An extremely fast deep spectral clustering method in Fourier domain for large-scale data

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Kun Qu, Man Zhang, Yang Yang, Hao Xue, Xiang-Jun Shen

Published: 2025, Last Modified: 21 Jan 2026Multim. Syst. 2025EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: Spectral clustering is a popular clustering technique. However, it suffers from high computational complexity as eigenvectors are computed from huge Laplacian graph, which is built from large-scale datasets. In this paper, we identify two insights into deep spectral clustering to alleviate the computational burden. Firstly, we transform the task of eigen-decomposition into the Fourier domain and prove that the time-consuming process to find eigenvectors in traditional spectral clustering methods can be replaced by finding a suitable predefined Fourier basis, with only a few computationally efficient element-wise product and sum operations. Secondly, we prove that only a small subset of samples is enough to estimate the final Fourier basis set of the entire dataset, thus dramatically decreasing the total computational complexity. Based on the above two findings, we propose an extremely fast deep spectral clustering method in the Fourier domain. We propose a fast-training block and embed it into an encoder-decoder network. The proposed module facilitates the deep spectral clustering method in the Fourier domain, which only needs to be fed with a small subset of samples to obtain a stable Fourier domain basis. To improve the generalization of the network, we design two novel reconstruction losses. The former one considers the fidelity between the input of the fast-training block and the output, while the second one measures the fidelity between the input of the network and the reconstructed output. Experiments on several large-scale datasets, such as SVHN, MNIST-8M, ImageNet-Dogs, Caltech-UCSD-Birds and ImageNet-100 et al., show that the proposed method achieves almost the same accuracy as SOTA deep clustering methods, but its speed is up to 230 times faster. Our code is available at https://github.com/xiaoyou4264/EFDSC.git.