An Effective Augmented Lagrangian Method for Fine-Grained Multi-View Optimization

The significance of multi-view learning in effectively mitigating the intricate intricacies entrenched within heterogeneous data has garnered substantial attention in recent years. Notwithstanding the favorable achievements showcased by recent strides in this area, a confluence of noteworthy challenges endures. To be specific, a majority of extant methodologies unceremoniously assign weights to data points viewwisely. This ineluctably disregards the intrinsic reality that disparate views confer diverse contributions to each individual sample, consequently neglecting the rich wellspring of sample-level structural insights harbored within the dataset. In this paper, we proposed an effective Augmented Lagrangian MethOd for fiNe-graineD (ALMOND) multi-view optimization. This innovative approach scrutinizes the interplay among multiple views at the granularity of individual samples, thereby fostering the enhanced preservation of local structural coherence. The Augmented Lagrangian Method (ALM) is elaborately incorporated into our framework, which enables us to achieve an optimal solution without involving an inexplicable intermediate variable as previous methods do. Empirical experiments on multi-view clustering tasks across heterogeneous datasets serve to incontrovertibly showcase the effectiveness of our proposed methodology, corroborating its preeminence over incumbent state-of-the-art alternatives.