Soft Subspace Fuzzy Clustering with Dimension Affinity Constraint

For high-dimensional data, the cluster structure often exists in a feature subset instead of the whole feature space. Soft subspace clustering can efficiently extract the important subspace by allocating a weight to each dimension on the basis of the contribution of this dimension to the cluster identification. However, this kind of method does not consider the correlations between data dimensions in the clustering process. In high-dimensional data, when two dimensions are closely correlated, they should have similar weight assignments, and vice versa. Inspired by the way of clustering with graph embedding technique, we present a novel soft subspace clustering algorithm with considering the correlations between data dimensions. In this method, a novel dimension affinity regularization term is included into the objective function to further highlight those correlated dimensions that are important to the formation of clusters and compress the feature subspaces. Moreover, the alternating direction method of multipliers is adopted to solve the linear optimization problem regarding the dimension weight lasso regularization. In addition, as an extension, the kernelized version is explored to address the non-linear data clustering. Experiments on the real-world datasets demonstrate the efficiency of the presented algorithms in comparison with the conventional clustering methods.