Scalable Subspace Clustering via Purity Kernel Tensor Learning

Subspace clustering is a fundamental task in machine learning, particularly for high-dimensional datasets where the goal is to group data points that lie in distinct subspaces. Traditional methods, such as Sparse Subspace Clustering (SSC) and Low-Rank Representation (LRR), have demonstrated good performance but often suffer from high computational costs, particularly when applied to large-scale data. To address these limitations, this paper introduces a novel technique called Purity Kernel Tensor Learning (PKTL). PKTL combines the power of tensor decomposition with a purity kernel function to improve both the efficiency and effectiveness of subspace clustering. By utilizing tensor-based representations, the method captures higher-order relationships in the data, allowing for a more robust clustering process. The purity kernel function measures the coherence within the clusters, enhancing the identification of subspaces in complex datasets. The proposed approach not only reduces computational complexity but also improves the clustering accuracy compared to existing methods. Experiments on synthetic and real-world datasets, including ORL, Yale, and MNIST, show that PKTL outperforms conventional subspace clustering algorithms, both in terms of clustering accuracy and scalability. The results demonstrate the potential of PKTL in handling large datasets while maintaining high performance, making it a promising approach for scalable subspace clustering in real-world applications.