Robust subspace clustering based on latent low rank representation with non-negative sparse Laplacian constraints

As a successful improvement on Low Rank Representation (LRR), Latent Low Rank Representation (LatLRR) has been one of the state-of-the-art models for subspace clustering due to the capability of discovering the low dimensional subspace structures of data, especially when the data samples are insufficient and/or extremely corrupted. However, the LatLRR method does not consider the nonlinear geometric structures within data, which leads to the loss of the locality information among data in the learning phase. Moreover, the coefficients of the learnt representation matrix can be negative, which lack the interpretability. To solve the above drawbacks of LatLRR, this paper introduces Laplacian, sparsity and non-negativity to LatLRR model and proposes a novel subspace clustering method, termed latent low rank representation with non-negative, sparse and laplacian constraints (NNSLLatLRR), in which we jointly take into account non-negativity, sparsity and laplacian properties of the learnt representation. As a result, the NNSLLatLRR can not only capture the global low dimensional structure and intrinsic non-linear geometric information of the data, but also enhance the interpretability of the learnt representation. Extensive experiments on two face benchmark datasets and a handwritten digit dataset show that our proposed method outperforms existing state-of-the-art subspace clustering methods.