Locally Regularized Sparse Graph by Fast Proximal Gradient Descent
<|reference_start|>Locally Regularized Sparse Graph by Fast Proximal Gradient Descent: Sparse graphs built by sparse representation has been demonstrated to be effective in clustering high-dimensional data. Albeit the compelling empirical performance, the vanilla sparse graph ignores the geometric information of the data by performing sparse representation for each datum separately. In order to obtain a sparse graph aligned with the local geometric structure of data, we propose a novel Support Regularized Sparse Graph, abbreviated as SRSG, for data clustering. SRSG encourages local smoothness on the neighborhoods of nearby data points by a well-defined support regularization term. We propose a fast proximal gradient descent method to solve the non-convex optimization problem of SRSG with the convergence matching the Nesterov's optimal convergence rate of first-order methods on smooth and convex objective function with Lipschitz continuous gradient. Extensive experimental results on various real data sets demonstrate the superiority of SRSG over other competing clustering methods.<|reference_end|>
@article{sun2024locally,
    title={Locally Regularized Sparse Graph by Fast Proximal Gradient Descent},
    author={Dongfang Sun, Yingzhen Yang},
    journal={arXiv preprint arXiv:2409.17090},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.17090},
    primaryClass={cs.LG math.OC}
}