Euclidean Distance is Not Your Swiss Army Knife

Graph-based multi-view learning, which has hitherto been used to discover the intrinsic patterns of graph data giving the credit to its convenience of implementation and effectiveness. Note that even though these approaches have been increasingly adopted in multi-view clustering and have generated promising outcomes, they are still faced with the sub-optimal solution. For one thing, multi-view data can be corrupted in the raw feature space. For the other, most existing approaches normally utilize euclidean distance to obtain the similarity between two samples, which can not be the best option for all types of real-world data and leads to inferior results. Therefore, to overcome the aforementioned issues, we integrate multi-metric learning, graph filtering, and subspace learning into a collaborative learning framework for multi-view clustering. Particularly, we prefer to recover a smooth representation of data by graph filtering, which can reserve the geometric structure of the original multi-view data and discard the corruptions simultaneously. Furthermore, instead of using euclidean distance as a Swiss army knife, multiple metrics are utilized to fully exploit the correlation of data based on the smooth representation, hence finally facilitating the downstream clustering task. Extensive experiments on multi-view clustering tasks validate our theoretical findings of ours and prove the improvement of our method over the SOTA approaches.