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Relevant bibliographies by topics / Data approximation

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Academic literature on the topic 'Data approximation'

Author: Grafiati

Published: 7 December 2024

Last updated: 26 July 2025

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Journal articles on the topic "Data approximation"

1

FROYLAND, GARY, KEVIN JUDD, ALISTAIR I. MEES, DAVID WATSON, and KENJI MURAO. "CONSTRUCTING INVARIANT MEASURES FROM DATA." International Journal of Bifurcation and Chaos 05, no. 04 (1995): 1181–92. http://dx.doi.org/10.1142/s0218127495000843.

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We present a method of approximating an invariant measure of a dynamical system from a finite set of experimental data. Our reconstruction technique automatically provides us with a partition of phase space, and we assign each set in the partition a certain weight. By refining the partition, we may make our approximation to an invariant measure of the reconstructed system as accurate as we wish. Our method provides us with both a singular and an absolutely continuous approximation, so that the most suitable representation may be chosen for a particular problem.

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Chen, Jing-Bo, Hong Liu, and Zhi-Fu Zhang. "A separable-kernel decomposition method for approximating the DSR continuation operator." GEOPHYSICS 72, no. 1 (2007): S25—S31. http://dx.doi.org/10.1190/1.2399368.

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We develop a separable-kernel decomposition method for approximating the double-square-root (DSR) continuation operator in one-way migrations in this paper. This new approach is a further development of separable approximations of the single-square-root (SSR) operator. The separable approximation of the DSR operator generally involves solving a complicated nonlinear system of integral equations. Instead of solving this nonlinear system directly, our new method consists of repeatedly applying the separable-kernel technique developed for the two-variable SSR operator to the multivariable DSR ope

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STOJANOVIĆ, MIRJANA. "PERTURBED SCHRÖDINGER EQUATION WITH SINGULAR POTENTIAL AND INITIAL DATA." Communications in Contemporary Mathematics 08, no. 04 (2006): 433–52. http://dx.doi.org/10.1142/s0219199706002180.

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We consider linear Schrödinger equation perturbed by delta distribution with singular potential and the initial data. Due to the singularities appearing in the equation, we introduce two kinds of approximations: the parameter's approximation for potential and the initial data given by mollifiers of different growth and the approximation for the Green function for Schrödinger equation with regularized derivatives. These approximations reduce the perturbed Schrödinger equation to the family of singular integral equations. We prove the existence-uniqueness theorems in Colombeau space [Formula: se

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Grubas, Serafim I., Georgy N. Loginov, and Anton A. Duchkov. "Traveltime-table compression using artificial neural networks for Kirchhoff-migration processing of microseismic data." GEOPHYSICS 85, no. 5 (2020): U121—U128. http://dx.doi.org/10.1190/geo2019-0427.1.

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Massive computation of seismic traveltimes is widely used in seismic processing, for example, for the Kirchhoff migration of seismic and microseismic data. Implementation of the Kirchhoff migration operators uses large precomputed traveltime tables (for all sources, receivers, and densely sampled imaging points). We have tested the idea of using artificial neural networks for approximating these traveltime tables. The neural network has to be trained for each velocity model, but then the whole traveltime table can be compressed by several orders of magnitude (up to six orders) to the size of l

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FRAHLING, GEREON, PIOTR INDYK, and CHRISTIAN SOHLER. "SAMPLING IN DYNAMIC DATA STREAMS AND APPLICATIONS." International Journal of Computational Geometry & Applications 18, no. 01n02 (2008): 3–28. http://dx.doi.org/10.1142/s0218195908002520.

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A dynamic geometric data stream is a sequence of m ADD/REMOVE operations of points from a discrete geometric space {1,…, Δ} d ?. ADD (p) inserts a point p from {1,…, Δ} d into the current point set P , REMOVE(p) deletes p from P . We develop low-storage data structures to (i) maintain ε-nets and ε-approximations of range spaces of P with small VC-dimension and (ii) maintain a (1 + ε)-approximation of the weight of the Euclidean minimum spanning tree of P . Our data structure for ε-nets uses [Formula: see text] bits of memory and returns with probability 1 – δ a set of [Formula: see text] point

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Mardia, K. V., and I. L. Dryden. "Shape distributions for landmark data." Advances in Applied Probability 21, no. 4 (1989): 742–55. http://dx.doi.org/10.2307/1427764.

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The paper obtains the exact distribution of Bookstein's shape variables under his plausible model for landmark data. We consider its properties including invariances, marginal distributions and the relationship with Kendall's uniform measure. Particular cases for triangles and quadrilaterals are highlighted. A normal approximation to the distribution is obtained, extending Bookstein's result for three landmarks. The adequacy of these approximations is also studied.

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Mardia, K. V., and I. L. Dryden. "Shape distributions for landmark data." Advances in Applied Probability 21, no. 04 (1989): 742–55. http://dx.doi.org/10.1017/s0001867800019029.

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The paper obtains the exact distribution of Bookstein's shape variables under his plausible model for landmark data. We consider its properties including invariances, marginal distributions and the relationship with Kendall's uniform measure. Particular cases for triangles and quadrilaterals are highlighted. A normal approximation to the distribution is obtained, extending Bookstein's result for three landmarks. The adequacy of these approximations is also studied.

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Birch, A. C., and A. G. Kosovichev. "Towards a Wave Theory Interpretation of Time-Distance Helioseismology Data." Symposium - International Astronomical Union 203 (2001): 180–82. http://dx.doi.org/10.1017/s0074180900219025.

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Time-distance helioseismology, which measures the time for acoustic waves to travel between points on the solar surface, has been used to study small-scale three-dimensional features in the sun, for example active regions, as well as large-scale features, such as meridional flow, that are not accessible by standard global helioseismology. Traditionally, travel times have been interpreted using geometrical ray theory, which is not always a good approximation. In order to develop a wave interpretation of time-distance data we employ the first Born approximation, which takes into account finite-w

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Nawar, A. S., R. Abu-Gdairi, M. K. El-Bably, and H. M. Atallah. "Enhancing Rheumatic Fever Analysis via Tritopological Approximation Spaces for Data Reduction." Malaysian Journal of Mathematical Sciences 18, no. 2 (2024): 321–41. http://dx.doi.org/10.47836/mjms.18.2.07.

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This paper introduces the concept of tritopological approximation space, extending conventional approximation space by drawing upon topological spaces and precisely defined binary relations within a universe of discourse. Through meticulous construction of subbases, this progressive paradigm shift facilitates a comprehensive analysis of rough sets within the domain of tritopological approximation spaces. Additionally, the study pioneer's multiple membership functions and inclusion functions, enhancing the analytical framework and enabling more effective redefinition of rough approximations. To

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Bathie, Gabriel, and Guillaume Lagarde. "A (1+?)-Approximation for Ultrametric Embedding in Subquadratic Time." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 15 (2025): 15516–23. https://doi.org/10.1609/aaai.v39i15.33703.

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Efficiently computing accurate representations of high-dimensional data is essential for data analysis and unsupervised learning. Dendrograms, also known as ultrametrics, are widely used representations that preserve hierarchical relationships within the data. However, popular methods for computing them, such as *linkage* algorithms, suffer from quadratic time and space complexity, making them impractical for large datasets. The "best ultrametric embedding" (a.k.a. "best ultrametric fit") problem, which aims to find the ultrametric that best preserves the distances between points in the origin

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Dissertations / Theses on the topic "Data approximation"

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Ross, Colin. "Applications of data fusion in data approximation." Thesis, University of Huddersfield, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.247372.

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Deligiannakis, Antonios. "Accurate data approximation in constrained environments." College Park, Md. : University of Maryland, 2005. http://hdl.handle.net/1903/2681.

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Thesis (Ph. D.) -- University of Maryland, College Park, 2005.<br>Thesis research directed by: Computer Science. Title from abstract of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.

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Tomek, Peter. "Approximation of Terrain Data Utilizing Splines." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2012. http://www.nusl.cz/ntk/nusl-236488.

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Pro optimalizaci letových trajektorií ve velmi malé nadmorské výšce, terenní vlastnosti musí být zahrnuty velice přesne. Proto rychlá a efektivní evaluace terenních dat je velice důležitá vzhledem nato, že čas potrebný pro optimalizaci musí být co nejkratší. Navyše, na optimalizaci letové trajektorie se využívájí metody založené na výpočtu gradientu. Proto musí být aproximační funkce terenních dat spojitá do určitého stupne derivace. Velice nádejná metoda na aproximaci terenních dat je aplikace víceroměrných simplex polynomů. Cílem této práce je implementovat funkci, která vyhodnotí dané teren

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Cao, Phuong Thao. "Approximation of OLAP queries on data warehouses." Phd thesis, Université Paris Sud - Paris XI, 2013. http://tel.archives-ouvertes.fr/tel-00905292.

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We study the approximate answers to OLAP queries on data warehouses. We consider the relative answers to OLAP queries on a schema, as distributions with the L1 distance and approximate the answers without storing the entire data warehouse. We first introduce three specific methods: the uniform sampling, the measure-based sampling and the statistical model. We introduce also an edit distance between data warehouses with edit operations adapted for data warehouses. Then, in the OLAP data exchange, we study how to sample each source and combine the samples to approximate any OLAP query. We next c

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Lehman, Eric (Eric Allen) 1970. "Approximation algorithms for grammar-based data compression." Thesis, Massachusetts Institute of Technology, 2002. http://hdl.handle.net/1721.1/87172.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2002.<br>Includes bibliographical references (p. 109-113).<br>This thesis considers the smallest grammar problem: find the smallest context-free grammar that generates exactly one given string. We show that this problem is intractable, and so our objective is to find approximation algorithms. This simple question is connected to many areas of research. Most importantly, there is a link to data compression; instead of storing a long string, one can store a small grammar that generates i

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Hou, Jun. "Function Approximation and Classification with Perturbed Data." The Ohio State University, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu1618266875924225.

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Zaman, Muhammad Adib Uz. "Bicubic L1 Spline Fits for 3D Data Approximation." Thesis, Northern Illinois University, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10751900.

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<p> Univariate cubic <i>L</i><sup>1</sup> spline fits have been successful to preserve the shapes of 2D data with abrupt changes. The reason is that the minimization of <i>L</i><sup>1</sup> norm of the data is considered, as opposite to <i>L</i><sup>2</sup> norm. While univariate <i>L</i><sup>1</sup> spline fits for 2D data are discussed by many, bivariate <i>L</i><sup>1</sup> spline fits for 3D data are yet to be fully explored. This thesis aims to develop bicubic <i>L</i><sup>1</sup> spline fits for 3D data approximation. This can be achieved by solving a bi-level optimization problem. One l

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Cooper, Philip. "Rational approximation of discrete data with asymptotic behaviour." Thesis, University of Huddersfield, 2007. http://eprints.hud.ac.uk/id/eprint/2026/.

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This thesis is concerned with the least-squares approximation of discrete data that appear to exhibit asymptotic behaviour. In particular, we consider using rational functions as they are able to display a number of types of asymptotic behaviour. The research is biased towards the development of simple and easily implemented algorithms that can be used for this purpose. We discuss a number of novel approximation forms, including the Semi-Infinite Rational Spline and the Asymptotic Polynomial. The Semi-Infinite Rational Spline is a piecewise rational function, continuous across a single knot, a

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Schmid, Dominik. "Scattered data approximation on the rotation group and generalizations." Aachen Shaker, 2009. http://d-nb.info/995021562/04.

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McQuarrie, Shane Alexander. "Data Assimilation in the Boussinesq Approximation for Mantle Convection." BYU ScholarsArchive, 2018. https://scholarsarchive.byu.edu/etd/6951.

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Many highly developed physical models poorly approximate actual physical systems due to natural random noise. For example, convection in the earth's mantle—a fundamental process for understanding the geochemical makeup of the earth's crust and the geologic history of the earth—exhibits chaotic behavior, so it is difficult to model accurately. In addition, it is impossible to directly measure temperature and fluid viscosity in the mantle, and any indirect measurements are not guaranteed to be highly accurate. Over the last 50 years, mathematicians have developed a rigorous framework for reconci

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Books on the topic "Data approximation"

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Iske, Armin. Approximation Theory and Algorithms for Data Analysis. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-05228-7.

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Motwani, Rajeev. Lecture notes on approximation algorithms. Dept. of Computer Science, Stanford University, 1992.

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C, Mason J., and Cox M. G, eds. Algorithms for approximation II: Based on the proceedings of the Second International Conference on Algorithms for Approximation, held at Royal Military College of Science, Shrivenham, July 1988. Chapman and Hall, 1990.

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Franke, Richard. Recent advances in the approximation of surfaces from scattered data. Naval Postgraduate School, 1987.

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Ivanov, Viktor Vladimirovich. Metody vychisleniĭ na ĖVM: Spravochnoe posobie. Nauk. dumka, 1986.

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Franke, Richard H. Least squares surface approximation to scattered data using multiquadric functions. Naval Postgraduate School, 1993.

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Molchanov, I. N. Mashinnye metody reshenii͡a︡ prikladnykh zadach algebra, priblizhenie funkt͡s︡iĭ. Nauk. dumka, 1987.

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8

K, Ray Bimal, ed. Polygonal approximation and scale-space analysis. Apple Academic Press, 2013.

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C, Mason J., Cox M. G, and Institute of Mathematics and Its Applications., eds. Algorithms for approximation: Based on the proceedings of the IMA Conference on Algorithms for the Approximation of Functions and Data, held at the Royal Military College of Science, Shrivenham, July 1985. Clarendon Press, 1987.

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Eitan, Tadmor, Institute for Computer Applications in Science and Engineering., and Langley Research Center, eds. Recovering pointwise values of discontinuous data within spectral accuracy. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1985.

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Book chapters on the topic "Data approximation"

1

Shekhar, Shashi, and Hui Xiong. "Data Approximation." In Encyclopedia of GIS. Springer US, 2008. http://dx.doi.org/10.1007/978-0-387-35973-1_237.

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Hutchings, Matthew, and Bertrand Gauthier. "Local Optimisation of Nyström Samples Through Stochastic Gradient Descent." In Machine Learning, Optimization, and Data Science. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-25599-1_10.

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AbstractWe study a relaxed version of the column-sampling problem for the Nyström approximation of kernel matrices, where approximations are defined from multisets of landmark points in the ambient space; such multisets are referred to as Nyström samples. We consider an unweighted variation of the radial squared-kernel discrepancy (SKD) criterion as a surrogate for the classical criteria used to assess the Nyström approximation accuracy; in this setting, we discuss how Nyström samples can be efficiently optimised through stochastic gradient descent. We perform numerical experiments which demon

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Markovsky, Ivan. "From Data to Models." In Low-Rank Approximation. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-89620-5_2.

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Deng, Shaobo, Huihui Lu, Sujie Guan, Min Li, and Hui Wang. "Approximation Relation for Rough Sets." In Data Mining and Big Data. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-7502-7_38.

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Rengaswamy, Raghunathan, and Resmi Suresh. "Function Approximation Methods." In Data Science for Engineers. CRC Press, 2022. http://dx.doi.org/10.1201/b23276-6.

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Iske, Armin. "Euclidean Approximation." In Approximation Theory and Algorithms for Data Analysis. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-05228-7_4.

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Iske, Armin. "Chebyshev Approximation." In Approximation Theory and Algorithms for Data Analysis. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-05228-7_5.

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Markovsky, Ivan. "Data-Driven Filtering and Control." In Low-Rank Approximation. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-89620-5_6.

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Adir, Allon, Ehud Aharoni, Nir Drucker, Ronen Levy, Hayim Shaul, and Omri Soceanu. "Approximation Methods Part II: Approximations of Standard Functions." In Homomorphic Encryption for Data Science (HE4DS). Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-65494-7_6.

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Wu, Weili, Yi Li, Panos M. Pardalos, and Ding-Zhu Du. "Data-Dependent Approximation in Social Computing." In Approximation and Optimization. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-12767-1_3.

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Conference papers on the topic "Data approximation"

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Ma, Guanqun, David Lenz, Tom Peterka, Hanqi Guo, and Bei Wang. "Critical Point Extraction from Multivariate Functional Approximation." In 2024 IEEE Topological Data Analysis and Visualization (TopoInVis). IEEE, 2024. http://dx.doi.org/10.1109/topoinvis64104.2024.00006.

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Sahrom, Nor Ashikin, Mohammad Izat Emir Zulkifly, and Siti Nur Idara Rosli. "Interval-Valued Fuzzy Bézier Surface Approximation." In 2024 5th International Conference on Artificial Intelligence and Data Sciences (AiDAS). IEEE, 2024. http://dx.doi.org/10.1109/aidas63860.2024.10730727.

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Dong, Xue, Fei Xia, Yoonseok Baek, Ziao Wang, and Sylvain Gigan. "Optical additive Kernel approximation using broadband scattering in complex media." In AI and Optical Data Sciences VI, edited by Masaya Notomi and Tingyi Zhou. SPIE, 2025. https://doi.org/10.1117/12.3043036.

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Barbas, Petros, Aristidis G. Vrahatis, and Sotiris K. Tasoulis. "RLAC: Random Line Approximation Clustering." In 2021 IEEE International Conference on Big Data (Big Data). IEEE, 2021. http://dx.doi.org/10.1109/bigdata52589.2021.9671596.

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Zhao, Danfeng, Zhou Huang, Feng Zhou, Antonio Liotta, and Dongmei Huang. "An Approximation Method for Large Graph Similarity." In 2020 IEEE International Conference on Big Data (Big Data). IEEE, 2020. http://dx.doi.org/10.1109/bigdata50022.2020.9378447.

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Das, Abhinandan, Johannes Gehrke, and Mirek Riedewald. "Approximation techniques for spatial data." In the 2004 ACM SIGMOD international conference. ACM Press, 2004. http://dx.doi.org/10.1145/1007568.1007646.

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Freedman, Daniel, and Pavel Kisilev. "Fast Data Reduction via KDE Approximation." In 2009 Data Compression Conference (DCC). IEEE, 2009. http://dx.doi.org/10.1109/dcc.2009.47.

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Panda, Biswanath, Mirek Riedewald, Johannes Gehrke, and Stephen B. Pope. "High-Speed Function Approximation." In Seventh IEEE International Conference on Data Mining (ICDM 2007). IEEE, 2007. http://dx.doi.org/10.1109/icdm.2007.107.

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Huang, Zhou, and Feng Zhou. "An Approximation Method for Querying Similar Large Graphs." In 2022 IEEE International Conference on Big Data (Big Data). IEEE, 2022. http://dx.doi.org/10.1109/bigdata55660.2022.10020310.

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Shahcheraghi, Maryam, Trevor Cappon, Samet Oymak, et al. "Matrix Profile Index Approximation for Streaming Time Series." In 2021 IEEE International Conference on Big Data (Big Data). IEEE, 2021. http://dx.doi.org/10.1109/bigdata52589.2021.9671484.

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Reports on the topic "Data approximation"

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Franke, Richard, Hans Hagen, and Gregory M. Nielson. Least Squares Surface Approximation to Scattered Data Using Multiquadric Functions. Defense Technical Information Center, 1992. http://dx.doi.org/10.21236/ada259804.

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Ray, Jaideep, Matthew Barone, Stefan Domino, Tania Banerjee, and Sanjay Ranka. Verification of Data-Driven Models of Physical Phenomena using Interpretable Approximation. Office of Scientific and Technical Information (OSTI), 2021. http://dx.doi.org/10.2172/1821318.

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Baraniuk, Richard, Ronald DeVore, Sanjeev Kulkarni, et al. Model Classes, Approximation, and Metrics for Dynamic Processing of Urban Terrain Data. Defense Technical Information Center, 2013. http://dx.doi.org/10.21236/ada586168.

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Franke, Richard. Using Legendre Functions for Spatial Covariance Approximation and Investigation of Radial Nonisotrophy for NOGAPS Data. Defense Technical Information Center, 2001. http://dx.doi.org/10.21236/ada389396.

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Wu, Yan, Sonia Fahmy, and Ness B. Shroff. On the Construction of a Maximum-Lifetime Data Gathering Tree in Sensor Networks: NP-Completeness and Approximation Algorithm. Defense Technical Information Center, 2008. http://dx.doi.org/10.21236/ada517885.

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Shah, Rajiv R. High-Level Adaptive Signal Processing Architecture with Applications to Radar Non-Gaussian Clutter. Volume 2. A New Technique for Distribution Approximation of Random Data. Defense Technical Information Center, 1995. http://dx.doi.org/10.21236/ada300902.

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Gorton, O., and J. Escher. Cross Sections for Neutron-Induced Reactions from Surrogate Data: Assessing the Use of the Weisskopf-Ewing Approximation for (n,n') and (n,2n) Reactions. Office of Scientific and Technical Information (OSTI), 2020. http://dx.doi.org/10.2172/1668500.

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Guan, Jiajing, Sophia Bragdon, and Jay Clausen. Predicting soil moisture content using Physics-Informed Neural Networks (PINNs). Engineer Research and Development Center (U.S.), 2024. http://dx.doi.org/10.21079/11681/48794.

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Environmental conditions such as the near-surface soil moisture content are valuable information in object detection problems. However, such information is generally unobtainable at the necessary scale without active sensing. Richards’ equation is a partial differential equation (PDE) that describes the infiltration process of unsaturated soil. Solving the Richards’ equation yields information about the volumetric soil moisture content, hydraulic conductivity, and capillary pressure head. However, Richards’ equation is difficult to approximate due to its nonlinearity. Numerical solvers such as

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Pasupuleti, Murali Krishna. Neural Computation and Learning Theory: Expressivity, Dynamics, and Biologically Inspired AI. National Education Services, 2025. https://doi.org/10.62311/nesx/rriv425.

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Abstract: Neural computation and learning theory provide the foundational principles for understanding how artificial and biological neural networks encode, process, and learn from data. This research explores expressivity, computational dynamics, and biologically inspired AI, focusing on theoretical expressivity limits, infinite-width neural networks, recurrent and spiking neural networks, attractor models, and synaptic plasticity. The study investigates mathematical models of function approximation, kernel methods, dynamical systems, and stability properties to assess the generalization capa

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Bunn, M. I., T. R. Carter, H. A. J. Russell, and C. E. Logan. A semiquantitative representation of uncertainty for the 3D Paleozoic bedrock model of Southern Ontario. Natural Resources Canada/CMSS/Information Management, 2023. http://dx.doi.org/10.4095/331658.

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The southern Ontario bedrock model is a valuable resource for researchers and practitioners, but its application is subject to uncertainty. To address this issue a semi-quantitative approach to visualize the relative effects of data sparsity for each layer, identify regions where a lack of data support reduces model confidence, and quantify potential errors in data collection and model construction is presented. This analysis summarizes several sources of error, including cartesian position error, error in the vertical position of the formation contact, error between the modelled topographic s

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