Big data interpolation using functional representation

Given a large set of measurement data, in order to identify a simple function that captures the essence of the data, we suggest representing the data by an abstract function, in particular by polynomials. We interpolate the datapoints to define a polynomial that would represent the data succinctly. The interpolation is challenging, since in practice the data can be noisy and even Byzantine where the Byzantine data represents an adversarial value that is not limited to being close to the correct measured data. We present two solutions, one that extends the Welch-Berlekamp technique (Error correction for algebraic block codes, 1986) to eliminate the outliers appearance in the case of multidimensional data, and copes with discrete noise and Byzantine data; and the other solution is based on Arora and Khot (J Comput Syst Sci 67(2):325–340, 2003) method which handles noisy data, and we have generalized it in the case of multidimensional noisy and Byzantine data.