Incremental autocorrelation calculation for big data using components

A computing system, the computing system comprising:

• one or more computing devices;
• each computing device comprising one or more processors;
• one or more storage media comprising a data set;
• and
• one or more calculation modules that, when executed by at least one of the one or more computing devices, determine an autocorrelation at a specified lag l for an adjusted computation window, wherein determination of the autocorrelation includes to:
• a. initialize a lag l (l>0), a computation window size counter n (n>2*l+1), a sum or a mean or both, and one or more other components of an autocorrelation at lag l for a pre-adjusted computation window containing n data elements of the data set;
• b. access or receive a data element of the data set to be added to the pre-adjusted computation window;
• c. adjust the pre-adjusted computation window by adding the to-be-added data element to the pre-adjusted computation window and adjusting the computation window size counter by increasing its value by 1;
• d. incrementally calculate a sum or a mean or both for the adjusted computation window;
• e. directly incrementally calculate one or more components of an autocorrelation at lag l other than a sum and a mean for the adjusted computation window based at least in part on the one or more components of the autocorrelation at lag l other than a sum and a mean initialized or calculated for the pre-adjusted computation window, wherein incremental calculation of the one or more components includes to mathematically add any contribution of the added data element to each of the one or more components of the autocorrelation at lag l initialized or calculated for the pre-adjusted computation window respectively without accessing and using all data elements in the adjusted computation window to reduce data access latency and operations performed by the computing system, thereby increasing calculation efficiency, saving computing resources and reducing the computing system's power consumption;
• and
• f. generate an autocorrelation at lag l for the adjusted computation window based on one or more of the incrementally calculated components.

A computing system program product for use at a configured computing system that 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 computing system program product comprising one or more non-transitory computing-device-readable storage media having stored thereon computing-device-executable instructions that, when executed by at least one of the one or more computing devices in the configured computing system, cause the configured computing system to perform a method for generating an autocorrelation at a specified lag for an adjusted computation window, the method including steps to:

• initialize, by the configured computing system, a lag l (l>0), a computation window size counter n (n>2*l+1), a sum or a mean or both, and one or more other components of an autocorrelation at lag l for a pre-adjusted computation window of a data set on at least one of the one or more storage media;
• access or receive, by the configured computing system, a data element of the data set to be added to the pre-adjusted computation window;
• adjust, by the configured computing system, the pre-adjusted computation window, by adding the to-be-added data element to the pre-adjusted computation window and increasing the computation window size counter by 1;
• incrementally calculate, by the configured computing system, a sum or a mean or both for the adjusted computation window;
• directly incrementally calculate, by the configured computing system, one or more components of an autocorrelation at lag l other than a sum and a mean for the adjusted computation window based at least in part on the one or more components of the autocorrelation at lag l other than a sum and a mean for the pre-adjusted computation window, including to:
• access or receive l data elements without counting the added data element from each side of the adjusted computation window respectively without accessing or receiving all data elements in the adjusted computation window to reduce data access latency, save computing resources and reduce the configured computing system's power consumption;
• access the one or more components of the autocorrelation at lag l other than a sum and a mean initialized or calculated for the pre-adjusted computation window;
• and
• add any contribution of the added data element to each of the accessed components mathematically based on the accessed or received data elements without using all data elements in the adjusted computation window to reduce the number of operations performed by the configured computing system thereby increasing calculation efficiency;
• and
• generate, by the configured computing system, an autocorrelation at lag l for the adjusted computation window based on one or more of the incrementally calculated components.