Estimating tukey depth using incremental quantile estimators

Abstract

Measures of distance or how data points are positioned relative to each other are fundamental in pattern recognition. The concept of depth measures how deep an arbitrary point is positioned in a dataset, and is an interesting concept in this regard. However, while this concept has received a lot of attention in the statistical literature, its application within pattern recognition is still limited.

To increase the applicability of the depth concept in pattern recognition, we address the well-known computational challenges associated with the depth concept, by suggesting to estimate depth using incremental quantile estimators. The suggested algorithm can not only estimate depth when the dataset is known in advance, but can also track depth for dynamically varying data streams by using recursive updates. The tracking ability of the algorithm was demonstrated based on a real-life application associated with detecting changes in human activity from real-time accelerometer observations. Given the flexibility of the suggested approach, it can detect virtually any kind of changes in the distributional patterns of the observations, and thus outperforms detection approaches based on the Mahalanobis distance.