Sparse Array Error Representation in Numeric Data
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Solution Overview
Problem
Checking for erroneous values in large data arrays is computationally expensive due to the need to examine each entry individually, especially when dealing with arrays containing information from multiple sources where errors can be present.
Innovation Solution
Generating a sparse array to represent invalid values in a data array, where zero-value entries are inferred from location information of non-zero entries, allowing for efficient storage and retrieval of invalid data entries, and creating a view into a larger data array using this sparse representation that preserves ordering for iterative operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If we check for erroneous values one at a time in large data arrays, then we can identify invalid data entries, but the computational cost becomes excessively high
Solution Approach 1:
The patent extracts only the erroneous values and their locations from the large data array, separating them from the valid data. By creating a sparse array that contains only the invalid entries with their positions and values, the system eliminates the need to examine every element in the original array, thus maintaining detection accuracy while dramatically improving computational efficiency.
Solution Approach 2:
The patent segments the data array into two distinct representations: the original dense array containing all data (valid and invalid) and a new sparse array containing only the erroneous entries. This segmentation allows the system to process only the problematic portions of data separately, reducing the overall computational burden while maintaining complete error detection capability.
2Loss of information
If we store all data entries in a dense array, then we maintain complete data information, but storing and processing invalid values becomes inefficient
Solution Approach 1:
The patent extracts only the erroneous values from the dense array and stores them in a separate sparse array structure. This extraction maintains complete information about invalid entries (their locations and values) while eliminating the inefficiency of storing and processing all valid entries alongside them, thus reducing data structure complexity without losing any information.
Solution Approach 2:
Instead of storing all valid values and marking invalid ones (conventional approach), the patent inverts the approach by storing only the invalid values and their positions. This inversion transforms the data structure from a dense representation of all data to a sparse representation of exceptions, reducing complexity while maintaining information completeness.
3Quantity of substance
If we create a sparse array with only non-zero entries, then storage space is reduced, but we must efficiently manage location and value information
Solution Approach 1:
The patent merges the location information and value information for erroneous entries into a unified sparse array structure. Each entry in the sparse array combines the position index and the actual invalid value, allowing efficient storage and retrieval operations. This merging reduces storage space by eliminating redundant zero entries while maintaining ease of operation through structured data organization.
Data Source
AI summary
In an embodiment, a computer system accesses various different data entries in dense data array, where at least one of those data entries in the dense data array is invalid. The computer system creates an associated sparse data array that includes multiple data entries with zero values as well as data entries with non-zero values. The non-zero data entries are configured to store location information and data values for each of the invalid data entries in the dense array. The zero-value data entries are inferred from the location information of the non-zero data entries. The computer system stores the location information and data values of the non-zero data entries in the sparse data array. Those data values stored in the sparse array are proportional to the number of invalid values in the dense array.