Incremental Covariance Calculation for Big Data Streams
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Solution Overview
Problem
Current methods for processing and analyzing Big Data, particularly streamed data, are inefficient and resource-intensive, leading to slow response times and significant waste of computing resources due to the need to recalculate covariance for large datasets, which is exacerbated by the rapid growth and complexity of data streams in applications like real-time stock analysis and online gaming.
Innovation Solution
A computing system that incrementally calculates covariance by maintaining a computation subset size counter and updating components based on previous calculations, allowing for efficient recalculation of covariance without revisiting all data elements, thereby reducing computational load and resource usage.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional covariance calculation methods are used on Big Data or streamed data, then calculation accuracy is maintained, but computing resources are significantly wasted and response time is slow
Solution Approach 1:
The patent pre-calculates and stores covariance components (such as sum of squares and cross-products) as data elements are received, rather than calculating everything from scratch when a recalculation is needed. This preliminary action allows the system to maintain updated covariance values incrementally, avoiding the need to reprocess entire datasets.
Solution Approach 2:
The covariance calculation is broken down into separate maintainable components (e.g., sum of x values, sum of y values, sum of x², sum of y², sum of xy) that can be independently updated. Each component is maintained separately as data streams in, and the final covariance is composed from these segments, reducing the computational burden of any single operation.
2Measurement precision
If all data elements in computation subsets are accessed for covariance recalculation, then accurate covariance is obtained, but the number of operations increases significantly with large n
Solution Approach 1:
The system pre-computes and maintains running totals of necessary statistical components (sums and sum of squares) as data arrives. When covariance recalculation is needed, these pre-maintained values are used directly rather than recomputing from all individual data points, ensuring accuracy while dramatically reducing recalculation time.
Solution Approach 2:
The covariance components are continuously updated as new data elements arrive in the stream, maintaining an ever-current state of the statistics. This continuous update mechanism ensures that when recalculation is needed, the system already has near-final values that require minimal adjustment, rather than starting from scratch.
3Quantity of substance
If computation subset size n is increased to handle larger datasets, then more data is processed, but each data element requires repeated access for every covariance calculation
Solution Approach 1:
The large computation subset is handled by segmenting the covariance calculation into independent component maintenances. Each component (sum of x, sum of y, sum of xy, etc.) is updated independently as data arrives, avoiding the need to access and process the entire large subset repeatedly for each calculation.
Solution Approach 2:
The patent introduces intermediate statistical components (running sums and sum of squares) that mediate between the raw data elements and the final covariance calculation. These intermediaries accumulate information as data streams in, serving as a buffer that reduces the need for repeated direct access to the full computation subset.
4Reliability
If entire computation subsets are stored for covariance calculation, then complete data is available for analysis, but storage requirements become prohibitive for large n
Solution Approach 1:
The patent extracts only the essential statistical components needed for covariance calculation (sums and sum of squares of relevant variables) from the full data subset, storing only these compressed representations rather than the complete raw data. This extraction maintains sufficient information for accurate covariance computation while dramatically reducing storage requirements.
Solution Approach 2:
The system transforms the raw data into different parameter representations (aggregate statistics like sums and sum of squares) that preserve the necessary information for covariance calculation but occupy minimal storage space. This parameter transformation allows the system to maintain reliability for covariance computations without storing voluminous raw data.
Data Source
AI summary
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.