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Non-negative matrix factorization (NMF) is a classical data analysis tool for clustering tasks. It usually considers the squared loss to measure the reconstruction error, thus it is sensitive to the presence of outliers. Looking into the literature, most of the existing robust NMF models focus on statistics-based robust estimators with known distribution assumptions. Besides those estimators, whether can we seek another function without the distribution assumption to boost the robustness of NMF? To solve the problem, we propose a robust NMF termed as tanhNMF for short, which rethinks the hyperbolic tangent (tanh) function as a robust loss to evaluate the reconstruction error. Moreover, to capture geometric structure within the data, we devise a locality constraint to regularize tanhNMF to model data locality. Owing to the non-convex tanh function, it is non-trivial to optimize tanhNMF. Following the paradigm of the half-quadratic algorithm, we easily solve an adaptive weighted NMF instead of original tanhNMF. The experiments of face clustering on four popular facial datasets with/without corruptions show that the proposed method achieves the satisfactory performance against several representative baselines including NMF and its robust counterparts. This also implies that the proposed tanh function could serve as an alternative robust loss for NMF. INDEX TERMS Non-negative matrix factorization, robust NMF, the hyperbolic tangent function, half-quadratic algorithm, locality constraint.

Non-negative matrix factorization (NMF) known as learnt parts-based representation has become a data analysis tool for clustering tasks. It provides an alternative learning paradigm to cope with non-negative data clustering. In this paradigm, concept factorization (CF) and symmetric non-negative factorization (SymNMF) are two typically important representative models. In general, they have distinct behaviors: in CF, each cluster is modeled as a linear combination of samples, and vice versa, i.e., sample reconstruction, while SymNMF built on pair-wise sample similarity measure, is to preserve similarity of samples in a low-dimensional subspace, namely similarity reconstruction. In this paper, we propose a similarity-based concept factorization (SCF) as a synthesis of the two behaviors. This design can be formulated as: the similarity of reconstructed samples by CF is close to that of original samples. To optimize it, we develop an optimization algorithm which leverages the alternating direction of multipliers (ADMM) method to solve each sub-problem of SCF. Besides, we take a further step to consider the robust issue of similarity reconstruction and explore a robust SCF model (RSCF), which penalizes the hardest pairwise similarity reconstruction via l ∞. Thus, RSCF enjoys similarity preservation, robustness to similarity perturbation, and ability of reconstructing samples. Extensive experiments validate such properties and show that the proposed SCF and RSCF achieve large performance gains as compared to their counterparts. INDEX TERMS Non-negative matrix factorization, concept factorization, l ∞ norm, the optimal gradient method, sorting-based algorithm.

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Road extraction is important for road network renewal, intelligent transportation systems and smart cities. This paper proposes an effective method to improve road extraction accuracy and reconstruct the broken road lines caused by ground occlusion. Firstly, an attention mechanism-based convolution neural network is established to enhance feature extraction capability. By highlighting key areas and restraining interference features, the road extraction accuracy is improved. Secondly, for the common broken road problem in the extraction results, a heuristic method based on connected domain analysis is proposed to reconstruct the road. An experiment is carried out on a benchmark dataset to prove the effectiveness of this method, and the result is compared with that of several famous deep learning models including FCN8s, SegNet, U-Net and D-Linknet. The comparison shows that this model increases the IOU value and the F1 score by 3.35%-12.8% and 2.41-9.8, respectively. Additionally, the result proves the proposed method is effective at extracting roads from occluded areas.