So here is a regularization that takes into account the graph in which the data lives ( I need to add this category in the subspace clsutering section of the advanced matrix factorization jungle page).
Obviously there is no closed expression for it like in k-Means Clustering.
Dual Graph Regularized Latent Low-Rank Representation for Subspace Clustering by Ming Yin, Junbin Gao, Zhouchen Lin, Qinfeng Shi, and Yi Guo
Low-rank representation (LRR) has received considerable attention in subspace segmentation due to its effectiveness in exploring low-dimensional subspace structures embedded in data. To preserve the intrinsic geometrical structure of data, a graph regularizer has been introduced into LRR framework for learning the locality and similarity information within data. However, it is often the case that not only the high-dimensional data reside on a non-linear low-dimensional manifold in the ambient space, but also their features lie on a manifold in feature space. In this paper, we propose a dual graph regularized LRR model (DGLRR) by enforcing preservation of geometric information in both the ambient space and the feature space. The proposed method aims for simultaneously considering the geometric structures of the data manifold and the feature manifold. Furthermore, we extend the DGLRR model to include non-negative constraint, leading to a parts-based representation of data. Experiments are conducted on several image data sets to demonstrate that the proposed method outperforms the state-of-the-art approaches in image clustering.
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