Towards Projected Clustering with Aggregated Mapping.

Projected clustering is the foundation of deep clustering models. Aiming at catching the essence of deep clustering, we propose a novel projected clustering framework by summarizing the core properties of prevalent powerful models, especially deep models. At first, we introduce the aggregated mapping, consisting of projection learning and neighbor estimation, to obtain clustering-friendly representation. Importantly, we theoretically prove that the simple clustering-friendly representation learning may suffer from severe degeneration, which can be regarded as over-fitting. Roughly speaking, the well-trained model would group neighboring points into plenty of sub-clusters. These small sub-clusters may scatter randomly due to no connection between them. The degeneration may occur more frequently with the increasing of model capacity. We accordingly develop a self-evolution mechanism that implicitly aggregates the sub-clusters and the proposed method can alleviate the potential risk of over-fitting and obtain prominent improvement. The ablation experiments support the theoretical analysis and verify the effectiveness of the neighbor-aggregation mechanism. Finally, we show how to choose the unsupervised projection function through two specific examples, including a linear method (namely locality analysis) and a non-linear model.