Clustering System Using Kernel Mixture Weight Pruning
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Solution Overview
Problem
Existing clustering techniques, such as k-means, often fall into local optimality and lack reproducibility due to random initialization, and convex clustering methods like EM algorithms require excessive computational resources.
Innovation Solution
A method that calculates kernels based on similarity distributions, assigns non-negative mixture weights, and applies operations to active components to ensure global optimality, including pruning and uni-dimensional optimization, to efficiently cluster data items.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If convex clustering with EM algorithm is used, then global optimality is achieved, but computational time becomes extremely long
Solution Approach 1:
The patent segments the complex EM algorithm into two distinct phases: an E-step that computes responsibilities and updates mixture weights, and a pruning step that removes components with weights below a threshold. This segmentation allows the algorithm to achieve global optimality through the E-step while controlling computational time by eliminating unnecessary components in the pruning step.
Solution Approach 2:
The patent applies preliminary action by performing pruning operations during the iterative process rather than after convergence. By removing insignificant components early in the iteration process, the algorithm reduces the number of components that need to be processed in subsequent iterations, thereby reducing total computational time while maintaining global optimality.
2Productivity
If simple clustering techniques like k-means are used, then computational complexity is low, but the algorithm falls into local optimality
Solution Approach 1:
The patent merges the advantages of simple clustering algorithms (computational efficiency) with convex clustering (global optimality) by combining the E-step from EM algorithms with a pruning mechanism. The E-step provides global optimality guarantees while the pruning step maintains computational efficiency by reducing the number of active components, thus achieving both speed and reliability.
3Ease of manufacture
If random initialization is used in clustering, then the algorithm is simple to implement, but reproducibility is lost
Solution Approach 1:
The patent applies self-service by using data-driven initialization where the algorithm automatically identifies initial components and weights from the data itself rather than relying on random initialization. The pruning mechanism then refines these initial components, ensuring reproducible results while maintaining implementation simplicity. The algorithm serves itself by selecting meaningful initial components without external intervention.
Data Source
AI summary
A method for clustering a plurality of data items stored in a computer includes calculating, with the computer, a plurality of components comprising kernels based on a distribution that gives similarity between the data items, wherein a non-negative mixture weight is assigned to each of the kernels; preparing a set of active components that are composed of subscripts of the mixture weights; applying operations to the set of active components; and determining whether the mixture weight has converged, and if not converged yet, reapplying the operations to the set of components, and if the mixture weight has converged, clustering the data items based on the mixture weight.