Data Interpolation: An Efficient Sampling Alternative for Big Data Aggregation

Given a large set of measurement sensor data, in order to identify a simple function that captures the essence of the data gathered by the sensors, we suggest representing the data by (spatial) functions, in particular by polynomials. Given a (sampled) set of values, we interpolate the datapoints to define a polynomial that would represent the data. 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 in the case of multidimensional data, and copes with discrete noise and Byzantine data, and the other based on Arora and Khot techniques, extending them in the case of multidimensional noisy and Byzantine data. ∗Department of Computer Science, Ben-Gurion University, Beer-Sheva, 84105, Israel. Email: [email protected]. Partially supported by a Russian Israeli grant from the Israeli Ministry of Science and Technology and the Russian Foundation for Basic Research, the Rita Altura Trust Chair in Computer Sciences, the Lynne and William Frankel Center for Computer Sciences, Israel Science Foundation (grant number 428/11), Cabarnit Cyber Security MAGNET Consortium, Grant from the Institute for Future Defense Technologies Research named for the Medvedi of the Technion, MAFAT, and Israeli Internet Association †Department of Computer Science, Ben-Gurion University, Beer-Sheva, 84105, Israel. Email:[email protected]. Partially supported by Deutsche Telekom, Rita Altura Trust Chair in Computer Sciences, Lynne and William Frankel Center for Computer Sciences, Israel Science Foundation (grant number 428/11) and Cabarnit Cyber Security MAGNET Consortium. ‡Department of Communication Systems Engineering, Ben-Gurion University, Beer-Sheva, 84105, Israel. Email: [email protected].