Online Partitioned Local Depth for semi-supervised applications

TL;DR

The paper introduces online PaLD, an online extension of the partitioned local depth framework designed for fixed-reference semi-supervised and online anomaly detection tasks. By performing an upfront $O(n^3)$ preprocessing to construct a queryable cohesion network, it enables exact online integration of each new datum at $O(n^2)$ time, balancing accuracy with scalability. The authors present a concrete query formulation, including CohesionToNew and CohesionToS routines, and validate speedups while showcasing two health-care-centric applications: online anomaly detection and high-dimensional semi-supervised classification. The work discusses practical considerations, potential hybridization with approximation methods, and avenues for extending the approach to generalized PaLD frameworks and large-scale data contexts.

Abstract

We introduce an extension of the partitioned local depth (PaLD) algorithm that is adapted to online applications such as semi-supervised prediction. The new algorithm we present, online PaLD, is well-suited to situations where it is a possible to pre-compute a cohesion network from a reference dataset. After $O(n^3)$ steps to construct a queryable data structure, online PaLD can extend the cohesion network to a new data point in $O(n^2)$ time. Our approach complements previous speed up approaches based on approximation and parallelism. For illustrations, we present applications to online anomaly detection and semi-supervised classification for health-care datasets.

Figures (2)

• Figure 1: Example local focus for a fixed point $x$ and a random point $Y$ in two dimensions. Red points are outside the focus. Those in green (and $Z$ in blue) are in the focus and closer to $x$ while those in grey are closer to $Y$. Figure from bfl24.
• Figure 2: Visualization of the decision boundary between two reference classes or clusters.