Automated Parameter Selection via Eigen Decomposition
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Solution Overview
Problem
Traditional methods for variable selection in cluster analysis, such as PCA, become cumbersome as the number of parameters grows, requiring manual input and increasing time consumption, and fail to systematically consider eigenvector coefficients in selecting representative parameters for space dilation.
Innovation Solution
A method involving eigen decomposition of a covariance matrix to create a decomposed matrix and eigenvalue vector, followed by rank ordering of eigenvector coefficients to determine a score for each parameter, allowing for the identification of a parameter set that maximizes space dilation through automated and systematic parameter selection.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Extent of automation
If traditional PCA methods are used for variable selection, then the process becomes manual and time-consuming, but the selection of representative parameters for space dilation is not systematic
Solution Approach 1:
The system performs self-service by automatically calculating eigen decompositions, ranking parameters based on eigenvalue criteria, and selecting representative parameters without requiring manual researcher input. The algorithm independently evaluates all parameters using the eigenvalue threshold criterion and selects the top N parameters that maximize space dilation.
Solution Approach 2:
The invention changes the selection criterion from manual researcher judgment to an objective mathematical parameter-based criterion (eigenvalue threshold). By using eigenvalues and eigenvectors from the covariance matrix decomposition, the system systematically identifies parameters that contribute most to variance and space dilation, replacing subjective manual selection with quantitative automated selection.
2Measurement precision
If too many variables are selected for cluster analysis, then space dilation decreases because extreme values blend with less extreme values, but selecting fewer variables may lose important discriminatory information
Solution Approach 1:
The system applies partial action by selecting only the essential subset of parameters (top N parameters with highest eigenvalues) rather than using all available parameters. This partial selection achieves the optimal balance by including enough parameters to maintain discriminatory information while excluding redundant ones that would cause extreme values to blend with less extreme values, thereby maximizing space dilation.
Solution Approach 2:
The invention replaces the mechanical trial-and-error approach of variable selection with a mathematical substitution using eigen decomposition. By substituting the manual selection process with eigenvalue-based ranking, the system objectively identifies the optimal number of parameters needed to maintain space dilation without losing critical discriminatory information.
3Ease of operation
If manual parameter selection is performed, then researcher judgment can guide the process, but the process becomes cumbersome and increases time consumption as the number of parameters grows
Solution Approach 1:
The invention substitutes the mechanical manual review process with an automated computational system. The computer executes eigen decomposition algorithms and automatically ranks parameters based on eigenvalue criteria, replacing the cumbersome manual evaluation of numerous parameters with an efficient mathematical computation that scales well with increasing parameter numbers.
Solution Approach 2:
The system performs self-service by automatically computing the covariance matrix, performing eigen decomposition, ranking all parameters based on their eigenvalues, and selecting the top N parameters without requiring manual researcher intervention. This eliminates the cumbersome nature of manual selection while maintaining scientific rigor through objective mathematical criteria.
Data Source
AI summary
A method of identifying a set of parameters representative of a data set is provided. An eigen decomposition of a covariance matrix is calculated to form a decomposed matrix and an eigenvalue vector. The covariance matrix is calculated for a matrix of data including a plurality of data values for each of a plurality of parameters. The decomposed matrix includes a number of eigenvectors equal to a number of the plurality of parameters with each eigenvector including a coefficient for each parameter. The eigenvalue vector includes an eigenvalue defined for each eigenvector. A first matrix is created by rank ordering the coefficient within each parameter of the plurality of parameters for each of the plurality of parameters. A score is determined for each parameter using the created first matrix and the eigenvalue vector. A parameter set is identified based on the determined score for each parameter.