Binary Hashing Parameter Optimization for Distance Preservation
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Solution Overview
Problem
Existing binary hashing techniques face limitations in achieving accurate near or nearest neighbor search with sufficient accuracy, especially when patterns are concentrated in low-dimensional spaces, and they often require high computational costs due to the need for parameter learning and complex computations.
Innovation Solution
A method that optimizes hash function parameters using a continuous valued sigmoid function to transform data into binary codes, minimizing a cost function based on a distance matrix, which preserves distances within a certain threshold while decreasing for larger distances, thereby improving accuracy without significantly increasing computational complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the bit length K is increased to improve approximation accuracy, then the Hamming distance approaches the Euclidean distance more closely, but the computational cost and data length increase
Solution Approach 1:
The patent transforms the discrete binary hashing problem into a continuous optimization problem by using a sigmoid function to generate continuous-valued hash values. This allows the system to achieve better approximation accuracy without necessarily increasing the bit length K, as the continuous values provide finer granularity for distance representation. The key parameter change is moving from discrete binary values {-1, 1} to continuous values in the range (0, 1) through the sigmoid transformation.
Solution Approach 2:
The patent introduces a continuous-valued intermediary representation between the original high-dimensional data and the final binary codes. The sigmoid function acts as this intermediary, transforming the linear projection values into continuous hash values that better preserve distance relationships. This intermediary step allows for more accurate distance approximation without directly increasing the final binary code length, as the continuous values can be subsequently quantized or used in hybrid schemes.
2Measurement precision
If parameter learning is performed to improve hashing accuracy, then the near neighbor relation is better preserved, but the computational complexity increases
Solution Approach 1:
The patent employs an iterative optimization process where the hash function parameters (projection matrix and bias) are learned by minimizing a cost function that measures the discrepancy between Hamming distances and Euclidean distances. This feedback mechanism continuously adjusts the parameters based on how well the current hashing preserves neighborhood relationships, improving accuracy through guided optimization rather than random or heuristic parameter selection.
Solution Approach 2:
The patent replaces complex mechanical or geometric hashing constructions with a learned parametric model based on the sigmoid function. Instead of using fixed geometric transformations or complex hash function compositions, the system uses a simple linear projection followed by a sigmoid transformation, where the parameters are optimized through gradient-based methods. This substitution reduces the structural complexity while maintaining or improving accuracy through data-driven parameter optimization.
3Measurement precision
If a distance-preserving hash function is used to maintain distance relationships, then retrieval accuracy improves, but the hash function complexity increases
Solution Approach 1:
The patent changes the functional form of the hash function from simple linear thresholding to a sigmoid-based continuous transformation. This parameter change in the hash function's mathematical form enables better distance preservation because the sigmoid function's smooth gradient allows for more nuanced representation of distance relationships, particularly for points near the decision boundary, without requiring complex multi-layer transformations.
Solution Approach 2:
The sigmoid function introduces a smooth curved transformation instead of a sharp linear threshold. This curvature in the hash function allows for gradual transitions in hash values as the input distance changes, better preserving the continuous nature of distance relationships. The curved transformation effectively maps the linear projection space into a non-linear hash space that maintains distance proportions more accurately, particularly for near-neighbor relationships.
Data Source
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AI summary
There are provided a method, an apparatus, a system and a program for transforming into binary data based on learning of an entirely novel hash function, in which the transforming accuracy may be improved as the computation amount is suppressed from increasing. A hash function parameter optimization section that optimizes a parameter of a hash function is included. A data set of a plurality of items of data each represented by a data point on a space of D number dimensions is entered, D being a preset positive integer. The data set is transformed into a plurality of items of K-bit-long binary data, using, as each of K number hash functions that transforms the data into a binary representation based on a value of projection of the data point on a projection vector, a hash function having parameters optimized, where K is a preset positive integer. The hash function parameter optimization section finds a hash value, using a continuous valued hash function including, as a variable, the projection of the data point on the projection vector, and stores it as continuous valued learning data for binary transformation. Such parameter of the hash function that minimizes a cost function, defined based at least on a distance computed using a distance function and on a distance of the continuous valued learning data for binary transformation, is derived as the optimized parameter of the hash function. The distance function is such a one in which, as long as a distance between the data points is less than or equal to a predetermined distance parameter, the value of the function preserves the distance, but in which the value of the function decreases if the distance between the data points exceeds the distance parameter.