Fast algorithm for computing weighted projection quantiles and data depth for high-dimensional large data clouds

Abstract

In this paper we present a new algorithm based on a weighted projection quantiles for fast and frugal real time quantile estimation of large sized high dimensional data clouds. We present a projection quantile regression algorithm for high dimensional data. Second, we present a fast algorithm for computing the depth of a point or a new observation in relation to any high-dimensional data cloud, and propose a ranking system for multivariate data. Third, we briefly describe a real time rapid monitoring scheme similar to statistical process monitoring, for actionable analytics with big data. We believe these algorithms would be very useful for real time analysis of high dimensional `big data' sets including streaming data sets. The proposed algorithms would be of immense use in several application areas such as real time financial market analysis, real time remote health monitoring of patients using body area networked devices and real time pricing and inventory decisions in retail and manufacturing sector.