded set affects the distribution. The distribution is easily computable by integral approximation and usefully remains invariant under the group of congruence transformations on the bounded set. For these reasons, some fundamental methods based on this distribution have been used in shape analysis. Thus, this distribution is important to some practical methods based on the Euclidean metric. Although some articles have been devoted to the study of non-Euclidean metrics in pattern recognition including shape analysis, only a few attempts have so far been made using the distribution of such non-Euclidean metrics. In this paper, we present the expression for the distributions with several non-Euclidean metrics using a density for the set of lines. This expression can be efficiently calculated as a sum of distributions, by generating a finite set of lines. We concentrate on a bounded convex set in the plane to define a non-Euclidean metric. In examples of such metrics on the convex set, we discuss those well-known in taxicab and projective geometries. In the experimental results using several convex sets, we visualize the distributions with the non-Euclidean metrics by plotting their graphs. Comparing the distribution based on the Euclidean metric with those based on the non-Euclidean metrics, we reveal several differences among the distributions.This work was supported by JSPS, Japan KAKENHI [grant number 22K12171]
People’s Self-determination Transformed into National Self-determination: Trajectory of the Resurgence of Pacifism in the Protection of National Minorities (Research Article)
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Enola Gay's Flight Path and Initial Point of Bomb Run: Fact-Checking and Verifications 80 Years after the Atomic Bombing of Hiroshima.
Get PDFCombining Human Resource Development and Career Design Courses: Practical Research using Theory-based Methodology
Get PDF本論文は、人材育成が円滑に進むための理論と方法論を適用している事例について述べる実践研究である。問「人材育成が円滑に進むためには、理論と方法論において何が必要か? 」に対する方向性として、普遍性のある理論「AW Cycle: Accumulate-Wield Cycle」と方法論「5つの方法の循環」を見出している。最後に、実際にAW Cycleと5つの方法の循環を適用しているキャリアデザイン科目「キャリアデザインⅱ」における内容について記述している。This practical study describes cases where theories and methodologies are applied to ensure smooth human resource development. In response to clarifying the necessary aspects in terms of theory and methodology, this study identified the universal theory “AW Cycle: AccumulateWield Cycle” and the methodology “Circulation of Five Methods”. AW Cycle consists of two cycles: "ability to accumulate" and "ability to wield." Circulation of five methods consists of 1) task skill list, 2) keywords, 3) case studies, 4) simulated training, and 5) collaboration with veteran. Finally, the paper describes the contents of “Career Design ⅱ,” a career design subject, which applies the AW Cycle and the Circulation of Five Methods in practice
Restructuring of Regional Order by Non-Western Countries in Eurasia: Focusing on the Role of the Shanghai Cooperation Organization (Research Article)
Get PDFMaking clustering methods workable for shapes using the ordinary Procrustes sum of squares
Get PDFIn the last few decades, a number of clustering methods for vectorial data have matured. Occasionally, researchers are interested in making them workable for data of other types, such as an object’s shape. The current difficulty in applying them to shape clustering is that clustering must be invariant to several similarity transformations of shapes. Therefore, we use the ordinary Procrustes sum of squares (OSS) in Procrustes analysis, which refers to analysis that is invariant to the similarity transformations between shapes. Thus, in this study, we aim to make mature methods workable in shape clustering. To achieve this, the essential points that we need to address are to rewrite the optimization problem associated with each method and to present a feasible method for computing the solution to the problem. As a result, we base the method on the OSS, its derivative, or a symmetric matrix concerning the OSS. Another aim of this study is to identify specific applications of shape clustering. We demonstrate the applications through experiments using datasets that contain skewed line drawings, American football formations, and baseball pitch trajectories. We examine the OSS-based methods by considering shape classification and determining the best method for implementing the OSS. As a result, regardless of the dataset, we demonstrate that the OSS in every method is more effective than other shape distances and that the convex clustering method incorporating the OSS is best performed in several ways
