Approximating Higher-Order Distances Using Random Projections
This addresses a known bottleneck in distance-based methods for machine learning practitioners dealing with high-dimensional data, though it is incremental as it partially fills a gap for p > 2.
The paper tackles the problem of efficiently estimating higher-order lp distances (e.g., l4) for large-scale machine learning applications, where existing methods are limited to p <= 2, and provides a simple method with theoretical analysis, extending to even p values like 6, 8, and 10.
We provide a simple method and relevant theoretical analysis for efficiently estimating higher-order lp distances. While the analysis mainly focuses on l4, our methodology extends naturally to p = 6,8,10..., (i.e., when p is even). Distance-based methods are popular in machine learning. In large-scale applications, storing, computing, and retrieving the distances can be both space and time prohibitive. Efficient algorithms exist for estimating lp distances if 0 < p <= 2. The task for p > 2 is known to be difficult. Our work partially fills this gap.