Journal articles: 'Distance de covariance'

1

Székely, Gábor J., and Maria L. Rizzo. "Brownian distance covariance." Annals of Applied Statistics 3, no. 4 (December 2009): 1236–65. http://dx.doi.org/10.1214/09-aoas312.

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Székely, Gábor J., and Maria L. Rizzo. "Rejoinder: Brownian distance covariance." Annals of Applied Statistics 3, no. 4 (December 2009): 1303–8. http://dx.doi.org/10.1214/09-aoas312rej.

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Cope, Leslie. "Discussion of: Brownian distance covariance." Annals of Applied Statistics 3, no. 4 (December 2009): 1279–81. http://dx.doi.org/10.1214/00-aoas312c.

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Bickel, Peter J., and Ying Xu. "Discussion of: Brownian distance covariance." Annals of Applied Statistics 3, no. 4 (December 2009): 1266–69. http://dx.doi.org/10.1214/09-aoas312a.

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Kosorok, Michael R. "Discussion of: Brownian distance covariance." Annals of Applied Statistics 3, no. 4 (December 2009): 1270–78. http://dx.doi.org/10.1214/09-aoas312b.

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Feuerverger, Andrey. "Discussion of: Brownian distance covariance." Annals of Applied Statistics 3, no. 4 (December 2009): 1282–84. http://dx.doi.org/10.1214/09-aoas312d.

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Gretton, Arthur, Kenji Fukumizu, and Bharath K. Sriperumbudur. "Discussion of: Brownian distance covariance." Annals of Applied Statistics 3, no. 4 (December 2009): 1285–94. http://dx.doi.org/10.1214/09-aoas312e.

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Rémillard, Bruno. "Discussion of: Brownian distance covariance." Annals of Applied Statistics 3, no. 4 (December 2009): 1295–98. http://dx.doi.org/10.1214/09-aoas312f.

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Genovese, Christopher R. "Discussion of: Brownian distance covariance." Annals of Applied Statistics 3, no. 4 (December 2009): 1299–302. http://dx.doi.org/10.1214/09-aoas312g.

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Huo, Xiaoming, and Gábor J. Székely. "Fast Computing for Distance Covariance." Technometrics 58, no. 4 (October 1, 2016): 435–47. http://dx.doi.org/10.1080/00401706.2015.1054435.

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Matsui, Muneya, Thomas Mikosch, and Gennady Samorodnitsky. "Distance covariance for stochastic processes." Probability and Mathematical Statistics 37, no. 2 (May 14, 2018): 355–72. http://dx.doi.org/10.19195/0208-4147.37.2.9.

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DISTANCE COVARIANCE FOR STOCHASTIC PROCESSESThe distance covariance of two random vectors is a measure of their dependence. The empirical distance covariance and correlation can be used as statistical tools for testing whether two random vectors are independent. We propose an analog of the distance covariance for two stochastic processes defined on some interval. Their empirical analogs can be used to test the independence of two processes.

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12

Lyons, Russell. "Distance covariance in metric spaces." Annals of Probability 41, no. 5 (September 2013): 3284–305. http://dx.doi.org/10.1214/12-aop803.

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Dehling, Herold, Muneya Matsui, Thomas Mikosch, Gennady Samorodnitsky, and Laleh Tafakori. "Distance covariance for discretized stochastic processes." Bernoulli 26, no. 4 (November 2020): 2758–89. http://dx.doi.org/10.3150/20-bej1206.

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14

Székely, Gábor J., and Maria L. Rizzo. "On the uniqueness of distance covariance." Statistics & Probability Letters 82, no. 12 (December 2012): 2278–82. http://dx.doi.org/10.1016/j.spl.2012.08.007.

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15

Sheng, Wenhui, and Xiangrong Yin. "Sufficient Dimension Reduction via Distance Covariance." Journal of Computational and Graphical Statistics 25, no. 1 (January 2, 2016): 91–104. http://dx.doi.org/10.1080/10618600.2015.1026601.

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16

Matteson, David S., and Ruey S. Tsay. "Independent Component Analysis via Distance Covariance." Journal of the American Statistical Association 112, no. 518 (March 30, 2017): 623–37. http://dx.doi.org/10.1080/01621459.2016.1150851.

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17

Kosorok, Michael R. "Correction: Discussion of Brownian distance covariance." Annals of Applied Statistics 7, no. 2 (June 2013): 1247. http://dx.doi.org/10.1214/13-aoas636.

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Böttcher, Björn, Martin Keller-Ressel, and René L. Schilling. "Detecting independence of random vectors: generalized distance covariance and Gaussian covariance." Modern Stochastics: Theory and Applications 5, no. 3 (2018): 353–83. http://dx.doi.org/10.15559/18-vmsta116.

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19

Pitsillou, Maria, and Konstantinos Fokianos. "dCovTS: Distance Covariance/Correlation for Time Series." R Journal 8, no. 2 (2016): 324. http://dx.doi.org/10.32614/rj-2016-049.

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20

Lyons, Russell. "Errata to “Distance covariance in metric spaces”." Annals of Probability 46, no. 4 (July 2018): 2400–2405. http://dx.doi.org/10.1214/17-aop1233.

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21

Edelmann, Dominic, Tobias Terzer, and Donald Richards. "A Basic Treatment of the Distance Covariance." Sankhya B 83, S1 (March 3, 2021): 12–25. http://dx.doi.org/10.1007/s13571-021-00248-z.

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22

Andrei, Adin-Cristian, and Patrick M. McCarthy. "An omnibus approach to assess covariate balance in observational studies using the distance covariance." Statistical Methods in Medical Research 29, no. 7 (September 27, 2019): 1846–66. http://dx.doi.org/10.1177/0962280219878215.

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Adequate baseline covariate balance among groups is critical in observational studies designed to estimate causal effects. Propensity score-based methods are popular ways to achieve covariate balance among groups. Existing methods are not easily generalizable to situations in which covariates of mixed type are collected nor do they provide a convenient way to compare the overall covariate vector distributions. Instead, covariate balance is assessed at the individual covariate level, thus the potential for increased overall type I error. We propose the use of the distance covariance, developed by Székely and colleagues, as an omnibus test of independence between covariate vectors and study group. We illustrate the advantages of this methodology in simulated data and in a cardiac surgery study designed to assess the impact of preoperative statin therapy on outcomes.

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23

Dai, Deliang. "Mahalanobis Distances on Factor Model Based Estimation." Econometrics 8, no. 1 (March 5, 2020): 10. http://dx.doi.org/10.3390/econometrics8010010.

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A factor model based covariance matrix is used to build a new form of Mahalanobis distance. The distribution and relative properties of the new Mahalanobis distances are derived. A new type of Mahalanobis distance based on the separated part of the factor model is defined. Contamination effects of outliers detected by the new defined Mahalanobis distances are also investigated. An empirical example indicates that the new proposed separated type of Mahalanobis distances predominate the original sample Mahalanobis distance.

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24

Zhu, Hanbing, Rui Li, Riquan Zhang, and Heng Lian. "Nonlinear functional canonical correlation analysis via distance covariance." Journal of Multivariate Analysis 180 (November 2020): 104662. http://dx.doi.org/10.1016/j.jmva.2020.104662.

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25

Soler, Tomás, and Steven D. Johnson. "Alternative Geometric Determination of Altazimuthal‐Distance Covariance Matrices." Journal of Surveying Engineering 113, no. 2 (June 1987): 57–69. http://dx.doi.org/10.1061/(asce)0733-9453(1987)113:2(57).

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26

Janson, Svante. "On distance covariance in metric and Hilbert spaces." Latin American Journal of Probability and Mathematical Statistics 18, no. 1 (2021): 1353. http://dx.doi.org/10.30757/alea.v18-50.

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27

Porcu, Emilio, Moreno Bevilacqua, and Marc G. Genton. "Spatio-Temporal Covariance and Cross-Covariance Functions of the Great Circle Distance on a Sphere." Journal of the American Statistical Association 111, no. 514 (April 2, 2016): 888–98. http://dx.doi.org/10.1080/01621459.2015.1072541.

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28

Sheng, Wenhui, and Xiangrong Yin. "Direction estimation in single-index models via distance covariance." Journal of Multivariate Analysis 122 (November 2013): 148–61. http://dx.doi.org/10.1016/j.jmva.2013.07.003.

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29

Yao, Shun, Xianyang Zhang, and Xiaofeng Shao. "Testing mutual independence in high dimension via distance covariance." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 80, no. 3 (October 31, 2017): 455–80. http://dx.doi.org/10.1111/rssb.12259.

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30

Chen, Xianyan, Qingcong Yuan, and Xiangrong Yin. "Sufficient dimension reduction via distance covariance with multivariate responses." Journal of Nonparametric Statistics 31, no. 2 (December 28, 2018): 268–88. http://dx.doi.org/10.1080/10485252.2018.1562065.

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31

Tamura, Roy N., and Dennis D. Boos. "Minimum Hellinger Distance Estimation for Multivariate Location and Covariance." Journal of the American Statistical Association 81, no. 393 (March 1986): 223–29. http://dx.doi.org/10.1080/01621459.1986.10478264.

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32

Haddad, Firas. "Modified hotelling’s T2 control charts using modified mahalanobis distance." International Journal of Electrical and Computer Engineering (IJECE) 11, no. 1 (February 1, 2021): 284. http://dx.doi.org/10.11591/ijece.v11i1.pp284-292.

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This paper proposed new adjusted Hotelling’s T^2 control chart for individual observations. For this objective, bootstrap method for producing the individual observations were employed. To do so, both arithmetic mean vector and the covariance matrix in the traditional Hotelling’s T^2 chart were substituted by the trimmed mean vector and the covariance matrix of the robust scale estimators〖 Q〗_n, respectively which, in turn, its performance is carried out by simulated. In fact, the calculation of false alarms and the probability of detection outlier is used for determining the validity of this modified chart. The findings revealed a considerable significance in its performance.

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33

Lee, Seok Jin, Chi Min Oh, and Chil Woo Lee. "Improved Face Recognition Using 2D-LDA with Weighted Covariance Scatter." Applied Mechanics and Materials 571-572 (June 2014): 741–46. http://dx.doi.org/10.4028/www.scientific.net/amm.571-572.741.

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In this paper, we propose a newly developed 2D-LDA method based on weighted covariance scatter for face recognition. Existing LDA uses the transform matrix that maximizes distances between classes. In LDA, we have to convert from an image to one-dimensional vector as training vector. In 2D-LDA, on the other hand, we can directly use two-dimensional image itself as training matrix, so that the classification performance can be enhanced about 20% comparing LDA, since the training matrix preserves the spatial information of two-dimensional image. However 2D-LDA uses same calculation schema for transformation matrix and therefore both LDA and 2D-LDA has the heteroscedastic problem which means that the class classification cannot obtain beneficial information of spatial distances of class clusters since LDA uses only data correlation-based covariance matrix of the training data without any reference to distances between classes. In this paper, we propose a new method to apply training matrix of 2D-LDA by using WPS-LDA idea that calculates the reciprocal of distance between classes and apply this weight to between class scatter matrix. To evaluate the performance of proposed algorithm, we use the ORL face database that includes 40 people and 10 images individually. The experimental result shows that the discriminating power of proposed 2D-LDA with weighted between class scatter has been improved up to 2% than original 2D-LDA. This method has good performance especially when the distance between two classes is very close and the dimension of projection axis is low.

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34

Koenker, Roger, José A. F. Machado, Christopher L. Skeels, and Alan H. Welsh. "Momentary Lapses: Moment Expansions and the Robustness of Minimum Distance Estimation." Econometric Theory 10, no. 1 (March 1994): 172–97. http://dx.doi.org/10.1017/s0266466600008288.

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This paper explores the robustness of minimum distance (GMM) estimators focusing particularly on the effect of intermediate covariance matrix estimation on final estimator performance. Asymptotic expansions to order Op(n−3/2) are employed to construct O(n−2) expansions for the variance of estimators constructed from preliminary least-squares and general M-estimators. In the former case, there is a rather curious robustifying effect due to estimation of the Eicker-White covariance matrix for error distributions with sufficiently large kurtosis.

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35

Zhen, Yicun, and Fuqing Zhang. "A Probabilistic Approach to Adaptive Covariance Localization for Serial Ensemble Square Root Filters." Monthly Weather Review 142, no. 12 (December 1, 2014): 4499–518. http://dx.doi.org/10.1175/mwr-d-13-00390.1.

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Abstract This study proposes a variational approach to adaptively determine the optimum radius of influence for ensemble covariance localization when uncorrelated observations are assimilated sequentially. The covariance localization is commonly used by various ensemble Kalman filters to limit the impact of covariance sampling errors when the ensemble size is small relative to the dimension of the state. The probabilistic approach is based on the premise of finding an optimum localization radius that minimizes the distance between the Kalman update using the localized sampling covariance versus using the true covariance, when the sequential ensemble Kalman square root filter method is used. The authors first examine the effectiveness of the proposed method for the cases when the true covariance is known or can be approximated by a sufficiently large ensemble size. Not surprisingly, it is found that the smaller the true covariance distance or the smaller the ensemble, the smaller the localization radius that is needed. The authors further generalize the method to the more usual scenario that the true covariance is unknown but can be represented or estimated probabilistically based on the ensemble sampling covariance. The mathematical formula for this probabilistic and adaptive approach with the use of the Jeffreys prior is derived. Promising results and limitations of this new method are discussed through experiments using the Lorenz-96 system.

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36

Cabo, A. J., and A. J. Baddeley. "Line transects, covariance functions and set convergence." Advances in Applied Probability 27, no. 03 (September 1995): 585–605. http://dx.doi.org/10.1017/s0001867800027063.

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We define the ‘linear scan transform' G of a set in ℝ d using information observable on its one-dimensional linear transects. This transform determines the set covariance function, interpoint distance distribution, and (for convex sets) the chord length distribution. Many basic integral-geometric formulae used in stereology can be expressed as identities for G. We modify a construction of Waksman (1987) to construct a metric η for ‘regular' subsets of ℝ d defined as the L 1 distance between their linear scan transforms. For convex sets only, η is topologically equivalent to the Hausdorff metric. The set covariance function (of a generally non-convex set) depends continuously on its set argument, with respect to η and the uniform metric on covariance functions.

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37

Cabo, A. J., and A. J. Baddeley. "Line transects, covariance functions and set convergence." Advances in Applied Probability 27, no. 3 (September 1995): 585–605. http://dx.doi.org/10.2307/1428125.

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We define the ‘linear scan transform' G of a set in ℝd using information observable on its one-dimensional linear transects. This transform determines the set covariance function, interpoint distance distribution, and (for convex sets) the chord length distribution. Many basic integral-geometric formulae used in stereology can be expressed as identities for G. We modify a construction of Waksman (1987) to construct a metric η for ‘regular' subsets of ℝd defined as the L1 distance between their linear scan transforms. For convex sets only, η is topologically equivalent to the Hausdorff metric. The set covariance function (of a generally non-convex set) depends continuously on its set argument, with respect to η and the uniform metric on covariance functions.

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38

MATSUZAWA, Tomoki, Eisuke ITO, Raissa RELATOR, Jun SESE, and Tsuyoshi KATO. "Stochastic Dykstra Algorithms for Distance Metric Learning with Covariance Descriptors." IEICE Transactions on Information and Systems E100.D, no. 4 (2017): 849–56. http://dx.doi.org/10.1587/transinf.2016edp7320.

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39

Shang, Jun, Maoyin Chen, and Donghua Zhou. "Covariance eigenpairs neighbour distance for fault detection in chemical processes." Canadian Journal of Chemical Engineering 96, no. 2 (August 24, 2017): 455–62. http://dx.doi.org/10.1002/cjce.22920.

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40

Hu, Rui, Xing Qiu, and Galina Glazko. "A new gene selection procedure based on the covariance distance." Bioinformatics 26, no. 3 (December 8, 2009): 348–54. http://dx.doi.org/10.1093/bioinformatics/btp672.

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41

Yoon, Jiho, and Chulhee Lee. "Edge Detection Using the Bhattacharyya Distance with Adjustable Block Space." Electronic Imaging 2020, no. 10 (January 26, 2020): 133–1. http://dx.doi.org/10.2352/issn.2470-1173.2020.10.ipas-133.

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In this paper, we propose a new edge detection method for color images, based on the Bhattacharyya distance with adjustable block space. First, the Wiener filter was used to remove the noise as pre-processing. To calculate the Bhattacharyya distance, a pair of blocks were extracted for each pixel. To detect subtle edges, we adjusted the block space. The mean vector and covariance matrix were computed from each block. Using the mean vectors and covariance matrices, we computed the Bhattacharyya distance, which was used to detect edges. By adjusting the block space, we were able to detect weak edges, which other edge detections failed to detect. Experimental results show promising results compared to some existing edge detection methods.

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42

Morgan, D. D. V., and M. K. V. Carr. "Analysis of Experiments Involving Line Source Sprinkler Irrigation." Experimental Agriculture 24, no. 2 (April 1988): 169–76. http://dx.doi.org/10.1017/s001447970001591x.

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SUMMARYThe line-source sprinkler irrigation system provides a continuously variable water application rate, which depends on distance from the line-source. The system is simple to set up and minimizes the amount of land required for experimental work. As the irrigation treatments are allocated systematically, the assumptions of analysis of variance are not satisfied. It is proposed that the effects of irrigation treatments be assessed using analysis of covariance, with distance from the sprinkler line as covariate, thus adjusting for a linear fertility trend. This method of analysis provides an approximate residual mean square for the fitting of response curves, but could be vulnerable to a quadratic fertility trend.

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43

Yih, Jeng Ming. "Supervised Clustering Algorithm for University Student Learning Algebra." Advanced Materials Research 542-543 (June 2012): 1376–79. http://dx.doi.org/10.4028/www.scientific.net/amr.542-543.1376.

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The popular fuzzy c-means algorithm based on Euclidean distance function converges to a local minimum of the objective function, which can only be used to detect spherical structural clusters. Gustafson-Kessel clustering algorithm and Gath-Geva clustering algorithm were developed to detect non-spherical structural clusters. However, Gustafson-Kessel clustering algorithm needs added constraint of fuzzy covariance matrix, Gath-Geva clustering algorithm can only be used for the data with multivariate Gaussian distribution. In GK-algorithm, modified Mahalanobis distance with preserved volume was used. However, the added fuzzy covariance matrices in their distance measure were not directly derived from the objective function. In this paper, an improved Normalized Supervised Clustering Algorithm Based on FCM by taking a new threshold value and a new convergent process is proposed. The experimental results of real data sets show that our proposed new algorithm has the best performance. Not only replacing the common covariance matrix with the correlation matrix in the objective function in the Normalized Supervised Clustering Algorithm.

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44

Raschhofer, Jakob, Gabriel Kerekes, Corinna Harmening, Hans Neuner, and Volker Schwieger. "Estimating Control Points for B-Spline Surfaces Using Fully Populated Synthetic Variance–Covariance Matrices for TLS Point Clouds." Remote Sensing 13, no. 16 (August 6, 2021): 3124. http://dx.doi.org/10.3390/rs13163124.

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A flexible approach for geometric modelling of point clouds obtained from Terrestrial Laser Scanning (TLS) is by means of B-splines. These functions have gained some popularity in the engineering geodesy as they provide a suitable basis for a spatially continuous and parametric deformation analysis. In the predominant studies on geometric modelling of point clouds by B-splines, uncorrelated and equally weighted measurements are assumed. Trying to overcome this, the elementary errors theory is applied for establishing fully populated covariance matrices of TLS observations that consider correlations in the observed point clouds. In this article, a systematic approach for establishing realistic synthetic variance–covariance matrices (SVCMs) is presented and afterward used to model TLS point clouds by B-splines. Additionally, three criteria are selected to analyze the impact of different SVCMs on the functional and stochastic components of the estimation results. Plausible levels for variances and covariances are obtained using a test specimen of several dm—dimension. It is used to identify the most dominant elementary errors under laboratory conditions. Starting values for the variance level are obtained from a TLS calibration. The impact of SVCMs with different structures and different numeric values are comparatively investigated. Main findings of the paper are that for the analyzed object size and distances, the structure of the covariance matrix does not significantly affect the location of the estimated surface control points, but their precision in terms of the corresponding standard deviations. Regarding the latter, properly setting the main diagonal terms of the SVCM is of superordinate importance compared to setting the off-diagonal ones. The investigation of some individual errors revealed that the influence of their standard deviation on the precision of the estimated parameters is primarily dependent on the scanning distance. When the distance stays the same, one-sided influences on the precision of the estimated control points can be observed with an increase in the standard deviations.

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45

ZHANG, XUGUANG, XIAOLI LI, MING LIANG, and YANJIE WANG. "COVARIANCE TRACKING WITH FORGETTING FACTOR AND RANDOM SAMPLING." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 19, no. 03 (June 2011): 547–58. http://dx.doi.org/10.1142/s021848851100712x.

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Covariance matching is an excellent algorithm of target tracking. In this paper, forgetting factor and random sampling methods are proposed to improve the robustness and efficiency of covariance tracking. First, a distance function between covariance matrixes is weighted by using a forgetting factor based on a fuzzy membership function to overcome the disturbances from similar targets. Then a random sampling method is applied to reduce the computing time in covariance matching and to facilitate real-time object tracking. Experiment results show that the algorithm proposed in this paper can effectively mitigate the clutter and occlusion problems at a high computing speed.

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46

Iwamura, Masakazu, Shinichiro Omachi, and Hirotomo Aso. "Estimation of true Mahalanobis distance from eigenvectors of sample covariance matrix." Systems and Computers in Japan 35, no. 9 (2004): 30–38. http://dx.doi.org/10.1002/scj.10519.

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47

Chen, Chin Chun. "Using Mahalanobis Clustering Algorithm for College Student Learning Fundamental Mathematics." Advanced Materials Research 476-478 (February 2012): 2129–32. http://dx.doi.org/10.4028/www.scientific.net/amr.476-478.2129.

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The popular fuzzy c-means algorithm based on Euclidean distance function converges to a local minimum of the objective function, which can only be used to detect spherical structural clusters. Gustafson-Kessel clustering algorithm and Gath-Geva clustering algorithm were developed to detect non-spherical structural clusters. However, Gustafson-Kessel clustering algorithm needs added constraint of fuzzy covariance matrix, Gath-Geva clustering algorithm can only be used for the data with multivariate Gaussian distribution. In GK-algorithm, modified Mahalanobis distance with preserved volume was used. However, the added fuzzy covariance matrices in their distance measure were not directly derived from the objective function. In this paper, an improved Normalized Mahalanobis Clustering Algorithm Based on FCM by taking a new threshold value and a new convergent process is proposed. The experimental results of real data sets show that our proposed new algorithm has the best performance. Not only replacing the common covariance matrix with the correlation matrix in the objective function in the Normalized Mahalanobis Clustering Algorithm Based on FCM.

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48

Luo, Xiaodong, and Ibrahim Hoteit. "Covariance Inflation in the Ensemble Kalman Filter: A Residual Nudging Perspective and Some Implications." Monthly Weather Review 141, no. 10 (September 25, 2013): 3360–68. http://dx.doi.org/10.1175/mwr-d-13-00067.1.

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Abstract This article examines the influence of covariance inflation on the distance between the measured observation and the simulated (or predicted) observation with respect to the state estimate. In order for the aforementioned distance to be bounded in a certain interval, some sufficient conditions are derived, indicating that the covariance inflation factor should be bounded in a certain interval, and that the inflation bounds are related to the maximum and minimum eigenvalues of certain matrices. Implications of these analytic results are discussed, and a numerical experiment is presented to verify the validity of the analysis conducted.

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49

Pak, Jung Min. "Switching Extended Kalman Filter Bank for Indoor Localization Using Wireless Sensor Networks." Electronics 10, no. 6 (March 18, 2021): 718. http://dx.doi.org/10.3390/electronics10060718.

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This paper presents a new filtering algorithm, switching extended Kalman filter bank (SEKFB), for indoor localization using wireless sensor networks. SEKFB overcomes the problem of uncertain process-noise covariance that arises when using the constant-velocity motion model for indoor localization. In the SEKFB algorithm, several extended Kalman filters (EKFs) run in parallel using a set of covariance hypotheses, and the most probable output obtained from the EKFs is selected using Mahalanobis distance evaluation. Simulations demonstrated that the SEKFB can provide accurate and reliable localization without the careful selection of process-noise covariance.

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50

Pinele, Julianna, João E. Strapasson, and Sueli I. R. Costa. "The Fisher-Rao Distance between Multivariate Normal Distributions: Special Cases, Boundsand Applications." Entropy 22, no. 4 (April 1, 2020): 404. http://dx.doi.org/10.3390/e22040404.

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The Fisher–Rao distance is a measure of dissimilarity between probability distributions, which, under certain regularity conditions of the statistical model, is up to a scaling factor the unique Riemannian metric invariant under Markov morphisms. It is related to the Shannon entropy and has been used to enlarge the perspective of analysis in a wide variety of domains such as image processing, radar systems, and morphological classification. Here, we approach this metric considered in the statistical model of normal multivariate probability distributions, for which there is not an explicit expression in general, by gathering known results (closed forms for submanifolds and bounds) and derive expressions for the distance between distributions with the same covariance matrix and between distributions with mirrored covariance matrices. An application of the Fisher–Rao distance to the simplification of Gaussian mixtures using the hierarchical clustering algorithm is also presented.

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Journal articles on the topic 'Distance de covariance'

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