Point-set kernel clustering for large-scale data
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Solution Overview
Problem
Existing clustering algorithms face challenges in achieving both high-quality clustering outcomes and runtime efficiency, with algorithms like density-peak clustering being computationally expensive and scalable kernel k-means being ineffective due to intractable dimensionality and data independence.
Innovation Solution
The point-set kernel clustering method uses an Isolation Kernel to convert data points into a feature map, allowing for efficient similarity measurement and cluster growth based on a user-defined similarity threshold, enabling the characterization of clusters of arbitrary shape and size while running significantly faster than existing algorithms.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If density-peak clustering is used to achieve high-quality clustering outcomes, then clustering effectiveness is improved, but computational complexity and runtime increase proportionally to the square of data size
Solution Approach 1:
The patent introduces a kernel function as an intermediary to transform the original data space into a feature space where clustering can be performed more efficiently. The kernel function computes similarities between data points without explicitly calculating high-dimensional feature vectors, thus maintaining clustering effectiveness while reducing computational complexity from O(n²) to O(n log n) or O(n).
Solution Approach 2:
The patent changes the parameter representation by transforming data points into kernel feature spaces. Instead of operating directly on raw data coordinates, the algorithm operates on kernel-transformed representations, which enables efficient similarity computation and cluster formation while preserving the underlying data structure and relationships.
2Productivity
If scalable kernel k-means is used to achieve runtime efficiency, then computational speed is improved, but clustering effectiveness deteriorates due to intractable dimensionality and data independence
Solution Approach 1:
The patent applies dimensionality transformation by mapping data into kernel feature spaces, where clusters can be formed more naturally. This dimensional transformation allows the algorithm to capture complex data structures and relationships that are lost in traditional k-means, thereby improving clustering effectiveness while maintaining computational efficiency through scalable kernel methods.
Solution Approach 2:
The patent performs preliminary data transformation using kernel functions before the actual clustering process. By pre-computing kernel matrices and transforming data representations in advance, the algorithm prepares the data in a form that is more amenable to effective clustering, thus improving outcomes without significantly increasing overall runtime.
3Quantity of substance
If traditional clustering algorithms are used to process large datasets, then comprehensive data analysis is achieved, but processing time becomes prohibitively long for millions of data points
Solution Approach 1:
The patent replaces the traditional mechanical approach of direct distance computation in high-dimensional spaces with a kernel-based computational system. This substitution uses mathematical transformations to compute similarities more efficiently, reducing the computational burden from quadratic to near-linear time complexity, thereby enabling processing of millions of data points in reasonable time.
Solution Approach 2:
The patent introduces dynamic scaling and adaptive parameter adjustment in the kernel clustering process. The algorithm dynamically adapts to data characteristics and scales efficiently with input size, allowing it to maintain effectiveness while processing varying quantities of data from thousands to millions of points without proportional increases in processing time.
Data Source
AI summary
A computer-implemented clustering method is disclosed for image segmentation, social network analysis, computational biology, market research, search engine and other applications. At the heart of the method is a point-set kernel that measures the similarity between a data point and a set of data points. The method has a procedure that employs the point-set kernel to expand from a seed point to a cluster; and finally identifies all clusters in the given dataset. Applying the method for image segmentation, it identifies several segments in the image, where points in each segment have high similarity: but points in one segment have low similarity with respect to other segments. The method is both effective and efficient that enables it to deal with large scale datasets. In contrast, existing clustering methods are either efficient or effective; and even efficient ones have difficulty dealing with large scale datasets without massive parallelization.