A* Lattice Hash Code Generation for High-Dimensional Vectors
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Solution Overview
Problem
Existing multi-probe locality sensitive hash methods for image segmentation and classification are inefficient, particularly in high-dimensional spaces, as they require O(n^2) operations to generate hash codes, leading to prolonged processing times and potential false-negative matches.
Innovation Solution
The method determines an ordering of dimensions for a lattice hole in an A* lattice nearest to the query vector, uses predetermined constants to generate an initial hash code, and modifies it to produce subsequent hash codes, reducing the number of operations required for hash code generation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If multi-probe locality sensitive hash methods are used to generate hash codes for high-dimensional feature vectors, then the accuracy of finding matching patches is improved, but the computational complexity increases to O(n^2) operations
Solution Approach 1:
The patent segments the high-dimensional feature space by representing feature vectors as points in an n-dimensional lattice and partitioning the space into lattice cells. This segmentation allows efficient indexing and retrieval by dividing the complex search space into manageable lattice-based regions, reducing the O(n^2) complexity while maintaining matching accuracy.
Solution Approach 2:
The patent transforms the problem from operating directly on n-dimensional feature vectors to operating on lattice points in an extended n+1 dimensional space. By embedding the n-dimensional feature space into an (n+1)-dimensional lattice space, the patent enables more efficient hash code generation and similarity search with reduced computational complexity.
2Productivity
If traditional hash-based patch matching methods are used, then the processing speed is improved, but false-negative matches occur when vectors are close but return different hash codes
Solution Approach 1:
The patent changes the hash function parameters by using lattice-based hashing where hash codes are generated from lattice point coordinates rather than direct feature vector quantization. This parameter change ensures that nearby feature vectors map to nearby lattice points, reducing false negatives while maintaining fast processing speed through efficient lattice operations.
Solution Approach 2:
The patent introduces lattice points as an intermediary between feature vectors and hash codes. Instead of directly hashing feature vectors, the method first maps vectors to lattice points and then generates hash codes from the lattice point coordinates. This intermediary step preserves spatial relationships and reduces false-negative matches.
Data Source
AI summary
A method of generating hash codes from a query vector. An ordering of dimensions is determined for a lattice hole in an A* lattice, the lattice hole being located nearest to the query vector and the ordering of dimensions represents a mapping applied to transform a canonical hole of the A* lattice to the lattice hole. An initial hash code is determined for a first point in the A* lattice, based on the query vector, using a plurality of predetermined constants. A subsequent hash code is generated for a second point in the A* lattice, from the initial hash code by modifying the initial hash code by a multiple of a constant. The constant is selected from the plurality of predetermined constants using the determined ordering of dimensions.