The Emptiness Inside: Finding Gaps, Valleys, and Lacunae with Geometric Data Analysis
The Emptiness Inside: Finding Gaps, Valleys, and Lacunae with Geometric Data Analysis
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DOI：
10.3847/1538-3881/ac961e
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发表时间：
2022-01
期刊：
影响因子：
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通讯作者：
Gabriella Contardo;D. Hogg;Jason A. S. Hunt;J. Peek;Yen-Chi Chen
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文献类型：
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作者：
Gabriella Contardo;D. Hogg;Jason A. S. Hunt;J. Peek;Yen-Chi Chen
数据缺口的发现在天体物理学中一直很重要。例如，动力系统中存在通过共振打开的运动学缺口，或者经验上很少见的具有特定半径的系外行星。数据集中的缺口是一种异常，但在一种不同寻常的意义上：它不是远离其他数据点的单个离群点，而是空间中的一个区域或一组点，与其周围环境相比是异常的。缝隙既有趣，又很难找到和描述，特别是当它们具有不平凡的形状时。在本文中，我们提出了一个统计量，它可以用来估计数据空间中一个点的(局部)“幸福感”。它使用密度估计的梯度和海森(因此需要两次可微的密度估计器)。这个统计量可以(几乎)在空间中的任何点上计算，并且不依赖于优化；它允许我们以一种通用和有效的方式突出显示任何维度和形状的密度不足的区域。我们举例说明了我们的方法在银河系盘面中附近恒星的速度分布，它显示了可能来自不同过程的间隙。识别和描述这些差距可能有助于确定它们的来源。我们在附录中提供了使用临界点和密度的海森性质来确定数据中的不足密度的实施说明和其他考虑因素。7 7这里给出的t方法的一个PYTHON实现可以在https://github.com/contardog/FindTheGap.上找到这里给出的测试方法的一个PYTHON实现可以在https://github.com/contardog/FindTheGap.上获得
Discoveries of gaps in data have been important in astrophysics. For example, there are kinematic gaps opened by resonances in dynamical systems, or exoplanets of a certain radius that are empirically rare. A gap in a data set is a kind of anomaly, but in an unusual sense: instead of being a single outlier data point, situated far from other data points, it is a region of the space, or a set of points, that is anomalous compared to its surroundings. Gaps are both interesting and hard to find and characterize, especially when they have nontrivial shapes. We present in this paper a statistic that can be used to estimate the (local) “gappiness” of a point in the data space. It uses the gradient and Hessian of the density estimate (and thus requires a twice-differentiable density estimator). This statistic can be computed at (almost) any point in the space and does not rely on optimization; it allows us to highlight underdense regions of any dimensionality and shape in a general and efficient way. We illustrate our method on the velocity distribution of nearby stars in the Milky Way disk plane, which exhibits gaps that could originate from different processes. Identifying and characterizing those gaps could help determine their origins. We provide in an appendix implementation notes and additional considerations for finding underdensities in data, using critical points and the properties of the Hessian of the density. 7 7 A Python implementation of t methods presented here is available at https://github.com/contardog/FindTheGap. A Python implementation of t methods presented here is available at https://github.com/contardog/FindTheGap.