Spatial Interpolation Using Multiple Regression

Many real world data mining applications involve analyzing geo-referenced data. Frequently, this type of data sets are incomplete in the sense that not all geographical coordinates have measured values of the variable(s) of interest. This incompleteness may be caused by poor data collection, measurement errors, costs management and many other factors. These missing values may cause several difficulties in many applications. Spatial imputation/interpolation methods try to fill in these unknown values in geo-referenced data sets. In this paper we propose a new spatial imputation method based on machine learning algorithms and a series of data pre-processing steps. The key distinguishing factor of this method is allowing the use of data from faraway regions, contrary to the state of the art on spatial data mining. Images (e.g. from a satellite or video surveillance cameras) may also suffer from this incompleteness where some pixels are missing, which again may be caused by many factors. An image can be seen as a spatial data set in a Cartesian coordinates system, where each pixel (location) registers some value (e.g. degree of gray on a black and white image). Being able to recover the original image from a partial or incomplete version of the reality is a key application in many domains (e.g. surveillance, security, etc.). In this paper we evaluate our general methodology for spatial interpolation on this type of problems. Namely, we check the ability of our method to fill in unknown pixels on several images. We compare it to state of the art methods and provide strong experimental evidence of the advantages of our proposal.