Abstract: The present invention extends to methods, systems, and computing system program products for elimination of rounding error accumulation in iterative calculations for Big Data or streamed data. Embodiments of the invention include iteratively calculating a function for a primary computation window of a pre-defined size while incrementally calculating the function for one or more backup computation windows started at different time points and whenever one of the backup computation windows reaches a size of the pre-defined size, swapping the primary computation window and the backup computation window. The result(s) of the function is/are generated by either the iterative calculation performed for the primary computation window or the incremental calculation performed for a backup computation window which reaches the pre-defined size.

Abstract: The present invention extends to methods, systems, and computing system program products for elimination of rounding error accumulation in iterative calculations for Big Data or streamed data. Embodiments of the invention include iteratively calculating a function for a primary computation window of a pre-defined size while incrementally calculating the function for one or more backup computation windows started at different time points and whenever one of the backup computation windows reaches a size of the pre-defined size, swapping the primary computation window and the backup computation window. The result(s) of the function is/are generated by either the iterative calculation performed for the primary computation window or the incremental calculation performed for a backup computation window which reaches the pre-defined size.

Abstract: The present invention extends to methods, systems, and computing system program products for elimination of rounding error accumulation in iterative calculations for Big Data or streamed data. Embodiments of the invention include iteratively calculating a function for a primary computation window of a pre-defined size while incrementally calculating the function for one or more backup computation windows started at different time points and whenever one of the backup computation windows reaches a size of the pre-define size, swapping the primary computation window and the backup computation window. The result(s) of the function is/are always generated by the iterative calculation performed for the primary computation window. Elimination of rounding error accumulation enables a computing system to steadily and smoothly run iterative calculations for unlimited number of iterations without rounding error accumulation.

Abstract: The present invention extends to methods, systems, and computing system program products for dynamic correlation batch calculation for Big Data. Embodiments of the invention include calculating a correlation for a modified computation set based on a group of components calculated for the pre-modified computation set and one or more groups of components calculated for a computation set to be excluded from the pre-modified computation set and a computation set to be included in the pre-modified computation set, where the size of the to-be-included computation set may or may not be equal to the size of the to-be-excluded computation set. When the size of the to-be-excluded computation set is smaller than half the size of the pre-modified computation set, dynamic correlation batch calculation may reduce computations thereby increasing calculation efficiency, saving computation resources, and reducing computing system's power consumption.

Abstract: The present invention extends to methods, systems, and computing system program products for decrementally calculating autocorrelation for Big Data. Embodiments of the invention include decrementally calculating one or more components of autocorrelation at a specified lag for an adjusted computation window based on the one or more components of an autocorrelation at the specified lag calculated for a previous computation window and then calculating the autocorrelation at the specified lag based on one or more of the decrementally calculated components. Decrementally calculating autocorrelation avoids visiting all data elements in the adjusted computation window and performing redundant computations thereby increasing calculation efficiency, saving computing resources and reducing computing system's power consumption.

Abstract: The present invention extends to methods, systems, and computing system program products for decrementally calculating simple linear regression coefficients for Big Data or streamed data. Embodiments of the invention include decrementally calculating one or more components of simple linear regression coefficients for a modified computation set based on the one or more components of simple linear regression coefficients calculated for a previous computation set and then calculating the simple linear regression coefficients for the modified computation set based on the decrementally calculated components. Decrementally calculating simple linear regression coefficients avoids visiting all data elements in the modified computation set and performing redundant computations thereby increasing calculation efficiency, saving computing resources and reducing computing system's power consumption.

Abstract: The present invention extends to methods, systems, and computing system program products for iteratively calculating a Z-score for Big Data. Embodiments of the invention include iteratively calculating one or more components of a Z-score for a modified computation subset based on the one or more components of a Z-score calculated for a previous computation subset and then calculating a Z-score for a selected data element in the modified computation subset based on one or more of the iteratively calculated components. Iteratively calculating a Z-score avoids visiting all data elements in the modified computation subset and performing redundant computations thereby increasing calculation efficiency, saving computing resources and reducing computing system's power consumption.

Abstract: The present invention extends to methods, systems, and computing system program products for incrementally calculating variance and/or standard deviation for Big Data or streamed data. Embodiments of the invention include incrementally calculating one or more components of a variance and/or a standard deviation for a modified computation subset based on one or more components of the variance and/or the standard deviation calculated for a previous computation subset and then calculating variance and/or standard deviation based on the incrementally calculated components. Incrementally calculating the components of a variance and/or a standard deviation avoids visiting all data elements in the modified computation subset and performing redundant computations thereby increasing calculation efficiency, saving computing resources and reducing computing system's power consumption.

Abstract: The present invention extends to methods, systems, and computing system program products for incrementally calculating Z-score for Big Data or streamed data. Embodiments of the invention include incrementally calculating one or more components of a Z-score for a modified computation subset based on one or more components of a Z-score calculated for a pre-modified computation subset and then calculating a Z-score for a selected data element in the modified computation subset based on one or more of the incrementally calculated components. Incrementally calculating Z-score avoids visiting all data elements in the modified computation subset and performing redundant computations thereby increasing calculation efficiency, saving computing resources and reducing computing system's power consumption.

Abstract: The present invention extends to methods, systems, and computing system program products for incrementally calculating skewness for Big Data or streamed data in real time by incrementally calculating one or more components of skewness. Embodiments of the invention include incrementally calculating one or more components of skewness in a modified computation subset based on the one or more components of the skewness calculated for a previous computation subset and then calculating the skewness based on the incrementally calculated components. Incrementally calculating skewness avoids visiting all data elements in the modified computation subset and performing redundant computations thereby increasing calculation efficiency, saving computing resources and reducing computing system's power consumption.

Abstract: The present invention extends to methods, systems, and computing system program products for iteratively calculating kurtosis for Big Data. Embodiments of the invention include iteratively calculating one or more components of a kurtosis in a modified computation subset based on the one or more components of the kurtosis calculated for a previous computation subset and then calculating the kurtosis based on the iteratively calculated components. Iteratively calculating kurtosis avoids visiting all data elements in the modified computation subset and performing redundant computations thereby increasing calculation efficiency, saving computing resources and reducing computing system's power consumption.

Abstract: The present invention extends to methods, systems, and computing system program products for iteratively calculating autocorrelation at a specified lag for streamed data in real time by iteratively calculating one or more components of autocorrelation at the specified lag l for a computation window of size n. Embodiments of the invention include iteratively calculating one or more components of autocorrelation at the specified lag l for an adjusted computation window based on the one or more components of the autocorrelation at the specified lag l calculated for a previous computation window and then calculating the autocorrelation at the specified lag l using the components. Iteratively calculating autocorrelation avoids visiting all data elements in the adjusted computation window and performing redundant computations thereby increasing calculation efficiency, saving computing resources and reducing computing system's power consumption.

Abstract: The present invention extends to methods, systems, and computing system program products for incrementally calculating autocorrelation for streamed data in real time. Embodiments of the invention include incrementally calculating one or more components of autocorrelation at a specified lag for an adjusted computation window based on the one or more components of the autocorrelation at the specified lag calculated for a previous computation window and then calculating the autocorrelation the specified lag using the components. Incrementally calculating autocorrelation avoids visiting and storing all data elements in the adjusted computation window and performing redundant computations thereby increasing calculation efficiency, saving computing resources and reducing computing system's power consumption.

Abstract: The present invention extends to methods, systems, and computing system program products for iteratively calculating autocorrelation at a specified lag for Big Data or streamed data in real time by iteratively calculating one or more components of autocorrelation at the specified lag l for a computation window of size n. Embodiments of the invention include iteratively calculating one or more components of autocorrelation at the specified lag l for an adjusted computation window based on the one or more components of the autocorrelation at the specified lag l calculated for a previous computation window and then calculating the autocorrelation at the specified lag l using the components. Iteratively calculating autocorrelation avoids visiting all data elements in the adjusted computation window and performing redundant computations thereby increasing calculation efficiency, saving computing resources and reducing computing system's power consumption.

Abstract: The present invention extends to methods, systems, and computing system program products for incrementally calculating autocorrelation for Big Data. Embodiments of the invention include incrementally calculating one or more components of an autocorrelation at a specified lag for an adjusted computation window by incrementally calculating one or more components of an autocorrelation at the specified lag calculated for a previous computation window and then calculating the autocorrelation at the specified lag for the adjusted computation window based on one or more incrementally calculated components. Incrementally calculating autocorrelation avoids visiting all data elements in the adjusted computation window and performing redundant computations thereby increasing calculation efficiency, saving computing resources and reducing computing system's power consumption.

Abstract: The present invention extends to methods, systems, and computing system program products for incrementally calculating kurtosis for Big Data or streamed data in real time by incrementally calculating one or more components of kurtosis. Embodiments of the invention include incrementally calculating one or more components of a kurtosis for a modified computation subset based on the one or more components of the kurtosis calculated for a pre-modified computation subset and then calculating the kurtosis based on the incrementally calculated components. Incrementally calculating kurtosis avoids visiting all data elements in the modified computation subset and performing redundant computations thereby increasing calculation efficiency, saving computing resources and reducing computing system's power consumption.

Abstract: The present invention extends to methods, systems, and computing system program products for incrementally calculating covariance for Big Data or streamed data. Embodiments of the invention include incrementally calculating one or more components of a covariance for two modified computation subsets based on one or more components of the covariance calculated for two previous computation subsets and then calculating covariance based on the incrementally calculated components. Incrementally calculating the components of a covariance avoids visiting all data elements in the modified computation subsets and performing redundant computations thereby increasing calculation efficiency, saving computing resources and reducing computing system's power consumption.

Abstract: The present invention extends to methods, systems, and computing system program products for decrementally calculating kurtosis for Big Data or streamed data. Embodiments of the invention include decrementally calculating one or more components of a kurtosis for an adjusted computation subset based on one or more components of the kurtosis calculated for a previous computation subset and then calculating the kurtosis based on the components. Decrementally calculating kurtosis avoids visiting all data elements in the adjusted computation subset and performing redundant computations thereby increasing calculation efficiency, saving computing resources and reducing computing system's power consumption.

Abstract: The present invention extends to methods, systems, and computing system program products for decrementally calculating correlation for Big Data or streamed data. Embodiments of the invention include decrementally calculating one or more components of a correlation for two modified computation subsets based on one or more components of the correlation calculated for two previous computation subsets and then calculating the correlation for the modified computation subsets based on the decrementally calculated components. Decrementally calculating the components of a correlation avoids visiting all data elements in the modified computation subsets and performing redundant computations thereby increasing calculation efficiency, saving computation resources, and reducing computing system's power consumption.

Abstract: The present invention extends to methods, systems, and computing system program products for iteratively calculating kurtosis for streamed data. Embodiments of the invention include iteratively calculating one or more components of a kurtosis in an adjusted computation window based on the one or more components of the kurtosis calculated for a previous computation window and then calculating the kurtosis based on the iteratively calculated components. Iteratively calculating a kurtosis avoids visiting all data elements in the adjusted computation window and performing redundant computations thereby increasing calculation efficiency, saving computing resources and reducing computing system's power consumption.