Inner Product Computation via Random Projection
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Solution Overview
Problem
Existing methods for computing inner products in image and video processing, such as Orthogonal Matching Pursuit, require significant computational resources and multiplication operations, which can be inefficient, especially when dealing with sparse vectors or large datasets.
Innovation Solution
The method employs a comparison random projection approach using a sparse matrix with ±1 entries, transforming vectors using a Hadamard matrix and a random ±1 diagonal matrix, allowing for computation of inner products through addition and subtraction without multiplications, and forming binary vectors to approximate inner products efficiently.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional inner product computation methods are used, then computation accuracy is maintained, but computational complexity and processing time increase significantly
Solution Approach 1:
The patent replaces traditional multiplication-based inner product computation with addition-based computation through random projection. By transforming vectors into binary vectors and using Hamming distance, the system substitutes multiplication operations with simpler addition operations, significantly reducing computational complexity while maintaining accuracy for sparse vectors
Solution Approach 2:
The patent changes the parameter space from real-valued inner products to binary Hamming distances. By projecting vectors onto a random binary code space, the system transforms the computation domain from multiplication-heavy to addition-heavy operations, improving processing speed for sparse vector representations
2Use of energy by stationary object
If multiplication operations are used for inner product computation, then computation precision is maintained, but power consumption increases
Solution Approach 1:
The system substitutes multiplication operations with addition operations through random projection transformation. By converting the inner product computation into a Hamming distance calculation on binary vectors, the system reduces power consumption while maintaining sufficient precision for sparse vector comparisons in image and video processing
3Productivity
If sparse random projection is used, then computation efficiency improves, but accuracy degrades for non-sparse vectors
Solution Approach 1:
The patent applies local quality by adapting the projection method to the sparsity characteristics of the input vectors. For sparse vectors (common in image and video processing), the system uses sparse random projection to achieve high efficiency. The method automatically leverages the sparsity property to reduce computational operations while maintaining accuracy, and can handle non-sparse vectors through the same framework with appropriate parameter selection
Data Source
AI summary
A computationally efficient approach to determining inner products between feature vectors is provided that eliminates or reduces the need for multiplication, and more specifically, provides an efficient and accurate basis selection for techniques such as Orthogonal Matching Pursuit.