Sparse Data Signature Vectors Without a Stored Measurement Matrix
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Solution Overview
Problem
Current compressive sensing techniques are impractical for high-dimensionality sparse vectors due to the large memory requirements for the measurement matrix, which is necessary for generating a compressed signature, especially when the location of sparse entries is unknown a priori.
Innovation Solution
A method to generate a compressed sensing signature without requiring a priori knowledge of the measurement matrix, using key-value pairs to calculate each element of the signature vector based on pseudo-random numbers generated from seeds created by the key and element identifier, allowing for efficient computation and reduced memory allocation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a measurement matrix is used to generate compressed signature of high-dimensionality sparse vectors, then the compressed representation can be obtained, but the memory requirements become prohibitively large
Solution Approach 1:
The patent extracts only the essential information needed for compression by directly processing non-zero elements of sparse vectors through hash functions and pseudo-random projections, eliminating the need to store and process the entire measurement matrix. This extraction approach computes compressed signatures on-the-fly from sparse data without requiring the full measurement matrix in memory.
Solution Approach 2:
The patent uses hash functions to map high-dimensional sparse vector indices to lower-dimensional signature indices, creating a compressed representation that copies only the necessary information. The pseudo-random projection values serve as compressed copies of the original data characteristics, enabling reconstruction without storing the full original vector or measurement matrix.
2Ease of operation
If the location of sparse entries is unknown a priori, then the data can be processed without prior transformation, but the computational complexity increases
Solution Approach 1:
The patent implements self-service by using the data's own non-zero elements and their indices to drive the compression process. The hash function processes each non-zero element's index to determine its contribution to signature elements, and the pseudo-random values are generated based on the element's position and value. This self-referential approach eliminates the need for external measurement matrices or prior knowledge of sparse locations.
Solution Approach 2:
The patent transforms the problem by changing parameters from fixed measurement matrix values to dynamic pseudo-random projections generated during processing. The hash function parameters and pseudo-random seed values adapt based on the actual data being processed, allowing the system to handle unknown sparse locations efficiently by generating appropriate projection values on-the-fly rather than requiring pre-computed fixed matrices.
Data Source
AI summary
A system and method for generating an m-dimensional signature vector in a computing device is provided. The signature vector may be generated from a plurality of key-value pairs, each comprising a unique identifier and an associated non-zero value. Each element of the m-dimensional signature vector is calculated based on a summation of a plurality of terms. Each of the terms is calculated from a respective key-value pair by generating a seed based on the key of the respective key-value pair and an element identifier associated with the vector element being calculated; generating a pseudo-random number from the generated seed; and multiplying the pseudo-random number by the value of the respective key-value pair, wherein m<<n.