1. A computing-system-implemented method for calculating a correlation for two modified computation subsets on a computing-device-based computing system which comprises one or more computing devices and one or more storage media, each of the one or more computing devices comprising one or more processors, the method comprising: initializing, by the computing-device-based computing system, a specified computation subset size counter n (n≥6), at least one of a sum and a mean for each of two pre-modified computation subsets and one or more other components of a correlation for the two pre-modified computation subsets, wherein the two pre-modified computation subsets contains n pairs of data elements from at least one data set on at least one of the one or more storage media or at least one data stream; accessing or receiving, by the computing-device-based computing system, a pair of data elements to be added to the two pre-modified computation subsets; modifying, by the computing-device-based computing system, the two pre-modified computation subsets by: adding the accessed or received pair of data elements to the two pre-modified computation subsets; and modifying the computation subset size counter; incrementally deriving, by the computing-device-based computing system, at least one of a sum and a mean for each of the two modified computation subsets; directly incrementally deriving, by the computing-device-based computing system and based at least in part on the one or more components of the correlation other than a sum and a mean for the two pre-modified computation subsets, one or more components of a correlation other than a sum and a mean for the two modified computation subsets, wherein the incrementally deriving includes: accessing the one or more components other than a sum and a mean for the two pre-modified computation subsets without accessing all data elements in the two modified computation subsets to reduce data accessing latency thereby saving computing resources and reducing the computing-device-based computing system's power consumption; and adding any contribution of the added pair of data elements to each of the accessed components mathematically wherein not all data elements in the two modified computation subsets are used during the incrementally deriving one or more components of the correlation to reduce the number of operations performed by the computing-device-based computing system, thereby increasing calculation efficiency; and generating, by the computing-device-based computing system, a correlation for the two modified computation subsets based on one or more of the incrementally derived components.