Error-Correcting Dimensionality Reduction for Accurate Data Processing
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Solution Overview
Problem
Current information reduction methods face challenges in finding a balance between data reduction, processing requirements, and the usefulness of the reduced data, particularly in big data and machine learning environments, where efficient data processing and accurate operations are crucial.
Innovation Solution
The implementation of multi-dimensional state-space representations and error correcting codes to convert data from a higher-dimensional space to a lower-dimensional space, allowing for effective operations and flexible tradeoffs in data reduction, using techniques such as hashing, compression, and error correction, while maintaining the accuracy of data processing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If data is reduced from higher-dimensional space to lower-dimensional space, then data processing efficiency is improved, but information loss increases
Solution Approach 1:
The patent transforms data by changing its dimensional parameters, converting from higher-dimensional space to lower-dimensional space through mathematical transformations. This allows efficient processing in reduced dimensions while using error correcting codes to maintain information integrity and enable recovery of original data characteristics.
Solution Approach 2:
Error correcting codes serve as an intermediary mechanism between the original high-dimensional data and the reduced low-dimensional representation. These codes embed redundancy in the transformed data, allowing accurate reconstruction and processing without complete information loss, thus mediating between dimensionality reduction and information preservation.
2Reliability
If error correcting codes are used in data reduction, then data integrity is improved, but processing complexity increases
Solution Approach 1:
Error correcting codes are incorporated into the data transformation process in advance, before the actual data processing occurs. This preliminary encoding ensures that integrity protection is built into the structure of the reduced data, allowing for reliable processing without adding complexity during the main operational phases.
3Measurement precision
If multi-dimensional state-space representations are used, then operational accuracy is improved, but computational requirements increase
Solution Approach 1:
The patent deliberately changes the dimensional representation of data, transforming complex multi-dimensional state-space representations into lower-dimensional forms. This dimensionality reduction maintains the essential operational accuracy needed for processing while significantly reducing the computational energy required to perform operations on the data.
Data Source
AI summary
Information reduction in data processing environments includes at least one of: one or more Error Correcting Codes that decode n-vectors into k-vectors and utilize said decoding to information-reduce data from a higher dimensional space into a lower dimensional space. The information reduction further provides for a hierarchy of information reduction allowing a variety of information reductions. Transformations are provided to utilize available data space, and data may be transformed using several techniques including windowing functions, filters in the time and frequency domains, or any numeric processing on the data.