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N-Step Sliding Recursion Formula of Variance and Its Implementation
Lang Yu,Gang He,Ahmad Khwaja Mutahir 한국정보처리학회 2020 Journal of information processing systems Vol.16 No.4
The degree of dispersion of a random variable can be described by the variance, which reflects the distance of the random variable from its mean. However, the time complexity of the traditional variance calculation algorithm is O(n), which results from full calculation of all samples. When the number of samples increases oron the occasion of high speed signal processing, algorithms with O(n) time complexity will cost huge amount of time and that may results in performance degradation of the whole system. A novel multistep recursive algorithm for variance calculation of the timevarying data series with O(1) time complexity (constant time) is proposed in this paper. Numerical simulation and experiments of the algorithm is presented and the results demonstrate that the proposed multistep recursive algorithm can effectively decrease computing time and hence significantly improve the variance calculation efficiency for timevarying data, which demonstrates the potential value for timeconsumption data analysis or high speed signal processing.
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