Multiple kernel clustering (MKC) has recently achieved remarkable progress in fusing multisource information to boost the clustering performance. However, the $\mathcal {O}({n}^{2})$ memory consumption and $\mathcal {O}({n}^{3})$ computational complexity prohibit these methods from being applied into median- or large-scale applications, where $n$ denotes the number of samples. To address these issues, we carefully redesign the formulation of subspace segmentation-based MKC, which reduces the memory and computational complexity to $\mathcal {O}({n})$ and $\mathcal {O}({n}^{2})$ , respectively. The proposed algorithm adopts a novel sampling strategy to enhance the performance and accelerate the speed of MKC. Specifically, we first mathematically model the sampling process and then learn it simultaneously during the procedure of information fusion. By this way, the generated anchor point set can better serve data reconstruction across different views, leading to improved discriminative capability of the reconstruction matrix and boosted clustering performance. Although the integrated sampling process makes the proposed algorithm less efficient than the linear complexity algorithms, the elaborate formulation makes our algorithm straightforward for parallelization. Through the acceleration of GPU and multicore techniques, our algorithm achieves superior performance against the compared state-of-the-art methods on six datasets with comparable time cost to the linear complexity algorithms.

中文翻译：

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具有压缩子空间对齐的多内核聚类


多核聚类（MKC）最近在融合多源信息以提高聚类性能方面取得了显着进展。然而，$\mathcal {O}({n}^{2})$ 内存消耗和 $\mathcal {O}({n}^{3})$ 计算复杂性阻碍了这些方法应用于中位数或大规模应用，其中$n$表示样本数量。为了解决这些问题，我们仔细地重新设计了基于子空间分割的MKC的公式，将内存和计算复杂度降低到$\mathcal {O}({n})$和$\mathcal {O}({n}^{ 2})$ ，分别。该算法采用新颖的采样策略来增强MKC的性能并加快速度。具体来说，我们首先对采样过程进行数学建模，然后在信息融合过程中同时学习它。通过这种方式，生成的锚点集可以更好地服务于不同视图的数据重建，从而提高重建矩阵的判别能力并提高聚类性能。尽管集成采样过程使得所提出的算法比线性复杂度算法效率低，但复杂的公式使得我们的算法易于并行化。通过 GPU 和多核技术的加速，我们的算法在六个数据集上实现了与最先进方法相比的卓越性能，并且时间成本与线性复杂度算法相当。