Noise robust image clustering based on reweighted low rank tensor approximation and $$l_{\frac{1}{2}}$$ regularization

In this paper, a noise robust tensor based image clustering approach is proposed which can also perform well in the presence of gross errors. Our major contribution is the improved submodule identification technique in noisy environment by incorporating three important improvements: better low rank representation using reweighted nuclear norm, $$l_\frac{1}{2}$$ regularization to accurately capture sparseness and an error term in the model for noise robustness. Reweighted nuclear norm is introduced in the clustering model to capture self-expressiveness property in a better manner. The $$l_\frac{1}{2}$$ norm regularization is applied in place of $$l_1$$ -norm to properly capture the correlation among data members. An error term is introduced into the model to separate noise and data, which brings a noise robust image clustering technique. Combined effect all the three factors results an accurate clustering method even under the presence of severe noise. The performance of the proposed method is tested on different datasets with varying amount of noise. It is found that the proposed method provides better classification accuracy in almost all conditions as compared with existing methods.