Smooth Clustering with Block-Diagonal Constrained Laplacian Regularizer

Spectral clustering is the most widely used subspace segmentation approaches,whose performance heavily depends on constructed affinity matrices that are usually learned either directly from the raw data or from their corresponding representations.The independence of affinity construction and spectral discovery always leads to a suboptimal clustering results.According to the smooth representation clustering method and the enforced grouping condition,we propose an approach named smooth clustering with block-diagonal constrained Laplacian regularizer(SCBL)to tackle this problem.First,an affinity regularization generated from the representation coefficients is formed under the conditions of non-negativity and fixed summation.Second,an improved rank constraint is imposed to promote the block diagonal structure of affinity matrix.Finally,all these properties are integrated into the model of smooth representation clustering for simultaneously optimizing the reconstruction coefficients and similarity metrics.Moreover,we derive an alternative variable optimization strategy with all the subproblems being convergent to the global minimum.Empirical experiments on3synthetic and8real world datasets show that SCBL outperforms the related clustering approaches.