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Brilhault A, Neuenschwander S, Rios RA. A new robust multivariate mode estimator for eye-tracking calibration. Behav Res Methods 2023; 55:516-553. [PMID: 35297014 DOI: 10.3758/s13428-022-01809-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 01/27/2022] [Indexed: 11/08/2022]
Abstract
We propose in this work a new method for estimating the main mode of multivariate distributions, with application to eye-tracking calibration. When performing eye-tracking experiments with poorly cooperative subjects, such as infants or monkeys, the calibration data generally suffer from high contamination. Outliers are typically organized in clusters, corresponding to fixations in the time intervals when subjects were not looking at the calibration points. In this type of multimodal distributions, most central tendency measures fail at estimating the principal fixation coordinates (the first mode), resulting in errors and inaccuracies when mapping the gaze to the screen coordinates. Here, we developed a new algorithm to identify the first mode of multivariate distributions, named BRIL, which relies on recursive depth-based filtering. This novel approach was tested on artificial mixtures of Gaussian and Uniform distributions, and compared to existing methods (conventional depth medians, robust estimators of location and scatter, and clustering-based approaches). We obtained outstanding performances, even for distributions containing very high proportions of outliers, both grouped in clusters and randomly distributed. Finally, we demonstrate the strength of our method in a real-world scenario using experimental data from eye-tracking calibrations with Capuchin monkeys, especially for highly contaminated distributions where other algorithms typically lack accuracy.
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Affiliation(s)
- Adrien Brilhault
- Department of Computer Science, Federal University of Bahia, Salvador, Brazil
| | | | - Ricardo Araujo Rios
- Department of Computer Science, Federal University of Bahia, Salvador, Brazil.
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Francisci G, Agostinelli C, Nieto-Reyes A, Vidyashankar AN. Analytical and statistical properties of local depth functions motivated by clustering applications. Electron J Stat 2023. [DOI: 10.1214/23-ejs2110] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/11/2023]
Affiliation(s)
| | | | - Alicia Nieto-Reyes
- Department of Mathematics, Statistics and Computer Science, Universidad de Cantabria
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Armaut S, Diel R, Laloë T. Depth level set estimation and associated risk measures. Electron J Stat 2022. [DOI: 10.1214/22-ejs2095] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Affiliation(s)
- Sara Armaut
- Université Côte d’Azur, Laboratoire Jean Alexandre Dieudonné, Parc Valrose, 06108 NICE Cedex 02, France
| | - Roland Diel
- Université Côte d’Azur, Laboratoire Jean Alexandre Dieudonné, Parc Valrose, 06108 NICE Cedex 02, France
| | - Thomas Laloë
- Université Côte d’Azur, Laboratoire Jean Alexandre Dieudonné, Parc Valrose, 06108 NICE Cedex 02, France
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Dehghan S, Faridrohani MR. Multivariate tests for the multi‐sample location problem based on depth function. Stat (Int Stat Inst) 2021. [DOI: 10.1002/sta4.423] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Sakineh Dehghan
- Department of Statistics, Faculty of Mathematical Sciences University of Shahid Beheshti Tehran Iran
| | - Mohammad Reza Faridrohani
- Department of Statistics, Faculty of Mathematical Sciences University of Shahid Beheshti Tehran Iran
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Tat S, Faridrohani MR. A new type of multivariate records: depth-based records. STATISTICS-ABINGDON 2021. [DOI: 10.1080/02331888.2021.1925280] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Samaneh Tat
- Department of Statistics, Faculty of Mathematics, Shahid Beheshti University, Tehran, Iran
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Awan J, Slavković A. Structure and Sensitivity in Differential Privacy: Comparing K-Norm Mechanisms. J Am Stat Assoc 2021. [DOI: 10.1080/01621459.2020.1773831] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Jordan Awan
- Department of Statistics, The Pennsylvania State University, University Park, PA
| | - Aleksandra Slavković
- Department of Statistics, The Pennsylvania State University, University Park, PA
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Affiliation(s)
- Kai Qi
- Department of Statistics, Florida State University, Tallahassee, FL 32306-4330
| | - Yang Chen
- Department of Statistics, Florida State University, Tallahassee, FL 32306-4330
| | - Wei Wu
- Department of Statistics, Florida State University, Tallahassee, FL 32306-4330
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Hydrological modelling in data-scarce catchments: Black Volta basin in West Africa. SN APPLIED SCIENCES 2020. [DOI: 10.1007/s42452-020-2454-4] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022] Open
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Affiliation(s)
| | - Julie Josse
- École Polytechnique, CMAP, INRIA XPOP, Palaiseau Cedex, France
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Liu X, Mosler K, Mozharovskyi P. Fast Computation of Tukey Trimmed Regions and Median in Dimension p > 2. J Comput Graph Stat 2019. [DOI: 10.1080/10618600.2018.1546595] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Xiaohui Liu
- School of Statistics, Research Center of Applied Statistics, Jiangxi University of Finance and Economics, Nanchang, China
| | - Karl Mosler
- Institute of Econometrics and Statistics, University of Cologne, Köln, Germany
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Chowdhury J, Chaudhuri P. Nonparametric depth and quantile regression for functional data. BERNOULLI 2019. [DOI: 10.3150/17-bej991] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Dehghan S, Faridrohani MR. Affine invariant depth-based tests for the multivariate one-sample location problem. TEST-SPAIN 2018. [DOI: 10.1007/s11749-018-0593-3] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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15
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Brunel VE. Concentration of the empirical level sets of Tukey’s halfspace depth. Probab Theory Relat Fields 2018. [DOI: 10.1007/s00440-018-0850-0] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
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Makinde OS, Fasoranbaku OA. On maximum depth classifiers: depth distribution approach. J Appl Stat 2018. [DOI: 10.1080/02664763.2017.1342783] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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Makinde OS, Adewumi AD. A comparison of depth functions in maximal depth classification rules. JOURNAL OF MODERN APPLIED STATISTICAL METHODS 2017. [DOI: 10.22237/jmasm/1493598120] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022]
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Kosiorowski D, Rydlewski JP, Snarska M. Detecting a structural change in functional time series using local Wilcoxon statistic. Stat Pap (Berl) 2017. [DOI: 10.1007/s00362-017-0891-y] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Kuelbs J, Zinn J. Convergence of quantile and depth regions. Stoch Process Their Appl 2016. [DOI: 10.1016/j.spa.2016.04.011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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He Y, Einmahl JHJ. Estimation of extreme depth-based quantile regions. J R Stat Soc Series B Stat Methodol 2016. [DOI: 10.1111/rssb.12163] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Affiliation(s)
- Yi He
- Tilburg University; The Netherlands
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Bell RC, Jones-Farmer LA, Billor N. A Distribution-Free Multivariate Phase I Location Control Chart for Subgrouped Data from Elliptical Distributions. Technometrics 2014. [DOI: 10.1080/00401706.2013.879264] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Denecke L, Müller CH. New robust tests for the parameters of the Weibull distribution for complete and censored data. METRIKA 2013. [DOI: 10.1007/s00184-013-0454-8] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Indexing Reverse Top-k Queries in Two Dimensions. DATABASE SYSTEMS FOR ADVANCED APPLICATIONS 2013. [DOI: 10.1007/978-3-642-37487-6_17] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
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Tsao M. An empirical depth function for multivariate data. Stat Probab Lett 2013. [DOI: 10.1016/j.spl.2012.09.007] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Terán P. Centrality as a gradual notion: A new bridge between fuzzy sets and statistics. Int J Approx Reason 2011. [DOI: 10.1016/j.ijar.2011.03.003] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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Zuo Y, Lai S. Exact computation of bivariate projection depth and the Stahel–Donoho estimator. Comput Stat Data Anal 2011. [DOI: 10.1016/j.csda.2010.09.010] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Hallin M, Paindaveine D, Šiman M. Multivariate quantiles and multiple-output regression quantiles: From L1 optimization to halfspace depth. Ann Stat 2010. [DOI: 10.1214/09-aos723] [Citation(s) in RCA: 155] [Impact Index Per Article: 11.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Wellmann R, Harmand P, Müller CH. Distribution-free tests for polynomial regression based on simplicial depth. J MULTIVARIATE ANAL 2009. [DOI: 10.1016/j.jmva.2008.06.009] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Dang X, Serfling R, Zhou W. Influence functions of some depth functions, and application to depth-weighted L-statistics. J Nonparametr Stat 2009. [DOI: 10.1080/10485250802447981] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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48
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Affiliation(s)
- Robert Serfling
- Department of Mathematical Sciences, University of Texas at Dallas
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49
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Li J, Liu RY. Multivariate spacings based on data depth: I. Construction of nonparametric multivariate tolerance regions. Ann Stat 2008. [DOI: 10.1214/07-aos505] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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50
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Cui X, Lin L, Yang G. An Extended Projection Data Depth and Its Applications to Discrimination. COMMUN STAT-THEOR M 2008. [DOI: 10.1080/03610920701858396] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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