Randomized Clustered Nystrom for Large-Scale Kernel Machines
This work addresses scalability issues in kernel methods for machine learning practitioners, offering an incremental improvement over existing Nyström methods.
The paper tackles the problem of generating low-rank approximations of kernel matrices for large-scale data by introducing a randomized algorithm that selects landmark points via K-means clustering on low-dimensional random projections, achieving competitive performance and efficiency as demonstrated in experiments.
The Nystrom method has been popular for generating the low-rank approximation of kernel matrices that arise in many machine learning problems. The approximation quality of the Nystrom method depends crucially on the number of selected landmark points and the selection procedure. In this paper, we present a novel algorithm to compute the optimal Nystrom low-approximation when the number of landmark points exceed the target rank. Moreover, we introduce a randomized algorithm for generating landmark points that is scalable to large-scale data sets. The proposed method performs K-means clustering on low-dimensional random projections of a data set and, thus, leads to significant savings for high-dimensional data sets. Our theoretical results characterize the tradeoffs between the accuracy and efficiency of our proposed method. Extensive experiments demonstrate the competitive performance as well as the efficiency of our proposed method.