We propose in this work a new method for estimating the main mode of multivariate distributions, with application to eye-tracking calibrations. 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 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 rely 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 distributions where other algorithms typically lack accuracy.
翻译:在这项工作中,我们提出了一个新的方法来估计多变量分布的主要模式,并应用到眼睛跟踪校准。当对诸如婴儿或猴子等合作性差的科目进行眼睛跟踪实验时,校准数据一般会受到高度污染。外部数据通常按组排列,与主体不看校准点的时间间隔相对应。在这种多式联运分布中,大多数中心趋势措施在估计主定点坐标(第一种模式)时都失败,导致在映射屏幕坐标时出现错误和不准确。在这里,我们开发了一种新的算法,以确定多种变量分布的第一种模式,即称为BRIL,它依靠的是循环式深度过滤法。这种新颖的方法通常在高斯和统一分布的人工混合物上进行测试,并与现有方法(常规深度中位、稳健的测距地点和散落点以及基于集群的方法)相比较。我们取得了出色的性能,即使在对屏幕坐标进行映射时,在屏幕坐标上映射出非常高的比例的分布时也是如此。我们用新的算法来确定多变量分布的第一个模式,即名为BRIL,它依靠递定式的深度过滤法。最后,我们用普通的模型来校验测算,在现实世界中,特别缺乏的模型中,我们的数据分布。