Simultaneous Subspace Clustering and Cluster Number Estimating Based on Triplet Relationship.

Area of Science:

• Data Science
• Machine Learning
• Computer Vision

Background:

• High-dimensional data often comprises low-dimensional subspaces.
• Existing subspace clustering methods use pairwise similarities, which are sensitive to data points at subspace intersections.
• Robust segmentation of complex data structures is a significant challenge.

Purpose of the Study:

• To develop a unified framework for simultaneous subspace clustering and determining the number of clusters.
• To enhance the robustness of subspace clustering by addressing limitations of pairwise similarity graphs.
• To introduce a novel data structure for improved data segmentation in high-dimensional spaces.

Main Methods:

• A hyper-correlation-based data structure, the "triplet relationship," is designed to capture high relevance and local compactness among three samples.
• The triplet relationship is derived from the self-representation matrix and used for iterative cluster assignment.
• A unified optimization scheme maximizes similarity between triplets from different clusters and minimizes correlation within the same cluster.

Main Results:

• The proposed algorithm automatically determines the number of clusters, avoiding over-segmentation through group fusion.
• Experimental results on synthetic and real-world datasets demonstrate the method's effectiveness and robustness.
• The triplet relationship provides a more stable basis for clustering compared to pairwise similarities.

Conclusions:

• The unified framework effectively addresses subspace clustering challenges in high-dimensional data.
• The triplet relationship offers a robust approach for data segmentation, particularly at subspace intersections.
• This method advances the field of unsupervised learning for complex, structured datasets.