Unsupervised Feature Selection via Latent Space Manifold Constraints
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Solution Overview
Problem
Existing unsupervised feature selection methods fail to fully utilize mutual connection information between high-dimensional data instances and are often affected by noise features and samples, as they perform feature selection in the original data space rather than a latent space.
Innovation Solution
An unsupervised feature selection method based on latent space learning and manifold constraints, which includes embedding latent space learning into a feature selection model, adding a graph Laplacian regularization term, and using an alternative iterative optimization strategy to select optimal features, thereby addressing noise robustness and preserving intrinsic data structure.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If feature selection is performed in the original data space, then the computational process is straightforward, but the performance is affected by noise features and samples
Solution Approach 1:
The patent transforms the feature selection problem from the original data space to a latent space constructed through non-negative matrix factorization. By representing data instances in a new dimensional space that captures intrinsic relationships, the method achieves robustness to noise while maintaining computational tractability through the structured decomposition of the similarity matrix.
Solution Approach 2:
The patent introduces a latent space as an intermediary representation between the original data and the feature selection process. This latent space, constructed via non-negative matrix factorization of the similarity matrix, serves as a mediator that filters out noise while preserving mutual connection information, enabling more reliable feature selection.
2Loss of information
If traditional unsupervised feature selection methods are used, then the implementation is simple, but the mutual connection information between data instances is not fully utilized
Solution Approach 1:
The patent performs preliminary construction of a similarity matrix and its latent space representation before the actual feature selection process. By pre-computing the non-negative matrix factorization of the similarity matrix, the method extracts and preserves mutual connection information in advance, making it available for subsequent feature selection without redundant computations.
Solution Approach 2:
The patent changes the representation parameters of data instances from original feature space to latent space coordinates. By transforming the problem into optimizing feature selection in the latent space defined by the factorized similarity matrix, the method fully utilizes mutual connection information while maintaining computational efficiency through the structured parameter transformation.
3Manufacturing precision
If more features are selected to preserve data structure, then the intrinsic structure is better preserved, but the computational time and memory burden increase
Solution Approach 1:
The patent extracts only the essential mutual connection information from the full similarity matrix through non-negative matrix factorization. By decomposing the similarity matrix into latent factor matrices, the method separates the critical structural information from redundant details, enabling feature selection that preserves intrinsic data structure with reduced computational requirements.
Solution Approach 2:
The patent performs feature selection in the latent dimension space rather than the original high-dimensional feature space. This dimensional transformation allows preservation of intrinsic data structure through the geometric relationships in latent space while operating with fewer effective dimensions, thereby reducing computational time and memory burden.
Data Source
AI summary
An unsupervised feature selection method based on latent space learning and manifold constraints includes: S11, inputting an original data matrix to obtain a feature selection model; S12, embedding latent space learning into the feature selection model to obtain a feature selection model with the latent space learning; S13, adding a graph Laplacian regularization term into the feature selection model with the latent space learning to obtain an objective function; S14, solving the objective function by adopting an alternative iterative optimization strategy; and S15, sequencing each feature in the original matrix, and selecting the first k features to obtain an optimal feature subset. Feature selection is performed in a learned potential latent space, and the space is robust to noise. The potential latent space is modeled by non-negative matrix decomposition of a similarity matrix, and the matrix decomposition can unambiguously reflect relationships between data instances.