Self-Representation Based Unsupervised Exemplar Selection in a Union of Subspaces.

Area of Science:

• Machine Learning
• Data Science
• Computer Science

Background:

• Selecting representative data points (exemplars) is crucial for tasks like dataset summarization and information extraction.
• Traditional methods like k-medoids assume data clusters around centroids and fail with data lying near a union of subspaces.

Purpose of the Study:

• To propose a new exemplar selection model capable of handling data distributed across a union of subspaces.
• To develop an efficient algorithm for solving the proposed exemplar selection model.
• To introduce an exemplar-based subspace clustering method.
• To demonstrate the effectiveness of selected exemplars for classification tasks.

Main Methods:

• A novel exemplar selection model is proposed, minimizing the l1 norm of representation coefficients for optimal data reconstruction.
• A farthest-first search algorithm is introduced for efficient exemplar selection, iteratively choosing the worst-represented point.
• An exemplar-based subspace clustering algorithm is developed, designed for robustness to imbalanced data and scalability.

Main Results:

• The proposed method effectively selects representatives from each subspace when data originates from a union of independent subspaces.
• The exemplar-based subspace clustering method demonstrates robustness to imbalanced datasets and efficiency for large-scale data.
• Classifiers trained on the selected exemplars achieve high accuracy in classifying the remaining data points.

Conclusions:

• The new exemplar selection model provides a powerful alternative to classical methods, particularly for complex data distributions.
• The developed farthest-first search algorithm ensures efficient and effective exemplar selection.
• The exemplar-based approach offers a scalable and robust solution for subspace clustering and data representation.