Sparse Data Signature Vectors Without Large Measurement Matrices
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Solution Overview
Problem
Current compressive sensing techniques require a large measurement matrix that is impractical for high-dimensionality sparse vectors, leading to unacceptably large memory allocation and computational complexity, 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 usage.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a large measurement matrix is used for compressive sensing of high-dimensionality sparse vectors, then the compressed signature can be generated, but the memory allocation and computational complexity become unacceptably large
Solution Approach 1:
The patent extracts only the necessary components for compression by directly processing non-zero elements of sparse vectors through key-value pairs, eliminating the need to store and process the entire large measurement matrix. This extraction approach generates compressed signatures without requiring the full measurement matrix in memory.
Solution Approach 2:
The patent segments the compression process into independent operations on individual key-value pairs, where each non-zero element is processed separately through hashing and modular arithmetic. This segmentation allows the computation to be distributed and avoids the need for a monolithic measurement matrix structure.
2Measurement precision
If a large measurement matrix is used for compressive sensing, then the compressed signature can be generated, but the computational complexity becomes unacceptably high
Solution Approach 1:
The patent implements self-service computation where the hashing function and modular arithmetic operations automatically generate the compression transformations needed for each key-value pair without requiring external measurement matrix data. The system serves its own compression needs through deterministic mathematical operations on the input data itself.
Solution Approach 2:
The patent changes the computational parameters from matrix multiplication operations to hashing and modular arithmetic operations. This parameter change transforms the computational complexity from O(mn) matrix operations to O(s) hash operations, where s is the sparsity level, dramatically improving computation efficiency.
3Ease of operation
If the location of sparse entries is unknown a priori, then the data can be processed without prior transformation, but the measurement matrix requirements become impractical
Solution Approach 1:
The patent creates a compressed copy of the sparse vector through deterministic hashing operations on the key-value pairs. This copying approach generates a signature that preserves the essential information without requiring the original measurement matrix structure, enabling storage-efficient representation of the sparse data.
Solution Approach 2:
The patent changes the representation parameters from dense vector form requiring measurement matrix multiplication to a hash-based signature form. This parameter change allows the system to work with unknown sparse locations by transforming the data into a compact representation that inherently handles sparsity without prior knowledge.
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.