[论文解读] Adaptively-weighted Integral Space for Fast Multiview Clustering

Man-Sheng Chen, Tuo Liu+3 more|arXiv (Cornell University)|Aug 25, 2022

Advanced Clustering Algorithms Research被引用 5

一句话总结

该论文提出了一种名为AIMC的新颖多视图聚类方法，具有近乎线性的时间复杂度，通过建模一种自适应加权潜在积分空间，联合学习共享聚类结构和视图特定表示。通过使用具有自适应置信度权重的视图生成模型以及正交中心点学习，AIMC在大规模数据集上实现了最先进的性能，且相比现有方法显著降低了计算成本。

ABSTRACT

Multiview clustering has been extensively studied to take advantage of multi-source information to improve the clustering performance. In general, most of the existing works typically compute an n * n affinity graph by some similarity/distance metrics (e.g. the Euclidean distance) or learned representations, and explore the pairwise correlations across views. But unfortunately, a quadratic or even cubic complexity is often needed, bringing about difficulty in clustering largescale datasets. Some efforts have been made recently to capture data distribution in multiple views by selecting view-wise anchor representations with k-means, or by direct matrix factorization on the original observations. Despite the significant success, few of them have considered the view-insufficiency issue, implicitly holding the assumption that each individual view is sufficient to recover the cluster structure. Moreover, the latent integral space as well as the shared cluster structure from multiple insufficient views is not able to be simultaneously discovered. In view of this, we propose an Adaptively-weighted Integral Space for Fast Multiview Clustering (AIMC) with nearly linear complexity. Specifically, view generation models are designed to reconstruct the view observations from the latent integral space with diverse adaptive contributions. Meanwhile, a centroid representation with orthogonality constraint and cluster partition are seamlessly constructed to approximate the latent integral space. An alternate minimizing algorithm is developed to solve the optimization problem, which is proved to have linear time complexity w.r.t. the sample size. Extensive experiments conducted on several realworld datasets confirm the superiority of the proposed AIMC method compared with the state-of-the-art methods.

研究动机与目标

• 解决现有依赖 $n \times n$ 相似度图的多视图聚类方法存在的高计算复杂度问题。
• 通过联合发现来自多个信息不足视图的潜在积分空间和共享聚类结构，克服视图不足问题。
• 开发一种近乎线性时间复杂度的方法，适用于大规模多视图数据聚类。
• 将视图特定的重建与聚类划分学习整合到统一的优化框架中。

提出的方法

• 提出一种自适应加权潜在积分空间，通过视图特定的置信度权重对跨视图的共享聚类结构进行建模。
• 设计视图生成模型，从潜在积分空间重建观测视图，实现视图与积分空间之间的双向映射。
• 引入正交中心点表示与聚类划分学习，以近似潜在积分空间。
• 开发一种交替优化算法，联合最小化重建误差与畸变误差，证明其时间复杂度相对于样本数量为线性。
• 使用自适应置信度权重反映每个视图在重建潜在空间时的可靠性。
• 采用统一的目标函数，结合数据重建与聚类损失，实现端到端学习。

实验结果

研究问题

• RQ1 能否有效学习到一个潜在积分空间，以表示多个信息不足视图之间的共享聚类结构？
• RQ2 能否将多视图聚类的计算复杂度降低至近乎线性时间，同时保持高性能？
• RQ3 如何在统一框架中联合优化视图特定表示与共享聚类结构？
• RQ4 自适应置信度权重是否能在视图质量或信息量不同时提升聚类的鲁棒性？

主要发现

• 在九个真实世界数据集上，AIMC在NMI和ACC指标上均优于所有对比方法，表现最佳。
• 平均而言，该方法在计算时间上排名第二，且在最大数据集（YTF-100）上运行时间最短，表明其具有出色的可扩展性。
• 在YTF-100数据集上，AIMC相比第二好的方法在NMI上提升了10.34%，证明其在大规模数据上的卓越性能。
• 参数分析表明，该方法在视图生成模型不同维度下均表现稳定，且在合理范围内可达到最优性能。
• 收敛性分析表明，目标函数值单调下降，并在10次迭代内达到最小值，表明收敛速度快。