Discriminative Subspace Clustering Based on Local Hyperdisk for High-Dimensional Big Data

In many high-dimensional big data clustering methods, subspace learning is a commonly used technique. Traditional subspace-based methods project high-dimensional data into low-dimensional space to perform dimensionality reduction and clustering. Dimensionality reduction can reduce computational complexity, but it also leads to the loss of some key features. To deal with this issue, we propose a novel clustering algorithm based on a hyperdisk representation that provides a tighter approximation of sample regions. Specifically, the hyperdisk is defined as the intersection between the affine packet and a hypersphere, forming a disk-like region that offers a more compact representation of the class boundaries. This model achieves a balance between the loose approximation of the affine packet and the strict constraints of the convex hull, thereby enhancing the stability and reliability of the algorithm in low-sample high-dimensional classification scenarios compared to traditional hyperellipse models. For optimization, a standard quadratic programming algorithm is utilized to solve the proposed formulation. The performance of the algorithm is comprehensively evaluated from multiple perspectives, and its effectiveness is demonstrated through extensive experimental results.