Breaking the curse of dimensionality with Isolation Kernel
This addresses a foundational problem in machine learning by providing a kernel that overcomes dimensionality limitations, potentially impacting all high-dimensional data applications.
The paper tackles the curse of dimensionality by demonstrating that Isolation Kernel consistently outperforms other kernels in tasks like search, clustering, classification, and visualization across dimensions, with theoretical proof of its ability to break the curse.
The curse of dimensionality has been studied in different aspects. However, breaking the curse has been elusive. We show for the first time that it is possible to break the curse using the recently introduced Isolation Kernel. We show that only Isolation Kernel performs consistently well in indexed search, spectral & density peaks clustering, SVM classification and t-SNE visualization in both low and high dimensions, compared with distance, Gaussian and linear kernels. This is also supported by our theoretical analyses that Isolation Kernel is the only kernel that has the provable ability to break the curse, compared with existing metric-based Lipschitz continuous kernels.