Cluster Number Estimation Using Gap Statistic
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Solution Overview
Problem
Current clustering methods lack an efficient approach to determine the optimal number of clusters in a dataset, as they often rely on subjective decisions or heuristic algorithms, which can lead to suboptimal results.
Innovation Solution
A method that uses a clustering algorithm to define initial clusters, creates a reference distribution within cluster boundaries, and iteratively refines the cluster number by computing a gap statistic based on residual sums of squares, allowing for an objective determination of the best number of clusters.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If subjective decisions or heuristic algorithms are used to determine the number of clusters, then the process is simple and quick, but the accuracy and reliability of clustering results deteriorate
Solution Approach 1:
The patent replaces subjective human decisions and simple heuristic algorithms with an automated computational system that uses clustering algorithms, gap statistics, and iterative optimization to objectively determine the optimal number of clusters, thereby improving accuracy while managing complexity through automation
Solution Approach 2:
The patent implements a feedback mechanism where the clustering algorithm iteratively refines cluster assignments and recalculates the gap statistic, using the results of each iteration to adjust and improve subsequent clustering configurations until the optimal number of clusters is identified
2Adaptability or versatility
If a fixed number of clusters is defined beforehand, then the clustering process is straightforward, but the ability to discover the true optimal structure deteriorates
Solution Approach 1:
The patent transforms the static, fixed approach to cluster number determination into a dynamic process that iteratively tests multiple cluster configurations, allowing the system to adapt and discover the optimal number of clusters based on the data rather than relying on predetermined values
Solution Approach 2:
The patent systematically varies the number of clusters as a parameter across multiple iterations, computing gap statistics for different cluster counts to identify which configuration optimizes clustering quality, thereby enabling the system to adapt to the true data structure
3Reliability
If multiple iterations with different cluster numbers are performed, then the determination of optimal clusters improves, but the computational time and resources increase
Solution Approach 1:
The patent performs preliminary clustering operations to establish initial cluster configurations and compute baseline gap statistics, using these preliminary results to guide subsequent iterations and avoid redundant computations, thereby improving reliability while managing time consumption
Data Source
AI summary
A method of determining a number of clusters for a dataset is provided. Centroid locations for a defined number of clusters are determined using a clustering algorithm. Boundaries for each of the defined clusters are defined. A reference distribution that includes a plurality of data points is created. The plurality of data points are within the defined boundary of at least one cluster of the defined clusters. Second centroid locations for the defined number of clusters are determined using the clustering algorithm and the reference distribution. A gap statistic for the defined number of clusters based on a comparison between a first residual sum of squares and a second residual sum of squares is computed. The processing is repeated for a next number of clusters to create. An estimated best number of clusters for the received data is determined by comparing the gap statistic computed for each iteration of the number of clusters.