Ballquantile

Ballquantile is a statistical concept used in data analysis and visualization. It refers to the quantile of data that falls within a defined spherical region. This concept is particularly relevant in multidimensional datasets where traditional linear quantiles might not fully capture the distribution of data.

Imagine a set of data points scattered in a multi-dimensional space. A ballquantile considers a hypersphere, or a "ball," centered at a specific point, usually the median or mean of the data. The ballquantile then quantifies the proportion of data points that lie within or on the boundary of this ball. For instance, a 0.5 ballquantile would represent the radius of the ball that contains 50% of the data points.

This measure provides insights into the concentration and spread of data in a radial direction. It can be useful for understanding the typical extent of a cluster of points or identifying outliers that lie far from the central mass of the data. Unlike standard quantiles which measure position along a single axis, ballquantiles offer a way to assess data density in a spherical neighborhood. Its application can be found in fields like machine learning for clustering and anomaly detection, as well as in geographical data analysis to understand spatial distributions.