Comparison of linear correlation and a statistical dependency measure for inferring spatial relation of temperature sensors in buildings

Abstract

A large number of facility management tasks relying on sensor measurements require knowledge of the context under which the readings were collected. However, this context information (i.e. 'spatial metadata') is generally recorded manually, a process that is error-prone and time consuming considering the number of sensors located in a building. Therefore, as other researchers have pointed out, there is a need to automatically determine the location information. Inferring the relative locations of sensors with respect to each other is arguably the first step to take and previous work in this area has already shown promising initial results. In this paper, we explore whether linear correlation or a statistical dependency measure (in this case distance correlation) are better suited to infer spatial relations between a pair of temperature sensors in a commercial building. We conducted analyses on three different test beds where temperature measurements from 10 sensors were collected every minute. We consider every possible size of data subsets within a year to explore time-windowing effects. We also examine how different physical distances between sensors affect the results. We conclude that a linear correlation (the normalized covariance matrix) captures the spatial relationship in most situations although it is significantly sensitive to choosing the appropriate window size.