“…-Concerning the first point, the authors are currently working on a novel approach for data spread description by using the notion of the skeleton of a given shape. The skeleton of a shape can be defined as the set of ideal or theoretical points, belonging to the interior of a shape, that have the property to be nearest from the adherence of this shape [44][45][46][47]. Hence, for non-Gaussian data, the skeleton of the dataset can constitute a reliable geometrical feature to replace the centres of the clusters in the case of Gaussian and like-Gaussian datasets, -In higher dimensions, the initial speed rate is to be estimated as the derivative of the solid angle in n-space according to the displacement vector đ â norm so that Fig.…”
Kmeans is one of the most algorithms that are utilized in data analysis adopting a variety of different metrics; but kmeans was shown to be sensitive to sensitive to the initialization step. Hence, in this paper, a new Geometry-Inference based Clustering heuristic is proposed for selecting the optimal numbers of clusters for kmeans of in other terms, the algorithm initialization. The conceptual approach proposes the âInitial speed rateâ as the main geometric parameter to be statistically analysed. The distributions of this latter are then fitted using classical parametric probability distributions. The resulting fitted parameters show salient 2-stages linear behaviour according to the number of clusters within the kmeans process. Thus, the optimal number of clusters k* was assigned to the intersection of the 2 detected lines for all datasets adopted in this work. The benchmark analysis showed that the proposed heuristic is very competitive compared to other kmeans classical metrics.
“…-Concerning the first point, the authors are currently working on a novel approach for data spread description by using the notion of the skeleton of a given shape. The skeleton of a shape can be defined as the set of ideal or theoretical points, belonging to the interior of a shape, that have the property to be nearest from the adherence of this shape [44][45][46][47]. Hence, for non-Gaussian data, the skeleton of the dataset can constitute a reliable geometrical feature to replace the centres of the clusters in the case of Gaussian and like-Gaussian datasets, -In higher dimensions, the initial speed rate is to be estimated as the derivative of the solid angle in n-space according to the displacement vector đ â norm so that Fig.…”
Kmeans is one of the most algorithms that are utilized in data analysis adopting a variety of different metrics; but kmeans was shown to be sensitive to sensitive to the initialization step. Hence, in this paper, a new Geometry-Inference based Clustering heuristic is proposed for selecting the optimal numbers of clusters for kmeans of in other terms, the algorithm initialization. The conceptual approach proposes the âInitial speed rateâ as the main geometric parameter to be statistically analysed. The distributions of this latter are then fitted using classical parametric probability distributions. The resulting fitted parameters show salient 2-stages linear behaviour according to the number of clusters within the kmeans process. Thus, the optimal number of clusters k* was assigned to the intersection of the 2 detected lines for all datasets adopted in this work. The benchmark analysis showed that the proposed heuristic is very competitive compared to other kmeans classical metrics.
“…Fengcheng Liu [5] suggests an improved form optimization technique that considers the sensitivity to structural flaws. The result is a strong 714 FINITE ELEMENT MODELING AND CONVERGENCE ANALYSIS construction with a low tolerance to imperfections and improved buckling load capability, similarly to the "GE-SEZ" structure proposed by EL JAI et al [19]. These techniques are typically embedded in mechanical optimization loops that make use of genetic optimization algorithms and finite elements method for mechanical computations [2,6,7,8,9,10,11].…”
Branching structures are gaining popularity in the field of advanced structures and building design; they offer high performance in terms of strength and lightweight design, along with the flexibility and precision enabled by modern processing technologies like Additive Manufacturing. This paper provides a concise overview of a geometric design procedure for a novel ribbed class of structures which was previously developed by the authors as a biomimetic optimal Micro-architected dome. Hereinafter, linear lattice models are suggested to carry out structural calculations using the finite element method (FEM). The objective is to examine discretization thresholding and strain energy convergence criteria. Results show that convergence is reached for numbers of elements per leg, ranging from 2 to 6, depending on the geometrical configuration of the dome being studied. The strain energy balance also exposes the influence of each internal force on the total mechanical response of the structure, pinpointing bending moment and axial force as the main decisive factors. As a perspective, the study will focus on limit state design calculations and Analysis of how the local geometry influences the overall stability and strength of this new design.
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