Relevant bibliographies by topics / Euclidean distance degree

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Euclidean distance degree'

Author: Grafiati
Published: 10 March 2023

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Journal articles on the topic "Euclidean distance degree"

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Maxim, Laurentiu G., Jose Israel Rodriguez, and Botong Wang. "Defect of Euclidean distance degree." Advances in Applied Mathematics 121 (October 2020): 102101. http://dx.doi.org/10.1016/j.aam.2020.102101.

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Lee, Hwangrae. "The Euclidean distance degree of Fermat hypersurfaces." Journal of Symbolic Computation 80 (May 2017): 502–10. http://dx.doi.org/10.1016/j.jsc.2016.07.006.

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Maxim, Laurentiu G., Jose I. Rodriguez, and Botong Wang. "Euclidean Distance Degree of the Multiview Variety." SIAM Journal on Applied Algebra and Geometry 4, no. 1 (January 2020): 28–48. http://dx.doi.org/10.1137/18m1233406.

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Draisma, Jan, Emil Horobeţ, Giorgio Ottaviani, Bernd Sturmfels, and Rekha R. Thomas. "The Euclidean Distance Degree of an Algebraic Variety." Foundations of Computational Mathematics 16, no. 1 (January 6, 2015): 99–149. http://dx.doi.org/10.1007/s10208-014-9240-x.

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Pham, Thu-Thuy. "Euclidean distance degree of zero-set of two polynomials." Tạp chí Khoa học - Trường Đại học Sư phạm Hà Nội 2 1, no. 2 (December 28, 2022): 68–75. http://dx.doi.org/10.56764/hpu2.jos.2022.1.2.68-75.

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In this note, we recall the study of the Euclidean distance degree of an algebraic set X which is the zero-point set of a polynomial (see [BSW]). Specifically, consider a hypersurface defined by a general polynomial f with its support and contains the origin i.e 0 support of f. In the paper [BSW], the authors study about the Euclidean distance degree (EDD) and found that the EDD of this hypersurface is approximately by the mixed volume (MV) of some Newton polytopes. The main purpose of this note is to study the case that the manifold is defined by two polynomials . We show that the Euclidean distance degree is equal to the solution of the Lagrange multiplier equation. Furthermore, we also find out that the EDD of this variety is not greater than the mixed volume of Newton polytopes of the associated Lagrange multiplier equations.
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Aluffi, Paolo, and Corey Harris. "The Euclidean distance degree of smooth complex projective varieties." Algebra & Number Theory 12, no. 8 (December 4, 2018): 2005–32. http://dx.doi.org/10.2140/ant.2018.12.2005.

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Drusvyatskiy, Dmitriy, Hon-Leung Lee, Giorgio Ottaviani, and Rekha R. Thomas. "The euclidean distance degree of orthogonally invariant matrix varieties." Israel Journal of Mathematics 221, no. 1 (July 11, 2017): 291–316. http://dx.doi.org/10.1007/s11856-017-1545-4.

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DAS, GAUTAM, and PAUL J. HEFFERNAN. "CONSTRUCTING DEGREE-3 SPANNERS WITH OTHER SPARSENESS PROPERTIES." International Journal of Foundations of Computer Science 07, no. 02 (June 1996): 121–35. http://dx.doi.org/10.1142/s0129054196000105.

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Let V be any set of n points in k-dimensional Euclidean space. A subgraph of the complete Euclidean graph is a t-spanner if for all u and υ in V, the length of the shortest path from u to υ in the spanner is at most t times the Euclidean distance between u and υ. We show that for any δ>1, there exists a t-spanner (where t is a constant that depends only on δ and k) with the following properties: its maximum degree is 3, it has at most n·δ edges, its total edge weight is at most O(1) times the weight of the minimum spanning tree of V, and it can be constructed in O(n log n) time. The constants implicit in the O-notation depend on δ and k.
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Zou, Yan, Weijie Chen, Mingyu Tong, and Shuo Tao. "DEA Cross-Efficiency Aggregation with Deviation Degree Based on Standardized Euclidean Distance." Mathematical Problems in Engineering 2021 (March 10, 2021): 1–10. http://dx.doi.org/10.1155/2021/6682499.

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Data envelopment analysis (DEA) has been extended to cross-efficiency to provide better discrimination and ranking of decision-making units (DMUs). Current researches about cross-efficiency mainly focus on the non-uniqueness of optimal solution of linear programming and information aggregation. As a common distance metric, standardized Euclidean distance is introduced to define the discrimination power between two vectors and the deviation degree for measuring the difference between the individual preference and group ideal preference. Based on above definitions, an alternative method is presented to compare multiple optimal solutions, and further, a universal weighted cross-efficiency model considering both dynamic adjustment of weights and preference formulation is constructed for evaluation and ranking. Two numerical examples are given to illustrate the effectiveness of the comparison method for multiple optimal solutions and weights determination method of DMUs, respectively. At last, a practical application aimed at evaluating environmental treatment efficiency in western area of China is given. Comparative analysis shows that our model could be more moderate, flexible, and general than some available models and methods, which can extend the theoretical research of cross-efficiency evaluation.
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Remais, Justin, Adam Akullian, Lu Ding, and Edmund Seto. "Analytical methods for quantifying environmental connectivity for the control and surveillance of infectious disease spread." Journal of The Royal Society Interface 7, no. 49 (February 17, 2010): 1181–93. http://dx.doi.org/10.1098/rsif.2009.0523.

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The sustained transmission and spread of environmentally mediated infectious diseases is governed in part by the dispersal of parasites, disease vectors and intermediate hosts between sites of transmission. Functional geospatial models can be used to quantify and predict the degree to which environmental features facilitate or limit connectivity between target populations, yet typical models are limited in their geographical and analytical approach, providing simplistic, global measures of connectivity and lacking methods to assess the epidemiological implications of fine-scale heterogeneous landscapes. Here, functional spatial models are applied to problems of surveillance and control of the parasitic blood fluke Schistosoma japonicum and its intermediate snail host Oncomelania haupensis in western China. We advance functional connectivity methods by providing an analytical framework to (i) identify nodes of transmission where the degree of connectedness to other villages, and thus the potential for disease spread, is higher than is estimated using Euclidean distance alone and (ii) (re)organize transmission sites into disease surveillance units based on second-order relationships among nodes using non-Euclidean distance measures, termed effective geographical distance (EGD). Functional environmental models are parametrized using ecological information on the target organisms, and pair-wise distributions of inter-node EGD are estimated. A Monte Carlo rank product analysis is presented to identify nearby nodes under alternative distance models. Nodes are then iteratively embedded into EGD space and clustered using a k -means algorithm to group villages into ecologically meaningful surveillance groups. A consensus clustering approach is taken to derive the most stable cluster structure. The results indicate that novel relationships between nodes are revealed when non-Euclidean, ecologically determined distance measures are used to quantify connectivity in heterogeneous landscapes. These connections are not evident when analysing nodes in Euclidean space, and thus surveillance and control activities planned using Euclidean distance measures may be suboptimal. The methods developed here provide a quantitative framework for assessing the effectiveness of ecologically grounded surveillance systems and of control and prevention strategies for environmentally mediated diseases.
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Dissertations / Theses on the topic "Euclidean distance degree"

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Gustafsson, Lukas. "The Euclidean Distance Degree of Conics." Thesis, KTH, Matematik (Avd.), 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-252533.

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The Euclidean Distance Degree (EDD) of a variety is the number of critical points of the squared distance function of a general point outside the variety. In this thesis we give a classification of conics based on their EDD, originally attributed to Cayley. We show that circles and parabolas have EDD 2 and 3 respectively while all other conics have EDD 4. We reduce the computation of the EDD to finding solutions of the determinant of a certain generalized matrix, called the hyperdeterminant of type 2 × 3 × 3. This determinant is computed using the celebrated Schläfli decomposition.
The Euclidean Distance Degree (EDD) of a variety is the number of critical points of the squared distance function of a general point outside the variety. In this thesis we give a classification of conics based on their EDD, originally attributed to Cayley. We show that circles and parabolas have EDD 2 and 3 respectively while all other conics have EDD 4. We reduce the computation of the EDD to finding solutions of the determinant of a certain generalized matrix, called the hyperdeterminant of type 2 × 3 × 3. This determinant is computed using the celebrated Schläfli decomposition.
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Sodomaco, Luca. "The Distance Function from the Variety of partially symmetric rank-one Tensors." Doctoral thesis, 2020. http://hdl.handle.net/2158/1220535.

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The topic of this doctoral thesis is at the intersection between Real Algebraic Geometry, Optimization Theory and Multilinear Algebra. In particular, a relevant part of this thesis is dedicated to studying metric invariants of real algebraic varieties, with a particular interest in varieties in tensor spaces. In many applications, tensors arise as a useful way to store and organize experimental data. For example, it is widely known that tensor techniques are extremely useful in Algebraic Statistics. A strong relationship between classical algebraic geometry and multilinear algebra is established by the notion of tensor rank. Geometrically speaking, the problem of computing the rank of a tensor translates to a membership problem to a certain secant variety of a Segre product of projective spaces. In the last fifteen years, a new line of research in tensor theory has been undertaken and is commonly known as Spectral Theory of Tensors. One of the foundational motivations of this theory comes from the need, e.g., in some constrained optimization problems, to approximate a given tensor to its closest tensor of fixed lower rank, with respect to the Frobenius norm, also known as Bombieri norm. This is the so-called best rank- k approximation problem for real tensors. In this context, an important role is played by the singular vector tuples and the singular values of a tensor, which generalize the notions of eigenvector and eigenvalue of a matrix. Their symmetric counterpart is represented by the E-eigenvalues and the E-eigenvectors of a symmetric tensor. Of particular interest is the E-characteristic polynomial of a symmetric tensor, which has among its roots the E-eigenvalues of a symmetric tensor. For symmetric matrices, it coincides with the classical characteristic polynomial. We interpret the E-characteristic polynomial as an algebraic relation satisfied by the Frobenius distance between an assigned symmetric tensor and the dual affine cone of a Veronese variety. We show that the E-characteristic polynomial is monic only in the symmetric matrix case. We provide a rational formula for the product of the singular values of a partially symmetric tensor of hypercubic format. The formula generalizes the fact that the determinant of a symmetric matrix is equal to the product of its eigenvalues. This is the only case where no denominator occurs in the formula. Computing the distance from a variety of low-rank tensors is an important instance of a more general problem: computing the distance from a real algebraic variety X in a Euclidean space (V,q). We introduce a polynomial, called Euclidean Distance polynomial of X, which, for any data point u in V, has among its roots the distance ε from u to X. The ε^2-degree of the ED polynomial is the known Euclidean Distance degree of X. When X is transversal to the isotropic quadric Q={q=0}, we show that the ED polynomial of X is monic and we describe its lowest term completely.
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Book chapters on the topic "Euclidean distance degree"

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Feng, Yong, and Wuxin Chen. "Fuzzy Pattern Recognition Based on Generalized Euclidean Weight Distance Adjoined Degree and Its Application in Forecasting Hazard of Karst Collapse." In Communications in Computer and Information Science, 264–71. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-16388-3_29.

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Tapia, J. M., F. Chiclana, M. J. Del Moral, and E. Herrera-Viedma. "Improving Euclidean’s Consensus Degrees in Group Decision Making Problems Through a Uniform Extension." In Frontiers in Artificial Intelligence and Applications. IOS Press, 2021. http://dx.doi.org/10.3233/faia210033.

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In a Group Decision Making problem, several people try to reach a single common decision by selecting one of the possible alternatives according to their respective preferences. So, a consensus process is performed in order to increase the level of accord amongst people, called experts, before obtaining the final solution. Improving the consensus degree as much as possible is a very interesting task in the process. In the evaluation of the consensus degree, the measurement of the distance representing disagreement among the experts’ preferences should be considered. Different distance functions have been proposed to implement in consensus models. The Euclidean distance function is one of the most commonly used. This paper analyzes how to improve the consensus degrees, obtained through the Euclidean distance function, when the preferences of the experts are slightly modified by using one of the properties of the Uniform distribution. We fulfil an experimental study that shows the betterment in the consensus degrees when the Uniform extension is applied, taking into account different number of experts and alternatives.
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Yu, Gao-Feng, Deng-Feng Li, and Jin-Ming Qiu. "Interval-Valued Intuitionistic Fuzzy Multi-Attribute Decision Making Based on Satisfactory Degree." In Theoretical and Practical Advancements for Fuzzy System Integration, 49–71. IGI Global, 2017. http://dx.doi.org/10.4018/978-1-5225-1848-8.ch003.

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The aim of this paper is to propose a satisfactory degree method by using nonlinear programming for solving multi-attribute decision making (MADM) problems in which ratings of alternatives on attributes is expressed via interval-valued intuitionistic fuzzy (IVIF) sets and preference information on attributes is incomplete. Concretely, a nonlinear programming model is firstly explored to determine the satisfactory degree which is the ratio of the square of the weight Euclidean distance between an alternative and the IVIF negative ideal solution (IVIFNIS) to the sum of the square of the weight Euclidean distance between the IVIF negative ideal solution (IVIFNIS) and the IVIF positive ideal solution (IVIFPIS). Another nonlinear programming model is also developed to obtain satisfactory intuitionistic fuzzy sets, and then the general satisfactory degrees of the satisfactory intuitionistic fuzzy sets are used to generate the ranking order of the alternatives. Finally, a real example is employed to verify the applicability of the proposed approach and illustrate its practicality and effectiveness.
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Siddiquee, Mahfuzur Rahman, Naimul Haider, and Rashedur M. Rahman. "Movie Recommendation System Based on Fuzzy Inference System and Adaptive Neuro Fuzzy Inference System." In Fuzzy Systems, 573–608. IGI Global, 2017. http://dx.doi.org/10.4018/978-1-5225-1908-9.ch026.

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One of most prominent features that social networks or e-commerce sites now provide is recommendation of items. However, the recommendation task is challenging as high degree of accuracy is required. This paper analyzes the improvement in recommendation of movies using Fuzzy Inference System (FIS) and Adaptive Neuro Fuzzy Inference System (ANFIS). Two similarity measures have been used: one by taking account similar users' choice and the other by matching genres of similar movies rated by the user. For similarity calculation, four different techniques, namely Euclidean Distance, Manhattan Distance, Pearson Coefficient and Cosine Similarity are used. FIS and ANFIS system are used in decision making. The experiments have been carried out on Movie Lens dataset and a comparative performance analysis has been reported. Experimental results demonstrate that ANFIS outperforms FIS in most of the cases when Pearson Correlation metric is used for similarity calculation.
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Boiko, Yurii. "THE RIGHT-BANK UKRAINE INDUSTRIAL PRODUCTION AND INTRA-REGIONAL SPECIALIZATION IN THE MID-19TH CENTURY." In Global trends and prospects of socio-economic development of Ukraine. Publishing House “Baltija Publishing”, 2022. http://dx.doi.org/10.30525/978-9934-26-193-0-19.

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The proposed section of the collective monograph is devoted to the industrial development analysis of the Right-Bank Ukraine three provinces’ (Kyiv, Podillia, Volyn) with a total area of 154643 sq. km and a population of 4683860 in the mid-1840s. That was the time when the first clear signs of commodity industrial production appeared in a large number of local landowners’ estates, took place the spread of manufacturing, focused mainly on local raw materials and the local market. It was in the mid-1840s that not only descriptive but also statistical sources of historical and economic orientation became widespread, which is greatly expanding the researcher’s ability to create reconstructive models of ancient times economic processes. The purpose of our study is to identify the nature and degree of industrial specialization of the Right-Bank Ukraine’ 36 districts in various industries, marketability of production through its volume, fixed in monetary terms. The research methodology is determined by the features of the information base, which combines descriptive and statistical sources. Accordingly, first we give a general description of the local industry, its raw material base, organization and technology, the approximate range of consumers. In the second stage, based on the statistical data presented in the relevant tables, we use multidimensional statistical cluster analysis to make a meaningful classification of 36 districts by the nature and direction of their industrial specialization. As a result, we obtain a model which elements are grouped by common qualitative characteristics, the distance (degree of similarity or difference) between objects and groups can be measured by multidimensional scaling (in our case – the distance in Euclidean space). Macrogroup A from 7 districts of the northern part of the region with a population nearby 799600 was received 85,8% of industrial revenues from the processing of livestock products. Macrogroup E united 14 districts, mainly in the southern zone of the Dnieper Right-Bank, with a population of 1616370. It was characterized by in-depth specialization in the plant origin products processing, from which 96,7% of industrial profits were received. Macrogroup C represented by one district of Kyiv with the central regional city and a total population of 176280. Only here 76,5% of industrial profits came from the processing raw materials of mineral origin. Macrogroup D includes 8 districts in the south of the Right Bank with a population of 1090600 people and natural conditions equally suitable for crop and livestock production. Hence the balance of the processing industry and revenues from it – 48,5% of processing of crop products and 44,5% of processing of livestock products. Macrogroup B included 6 districts with a population of 816350, whose farms did not have a narrow production specialization: 26,1% of industrial profits came from processing of plant products, 33,6% from processing of livestock products, 40,3% of industrial profits from processing of minerals. The practical significance of our study is that the results obtained can be used in the construction of broader paleoeconomic reconstructions, in the educational process, in writing scientific articles and monographs. The originality and scientific novelty of the work lies in the formulation of the problem, the methodology used, the results obtained. Such a study for the Right-Bank Ukraine region of the mid-1840s is conducted for the first time.
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Yapıcı Pehlivan, Nimet, and Neşe Yalçın. "Neutrosophic TOPSIS Method for Sustainable Supplier Selection in a Discount Market Chain." In Handbook of Research on Advances and Applications of Fuzzy Sets and Logic, 692–715. IGI Global, 2022. http://dx.doi.org/10.4018/978-1-7998-7979-4.ch031.

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Sustainable supplier selection is one of the most important decisions for companies in sustainable supply chain management. Therefore, sustainable supplier performance evaluation and selection are of great importance in terms of economic, environmental, and social aspects of sustainable development. Sustainable supplier selection problem can be considered as a multiple-criteria decision-making (MCDM) problem. In the MCDM problems, decision-makers evaluate conflicting criteria and alternatives according to their own preferences/judgments. One of the most well-known MCDM methods is the technique for order preference by similarity to an ideal solution (TOPSIS). Neutrosophic set (NS) is an extension of fuzzy set where each element of the universe has the degrees of truth, indeterminacy, and falsity. A single-valued neutrosophic set (SVNS) is a special case of the neutrosophic set. This chapter aims to evaluate sustainable supplier selection in a Turkish discount market chain using the single-valued neutrosophic TOPSIS method based on normalized Euclidean and Hamming distances.
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Li, Deng-Feng, and Jiang-Xia Nan. "Extension of the TOPSIS for Multi-Attribute Group Decision Making under Atanassov IFS Environments." In Contemporary Theory and Pragmatic Approaches in Fuzzy Computing Utilization, 241–55. IGI Global, 2013. http://dx.doi.org/10.4018/978-1-4666-1870-1.ch017.

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This paper extends the technique for order preference by similarity to ideal solution (TOPSIS) for solving multi-attribute group decision making (MAGDM) problems under Atanassov intuitionistic fuzzy set (IFS) environments. In this methodology, weights of attributes and ratings of alternatives on attributes are extracted from fuzziness inherent in decision data and making process and described using Atanassov IFSs. An Euclidean distance measure is developed to calculate the differences between alternatives for each decision maker and an Atanassov IFS positive ideal solution (IFSPIS) as well as an Atanassov IFS negative ideal-solution (IFSNIS). Degrees of relative closeness to the Atanassov IFSPIS for all alternatives with respect to each decision maker in the group are calculated. Then all decision makers in the group may be regarded as “attributes” and a corresponding classical MADM problem is generated and hereby solved by the TOPSIS. The proposed methodology is validated and compared with other similar methods. A numerical example is examined to demonstrate the implementation process of the methodology proposed in this paper.
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Conference papers on the topic "Euclidean distance degree"

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Draisma, Jan, Emil Horobeţ, Giorgio Ottaviani, Bernd Sturmfels, and Rekha Thomas. "The euclidean distance degree." In the 2014 Symposium. New York, New York, USA: ACM Press, 2014. http://dx.doi.org/10.1145/2631948.2631951.

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Singh, Aman, and Babita Pandey. "An euclidean distance based KNN computational method for assessing degree of liver damage." In 2016 International Conference on Inventive Computation Technologies (ICICT). IEEE, 2016. http://dx.doi.org/10.1109/inventive.2016.7823222.

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Liu, Baixi, Hongzhao Liu, Daning Yuan, and Jianhua Rao. "A New Recognition Method for Damping Coefficients of Rod Pumping System of Directional Well." In ASME 8th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2006. http://dx.doi.org/10.1115/esda2006-95019.

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In this paper, a pattern recognition method is put forward to identify damping coefficients of rod pumping system of directional well by using characteristics space mapping. The 24-direction chain code is presented to encode the curve of dynamometer card. The parametric equation of the dynamometer card curve is transformed into Fourier series whose coefficients can be computed according to the curve’s chain codes. By means of those Fourier coefficients, shape characteristics of the curve are extracted. Euclidean distance is introduced as the measurement of similar degree between the shape characteristics of measured dynamometer card and that of simulated dynamometer card. Changing the value of viscous damping coefficient and Coulomb damping coefficient in the simulation program, different simulated dynamometer cards are obtained. Substituting their shape characteristics to the Euclidean distance, respectively, a series of distances are acquired. When the distance is little than the given error, the corresponding values of the damping coefficients in the simulation program are regarded as real damping coefficients of the rod pumping system of directional well. In the end, an example is provided to show the correctness and effectiveness of the presented method.
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Shubat, Oksana, and Irina Shmarova. "Identifying regional models of active grandparenting in Russia based on cluster analysis." In 36th ECMS International Conference on Modelling and Simulation. ECMS, 2022. http://dx.doi.org/10.7148/2022-0078.

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One of the important social roles the elderly perform is that of grandparents. Our study aims to identify groups of Russian regions with similar models of grandparental activity. The research focuses only on grandmothers. To determine these models, we applied the hierarchical cluster analysis. We used indicators that characterize potential (based on the age criterion) and active (based on intensive involvement in caring for grandchildren) grandparenting in Russian regions. In the process of clustering, we use the growth rates of active grandmothers in the total number of potential grandmothers in 2011-2014, 2014-2016, 2016-2018. The analysis based on the Ward method and the Euclidean distance allowed us to identify 4 models of grandparental activity (regarding grandmothers) in Russian regions. The models differ significantly in the specifics of changes in the degree of grandmothers' involvement in caring for their grandchildren. These models provide the framework for developing specific demographic policy measures with the regional heterogeneity in mind.
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