Abstract
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.
Partially supported by a Russian Israeli grant from the Israeli Ministry of Science and Technology #85387301-“Algorithmic approaches to energy savings” 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.
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Daltrophe, H., Dolev, S., Lotker, Z. (2013). Big Data Interpolation an Efficient Sampling Alternative for Sensor Data Aggregation. In: Bar-Noy, A., Halldórsson, M.M. (eds) Algorithms for Sensor Systems. ALGOSENSORS 2012. Lecture Notes in Computer Science, vol 7718. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36092-3_8
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DOI: https://doi.org/10.1007/978-3-642-36092-3_8
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