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Two-Step Nyström Sampling for Large-Scale Kernel Approximation
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DOI：10.1109/TBDATA.2025.3618472.png)
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Nyström approximation is one of the most popular approximation methods to accelerate kernel analysis on large-scale data sets. Nyström employs one single landmark set to obtain eigenvectors (low-rank decomposition) and projects the entire data set to the eigenvectors (embedding). Most existing methods focus on accelerating landmark selection. For extremely large-scale data sets, however, the embedding time cost, rather than that of low-rank decomposition, is critical. In addition, both accuracy and embedding time cost are dominated by the landmark set size. As a result, using more landmarks is the only way to improve accuracy at the cost of extremely high embedding costs. In this paper, we propose a method for the first time to decouple embedding cost from that of low-rank decomposition. We first obtain the eigenvectors from a large landmark set for a low error, and then optimize a small landmark set that minimizes the landmark-set-embedding error to ensure a low embedding cost. In return, our accuracy is close to that of the large landmark set but the small one dominates the embedding time cost. Our method can deal with popular kernels and be plugged into most existing methods. Experimental results demonstrate the superiority of the proposed method.
Keyword:
Clustering
kernel approximation
large-scale data
nyström approximation
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5.7
论文数:
860
被引数:
3.0K
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