Large-Scale Density-Based Clustering With Modified Ternary Search
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Solution Overview
Problem
Density-based clustering algorithms face challenges in parameter tuning, particularly in high-dimensional and large-scale datasets, leading to over-segmentation or under-segmentation, which affects the quality and interpretability of clustering results.
Innovation Solution
A modified ternary search algorithm is employed to efficiently tune density-based clustering algorithms by leveraging the near-unimodality of the neighborhood radius parameter, using initial upper and lower bounds that are closer to the optimal value, reducing computational time and resources.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional parameter tuning methods are used for density-based clustering, then the algorithm can identify clusters, but the computational time and resources increase significantly
Solution Approach 1:
The patent applies preliminary action by pre-selecting upper and lower bound values for the neighborhood radius parameter before executing the full clustering algorithm. This bounding strategy narrows the search space in advance, allowing the modified ternary search to converge faster to the optimal parameter value without exhaustive exploration of all possible values.
Solution Approach 2:
The patent implements parameter changes by transforming the parameter search problem into a bounded optimization problem. By changing the search approach from exhaustive or grid-based methods to a modified ternary search with intelligent bounds, the algorithm efficiently locates the optimal neighborhood radius parameter that maximizes clustering quality while minimizing computational resources.
2Measurement precision
If exhaustive search is used to find optimal parameter values, then clustering quality improves, but computational resources are excessively consumed
Solution Approach 1:
The patent performs preliminary action by establishing intelligent upper and lower bounds for the parameter search space before optimization begins. This preliminary bounding eliminates regions of the parameter space that cannot contain the optimal value, allowing the modified ternary search to focus computational effort only on relevant regions and achieve high accuracy without exhaustive search.
Solution Approach 2:
The patent substitutes the mechanical exhaustive search approach with a modified ternary search algorithm that leverages mathematical properties of the objective function. This substitution replaces brute-force enumeration with a smarter search strategy that converges logarithmically, dramatically improving computational efficiency while maintaining or enhancing parameter optimization accuracy.
3Productivity
If the neighborhood radius parameter is not properly tuned, then computational speed improves, but clustering results suffer from over-segmentation or under-segmentation
Solution Approach 1:
The patent applies parameter changes by systematically adjusting the neighborhood radius parameter through modified ternary search to find the optimal value. This optimized parameter setting ensures that clustering operates at the right balance between speed and quality, avoiding both over-segmentation (too small radius) and under-segmentation (too large radius) while maintaining efficient computational performance.
Data Source
AI summary
Systems and methods are provided for implementing large-scale density-based clustering functionalities. In examples, a system selects, for a dataset (which may be sampled at 100% or less), an upper bound value and a lower bound value of a neighborhood radius parameter of a density-based clustering algorithm. The system identifies, using a modified ternary search algorithm, an optimal neighborhood radius parameter value, based on the upper and lower bound values, outputs the optimal neighborhood radius parameter value and/or a corresponding optimal number of clusters within the dataset. The modified ternary search algorithm leverages the near-unimodality of the neighborhood radius parameter, while selection of the upper bound value leverages a characteristic in which the neighborhood radius parameter value increases as the sampling rate decreases, and selection of the lower bound value uses ternary search that takes the number of clusters as a parameter instead of the neighborhood radius parameter.