An adaptive graph learning method based on dual data representations for clustering

Adaptive graph learning methods for clustering, which adjust a data similarity matrix while taking into account its clustering capability, have drawn increasing attention in recent years due to their promising clustering performance. Existing adaptive graph learning methods are based on either original data or linearly projected data and thus rely on the assumption that either representation is a good indicator of the underlying data structure. However, this assumption is sometimes not met in high dimensional data. Studies have shown that high-dimensional data in many problems tend to lie on an embedded nonlinear manifold structure. Motivated by this observation, in this paper, we develop dual data representations, i.e., original data and a nonlinear embedding of the data obtained via an Extreme Learning Machine (ELM)-based neural network, and propose to use them as the more reliable basis for graph learning. The resulting algorithm based on ELM and Constrained Laplacian Rank (ELM-CLR) further improves the clustering capability and robustness, while retaining the advantages of adaptive graph learning, such as not requiring any post-processing to extract cluster indicators. The empirical study shows that the proposed algorithm outperforms the state-of-the-art graph-based clustering methods on a broad range of benchmark datasets.