Clustering Device Noise Suppression Self-Expression Matrix
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Solution Overview
Problem
Conventional subspace clustering methods are adversely affected by noise in real-world data sets, leading to incorrect determination of subspaces due to the inclusion of all data points in linear combinations, which can result in erroneous clustering results.
Innovation Solution
A clustering device and method that calculates a self-expression matrix minimizing an objective function with regularization terms to reduce the influence of noise, using random sampling and a modified regularization term to weight data points with large Euclidean norms, thereby suppressing noise and improving clustering accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If all data points are included in linear combinations for subspace clustering, then clustering coverage is improved, but noise adversely affects clustering accuracy
Solution Approach 1:
The patent extracts only the necessary data points for linear combination by using random sampling with replacement to select k data points from the original n data points. This extraction mechanism filters out redundant and noisy data points, retaining only those that contribute meaningfully to subspace representation, thereby reducing noise influence while maintaining clustering accuracy.
Solution Approach 2:
The patent changes the parameter of data point selection from deterministic inclusion of all points to stochastic sampling with replacement. By introducing randomness and controlling the sample size k, the method dynamically adjusts which data points participate in linear combination, enabling the system to ignore noisy outliers while preserving informative points for accurate clustering.
2Reliability
If regularization terms are added to reduce noise influence, then clustering accuracy is improved, but calculation complexity increases
Solution Approach 1:
Instead of applying complex regularization to all data points simultaneously, the patent applies partial action by selectively regularizing only the sampled k data points. This partial approach reduces the computational burden while still achieving noise reduction, as the regularization is applied to a subset rather than the entire dataset, maintaining accuracy without excessive complexity.
Data Source
AI summary
Clustering can be performed using a self-expression matrix in which noise is suppressed. A self-expression matrix is calculated that minimizes an objective function that is for obtaining, from among matrices included in a predetermined matrix set, a self-expression matrix whose elements are linear weights when data points in a data set are expressed by linear combinations of points, the objective function being represented by a term for obtaining the residual between data points in the data set and data points expressed by linear combinations of points using the self-expression matrix, a first regularization term that is multiplied by a predetermined weight and is for reducing linear weights of the data points that have a large Euclidean norm in the self-expression matrix, and a second regularization term for the self-expression matrix. A similarity matrix defined by the calculated self-expression matrix is then calculated. Then a clustering result is obtained by clustering the data set based on the similarity matrix.