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Journal articles on the topic 'Data approximation'

Author: Grafiati

Published: 7 December 2024

Last updated: 16 June 2025

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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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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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3

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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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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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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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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9

Dong, Bin, Zuowei Shen, and Jianbin Yang. "Approximation from Noisy Data." SIAM Journal on Numerical Analysis 59, no. 5 (2021): 2722–45. http://dx.doi.org/10.1137/20m1389091.

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10

Piegl, L. A., and W. Tiller. "Data Approximation Using Biarcs." Engineering with Computers 18, no. 1 (2002): 59–65. http://dx.doi.org/10.1007/s003660200005.

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11

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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Ullah, Insha, Sudhir Paul, Zhenjie Hong, and You-Gan Wang. "Significance tests for analyzing gene expression data with small sample sizes." Bioinformatics 35, no. 20 (2019): 3996–4003. http://dx.doi.org/10.1093/bioinformatics/btz189.

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Abstract Motivation Under two biologically different conditions, we are often interested in identifying differentially expressed genes. It is usually the case that the assumption of equal variances on the two groups is violated for many genes where a large number of them are required to be filtered or ranked. In these cases, exact tests are unavailable and the Welch’s approximate test is most reliable one. The Welch’s test involves two layers of approximations: approximating the distribution of the statistic by a t-distribution, which in turn depends on approximate degrees of freedom. This stu

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Chervov, Alexander, Jonathan Bac, and Andrei Zinovyev. "Minimum Spanning vs. Principal Trees for Structured Approximations of Multi-Dimensional Datasets." Entropy 22, no. 11 (2020): 1274. http://dx.doi.org/10.3390/e22111274.

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Construction of graph-based approximations for multi-dimensional data point clouds is widely used in a variety of areas. Notable examples of applications of such approximators are cellular trajectory inference in single-cell data analysis, analysis of clinical trajectories from synchronic datasets, and skeletonization of images. Several methods have been proposed to construct such approximating graphs, with some based on computation of minimum spanning trees and some based on principal graphs generalizing principal curves. In this article we propose a methodology to compare and benchmark these

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Abd El-Raheem, Abd El-Raheem M., and Mona Hosny. "Saddlepoint p-values for a class of nonparametric tests for the current status and panel count data under generalized permuted block design." AIMS Mathematics 8, no. 8 (2023): 18866–80. http://dx.doi.org/10.3934/math.2023960.

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<abstract><p>Current status and panel count data appear in many applied fields, including medicine, clinical trials, epidemiology, econometrics, demography, engineering and public health. Therefore, in this article, we use the saddlepoint approximation method to approximate the exact p-value of a number of nonparametric tests for the current status and panel count data under a generalized permuted block design. The saddlepoint approximation is referred to as higher-order approximation and it is more accurate than the methods that lead to approximations that are accurate to the firs

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Siswantining, Titin, Muhammad Ihsan, Saskya Mary Soemartojo, Devvi Sarwinda, Herley Shaori Al-Ash, and Ika Marta Sari. "MULTIPLE IMPUTATION FOR ORDINARY COUNT DATA BY NORMAL DISTRIBUTION APPROXIMATION." MEDIA STATISTIKA 14, no. 1 (2021): 68–78. http://dx.doi.org/10.14710/medstat.14.1.68-78.

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Missing values are a problem that is often encountered in various fields and must be addressed to obtain good statistical inference such as parameter estimation. Missing values can be found in any type of data, included count data that has Poisson distributed. One solution to overcome that problem is applying multiple imputation techniques. The multiple imputation technique for the case of count data consists of three main stages, namely the imputation, the analysis, and pooling parameter. The use of the normal distribution refers to the sampling distribution using the central limit theorem fo

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Bochkov, A. P., V. A. Prourzin, and O. V. Prourzin. "BIG DATA ANALYSIS OF RELIABILITY OF NON-RESTORABLE MULTICHANNEL SYSTEMS." H&ES Research 13, no. 4 (2021): 49–55. http://dx.doi.org/10.36724/2409-5419-2021-13-4-49-55.

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Introduction: methods for analyzing big data of reliability of multichannel systems with a loaded reserve with nonrecoverable elements are considered. Big data contains information on the operating time to failure of elements, obtained by monitoring the operation of similar systems. The main problem that arises when analyzing big data is related to its variety and veracity. Reliability data of system elements correspond to different operating conditions and different laws of failure distribution. The exponential approximation of failure distributions greatly simplifies reliability analysis. Ho

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Sil, Samik. "Fracture parameter estimation from well-log data." GEOPHYSICS 78, no. 3 (2013): D129—D134. http://dx.doi.org/10.1190/geo2012-0407.1.

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We evaluated a method of deriving seismic fracture parameters from vertical-well-log data with the assumption that the fractured medium is transversely isotropic with a horizontal axis of symmetry (HTI). One approximation we used is that the observed vertical P-wave velocity is the same as the background isotropic P-wave velocity of the HTI medium. Another assumption was that the fractures and cracks are noninteractive and penny shaped. Using these approximations, we generated the fracture compliance matrix for each layer. Fracture parameters were then derived by constructing the HTI stiffness

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18

Pratiwi, Indah Nur, Mohammad Syamsu Rosid, and Humbang Purba. "Reducing Residual Moveout for Long Offset Data in VTI Media Using Padé Approximation." E3S Web of Conferences 125 (2019): 15005. http://dx.doi.org/10.1051/e3sconf/201912515005.

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Modification of the hyperbolic travel time equation into non-hyperbolic travel time equation is important to increase the reduction residual moveout for long offset data. Some researchers have modified hyperbolic travel time equation into a non-hyperbolic travel time equation to obtain a more accurate value NMO velocity and parameter an-ellipticity or etha on the large offset to depth ratio (ODR) so that the residual moveout value is smaller mainly in large offset to depth ratio. The aims of research is to increase the reduction value of error residue at long offset data using Padé approximati

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19

Jauch, Jens, Felix Bleimund, Michael Frey, and Frank Gauterin. "An Iterative Method Based on the Marginalized Particle Filter for Nonlinear B-Spline Data Approximation and Trajectory Optimization." Mathematics 7, no. 4 (2019): 355. http://dx.doi.org/10.3390/math7040355.

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The B-spline function representation is commonly used for data approximation and trajectory definition, but filter-based methods for NWLS approximation are restricted to a bounded definition range. We present an algorithm termed NRBA for an iterative NWLS approximation of an unbounded set of data points by a B-spline function. NRBA is based on a MPF, in which a KF solves the linear subproblem optimally while a PF deals with nonlinear approximation goals. NRBA can adjust the bounded definition range of the approximating B-spline function during run-time such that, regardless of the initially ch

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20

Li, Renpu. "Set Approximation in Incomplete Data." Journal of Applied Sciences 13, no. 9 (2013): 1621–28. http://dx.doi.org/10.3923/jas.2013.1621.1628.

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21

Piegl, L. A., and W. Tiller. "Surface approximation to scanned data." Visual Computer 16, no. 7 (2000): 386–95. http://dx.doi.org/10.1007/pl00013393.

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22

Can, Emine. "Piecewise Cubic Approximation for Data." American Journal of Applied Mathematics 1, no. 2 (2013): 24. http://dx.doi.org/10.11648/j.ajam.20130102.11.

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23

Grohs, Philipp, Markus Sprecher, and Thomas Yu. "Scattered manifold-valued data approximation." Numerische Mathematik 135, no. 4 (2016): 987–1010. http://dx.doi.org/10.1007/s00211-016-0823-0.

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24

Gorban, A. N., N. R. Sumner, and A. Y. Zinovyev. "Topological grammars for data approximation." Applied Mathematics Letters 20, no. 4 (2007): 382–86. http://dx.doi.org/10.1016/j.aml.2006.04.022.

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25

Hřebíček, Jiří, Jan Kučera, Petr Švenda, and Vladimír A. Vasilenko. "IDA — interactive data approximation package." Computer Physics Communications 61, no. 1-2 (1990): 231–33. http://dx.doi.org/10.1016/0010-4655(90)90121-g.

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26

Wille, Emilio. "APPROXIMATING PROBABILITY DISTRIBUTION FUNCTIONS WITH FEW MOMENTS." Latin American Applied Research - An international journal 50, no. 1 (2019): 21–25. http://dx.doi.org/10.52292/j.laar.2020.132.

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A procedure is presented for approximating a given probability distribution function or statistical data considering a subset of their moments.This is done by a method of fitting moments of a piecewise linear functionto the moments of the known data. The approach has many advantages over popular approximation approaches. The procedure is demonstrated with commonly used cdfs (Exponential, Gamma, Log-Normal, Normal) andmore difficult problems involving sum and product of random variables,obtaining good agreement between the theoretical/simulation curves and the piecewise linear approximations.

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27

Ma, Shuai, and Jinpeng Huai. "Approximate computation for big data analytics." ACM SIGWEB Newsletter, Winter (January 2021): 1–8. http://dx.doi.org/10.1145/3447879.3447883.

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Over the past a few years, research and development has made significant progresses on big data analytics. A fundamental issue for big data analytics is the efficiency. If the optimal solution is unable to attain or unnecessary or has a price to high to pay, it is reasonable to sacrifice optimality with a "good" feasible solution that can be computed efficiently. Existing approximation techniques can be in general classified into approximation algorithms, approximate query processing for aggregate SQL queries and approximation computing for multiple layers of the system stack. In this article,

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Narayanan, Swathi J., Ilango Paramasivam, Rajen B. Bhatt, and M. Khalid. "A Study on the Approximation of Clustered Data to Parameterized Family of Fuzzy Membership Functions for the Induction of Fuzzy Decision Trees." Cybernetics and Information Technologies 15, no. 2 (2015): 75–96. http://dx.doi.org/10.1515/cait-2015-0030.

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Abstract This paper investigates the Triangular, Trapezoidal and Gaussian approximation methods for the purpose of induction of Fuzzy Decision Trees (FDT). The generation of FDT is done using a Fuzzy ID3 induction algorithm. In this work three fuzzy partitioning techniques which form the basis for our investigation are given attention, namely Fuzzy C Means clustering (FCM), Grid partitioning and Subtractive clustering (Subclust). Our contribution lies in studying the effect of various approximations on the generation of FDT giving specific attention to the classification accuracy of FDT. In th

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Borovsky, Andrei Viktorovich, Andrey Leonidovich Galkin, and Svetlana Sergeevna Kozlova. "Mathematical modeling of statistical data on the incidence of new coronavirus infection, taking into account the stratification by concomitant diagnoses." Vestnik of Astrakhan State Technical University. Series: Management, computer science and informatics 2024, no. 3 (2024): 95–106. http://dx.doi.org/10.24143/2072-9502-2024-3-95-106.

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The article considers the stratification of concomitant diagnoses of Covid-19 recovery statistics for the city of Irkutsk for 2020-2021. The previous study was conducted without taking into account such stratification. Various options for approximating real statistics by Gaussian and Lorentz functions, gamma distribution, and Johnson curves are considered. It is shown that the stratification of recovery statistics improves the approximation of Gaussian and Lorentz functions in comparison with integral statistics, and the construction of an approximation based on the Lorentz function always des

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Wang, Ziming, Chang Liu, Junjie Zhao, and Lijing Shao. "Extending the Fisher Information Matrix in Gravitational-wave Data Analysis." Astrophysical Journal 932, no. 2 (2022): 102. http://dx.doi.org/10.3847/1538-4357/ac6b99.

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Abstract The Fisher information matrix (FM) plays an important role in forecasts and inferences in many areas of physics. While giving fast parameter estimation with Gaussian likelihood approximation in the parameter space, the FM can only give the ellipsoidal posterior contours of the parameters and it loses the higher-order information beyond Gaussianity. We extend the FM in gravitational-wave (GW) data analysis by using the Derivative Approximation for LIkelihoods (DALI), a method to expand the likelihood, while keeping it positive definite and normalizable at every order, for more accurate

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31

DeVore, Ronald, Boris Hanin, and Guergana Petrova. "Neural network approximation." Acta Numerica 30 (May 2021): 327–444. http://dx.doi.org/10.1017/s0962492921000052.

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Neural networks (NNs) are the method of choice for building learning algorithms. They are now being investigated for other numerical tasks such as solving high-dimensional partial differential equations. Their popularity stems from their empirical success on several challenging learning problems (computer chess/Go, autonomous navigation, face recognition). However, most scholars agree that a convincing theoretical explanation for this success is still lacking. Since these applications revolve around approximating an unknown function from data observations, part of the answer must involve the a

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Skala, Vaclav, and Eliska Mourycova. "Meshfree Interpolation of Multidimensional Time-Varying Scattered Data." Computers 12, no. 12 (2023): 243. http://dx.doi.org/10.3390/computers12120243.

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Interpolating and approximating scattered scalar and vector data is fundamental in resolving numerous engineering challenges. These methodologies predominantly rely on establishing a triangulated structure within the data domain, typically constrained to the dimensions of 2D or 3D. Subsequently, an interpolation or approximation technique is employed to yield a smooth and coherent outcome. This contribution introduces a meshless methodology founded upon radial basis functions (RBFs). This approach exhibits a nearly dimensionless character, facilitating the interpolation of data evolving over t

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Zhang, Jiani, Jennifer Erway, Xiaofei Hu, Qiang Zhang, and Robert Plemmons. "Randomized SVD Methods in Hyperspectral Imaging." Journal of Electrical and Computer Engineering 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/409357.

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We present a randomized singular value decomposition (rSVD) method for the purposes of lossless compression, reconstruction, classification, and target detection with hyperspectral (HSI) data. Recent work in low-rank matrix approximations obtained from random projections suggests that these approximations are well suited for randomized dimensionality reduction. Approximation errors for the rSVD are evaluated on HSI, and comparisons are made to deterministic techniques and as well as to other randomized low-rank matrix approximation methods involving compressive principal component analysis. Nu

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34

Lin, Zi Zhi, and Si Hui Shu. "B-Spline Surface Approximation to Scanned Data Using Least Square Approximation." Applied Mechanics and Materials 571-572 (June 2014): 711–16. http://dx.doi.org/10.4028/www.scientific.net/amm.571-572.711.

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Lofting is widely used to approximate the scanned data in row-wise fashion, but this method is prone to result an astonishing number of control points in the process of making the rows curve compatible. A novel algorithm of B-spline surface approximation to the scanned data is presented in this paper to solve this problem. Firstly, the scanned data are interpolated by rows of curves; then these curves are approximated by other curves using least square approximation. In this process, all curves are approximated by a common knot vector, and it is different form the traditional method that each

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Marshalko, Grigory, and Julia Trufanova. "Polynomial Approximations for Several Neural Network Activation Functions." Informatics and Automation 21, no. 1 (2021): 161–80. http://dx.doi.org/10.15622/ia.2022.21.6.

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Active deployment of machine learning systems sets a task of their protection against different types of attacks that threaten confidentiality, integrity and accessibility of both processed data and trained models. One of the promising ways for such protection is the development of privacy-preserving machine learning systems, that use homomorphic encryption schemes to protect data and models. However, such schemes can only process polynomial functions, which means that we need to construct polynomial approximations for nonlinear functions used in neural models. The goal of this paper is the co

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36

Hunt, P. J. "Asymptotic Behaviour of an Integrated Video-Data Network." Probability in the Engineering and Informational Sciences 5, no. 4 (1991): 429–47. http://dx.doi.org/10.1017/s0269964800002217.

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We consider a communication network that can support both wideband video calls and narrowband data traffic. First we consider a single link and prove a weak convergence result to justify a piecewise-deterministic Markov process approximation to the system. We then generalize this approximation to allow priorities and more than one link. This second approximation is a generalization of the Erlang fixed-point approximation for loss networks and is justified via a diverse routing limit theorem.

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Zhang, Xiao Lei, and Jin Ming Wu. "Positive Approximation for Positive Scattered Data." Applied Mechanics and Materials 50-51 (February 2011): 683–87. http://dx.doi.org/10.4028/www.scientific.net/amm.50-51.683.

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The curve and surface fitting problem is very important in CAD and CAGD. However, it is important to construct a suitable function to interpolate or approximate which satisfies the underlying constraints since we have some additional information that is confined to interpolation or approximation. In this paper, we discuss the positive approximation for positive scattered data of any dimensionality by using radial basis functions. The approach is presented to compute positive approximation by solving a quadratic optimization problem. Numerical experiments are provided to illustrate the proposed

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Potts, Daniel, and Michael Schmischke. "Interpretable Approximation of High-Dimensional Data." SIAM Journal on Mathematics of Data Science 3, no. 4 (2021): 1301–23. http://dx.doi.org/10.1137/21m1407707.

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Markovsky, Ivan, and Florian Dörfler. "Data-driven dynamic interpolation and approximation." Automatica 135 (January 2022): 110008. http://dx.doi.org/10.1016/j.automatica.2021.110008.

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Das, A., J. Gehrke, and M. Riedewald. "Semantic approximation of data stream joins." IEEE Transactions on Knowledge and Data Engineering 17, no. 1 (2005): 44–59. http://dx.doi.org/10.1109/tkde.2005.17.

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Lazzeretti, Riccardo, Tommaso Pignata, and Mauro Barni. "Piecewise Function Approximation With Private Data." IEEE Transactions on Information Forensics and Security 11, no. 3 (2016): 642–57. http://dx.doi.org/10.1109/tifs.2015.2503268.

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Heinis, Thomas. "Approximation aids handling of big data." Nature 515, no. 7526 (2014): 198. http://dx.doi.org/10.1038/515198d.

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FLOATER, MICHAEL S. "PARAMETRIC TILINGS AND SCATTERED DATA APPROXIMATION." International Journal of Shape Modeling 04, no. 03n04 (1998): 165–82. http://dx.doi.org/10.1142/s021865439800012x.

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Cao, Yang, and Wenfei Fan. "Data driven approximation with bounded resources." Proceedings of the VLDB Endowment 10, no. 9 (2017): 973–84. http://dx.doi.org/10.14778/3099622.3099628.

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Ghashami, Mina, Jeff M. Phillips, and Feifei Li. "Continuous matrix approximation on distributed data." Proceedings of the VLDB Endowment 7, no. 10 (2014): 809–20. http://dx.doi.org/10.14778/2732951.2732954.

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Karczewicz, Marta, and Moncef Gabbouj. "ECG data compression by spline approximation." Signal Processing 59, no. 1 (1997): 43–59. http://dx.doi.org/10.1016/s0165-1684(97)00037-6.

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von Freyberg, Axel, and Andreas Fischer. "Holistic approximation of combined surface data." Precision Engineering 54 (October 2018): 396–402. http://dx.doi.org/10.1016/j.precisioneng.2018.07.009.

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Zhu, Xibin, Andrej Gisbrecht, Frank-Michael Schleif, and Barbara Hammer. "Approximation techniques for clustering dissimilarity data." Neurocomputing 90 (August 2012): 72–84. http://dx.doi.org/10.1016/j.neucom.2012.01.033.

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Dong, Bo, Matthew M. Lin, and Haesun Park. "Integer Matrix Approximation and Data Mining." Journal of Scientific Computing 75, no. 1 (2017): 198–224. http://dx.doi.org/10.1007/s10915-017-0531-7.

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Hońko, Piotr. "Compound approximation spaces for relational data." International Journal of Approximate Reasoning 71 (April 2016): 89–111. http://dx.doi.org/10.1016/j.ijar.2016.02.002.

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