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Low-rank representation (LRR) has recently attracted a great deal of attention due to its pleasing efficacy in exploring low-dimensional subspace structures embedded in data. For a given set of observed data corrupted with sparse errors, LRR aims at learning a lowest-rank representation of all data jointly. LRR has broad applications in pattern recognition, computer vision and signal processing. In the real world, data often reside on low-dimensional manifolds embedded in a high-dimensional ambient space. However, the LRR method does not take into account the non-linear geometric structures within data, thus the locality and similarity information among data may be missing in the learning process. To improve LRR in this regard, we propose a general Laplacian regularized low-rank representation framework for data representation where a hypergraph Laplacian regularizer can be readily introduced into, i.e., a Non-negative Sparse Hyper-Laplacian regularized LRR model (NSHLRR). By taking advantage of the graph regularizer, our proposed method not only can represent the global low-dimensional structures, but also capture the intrinsic non-linear geometric information in data. The extensive experimental results on image clustering, semi-supervised image classification and dimensionality reduction tasks demonstrate the effectiveness of the proposed method.

The unfolding high-speed railway (HSR) network is expected to have a great impact on Chinese cities. This paper discusses the international experience of the direct and indirect development effects of the HSR network on cities at the regional, urban and station-area level. It then discusses the potential development implications and planning challenges for China by translating the international experience into a Chinese context. Finally, future topics for research are identified.

BackgroundBreast cancer (breast Ca) is recognised as a major public health problem in the world. Data on reproductive factors associated with breast Ca in the Central African Republic (CAR) is very limited. This study aimed to identify reproductive variables as risk factors for breast Ca in CAR women.MethodsA case–control study was conducted among 174 cases of breast Ca confirmed at the Pathology Unit of the National Laboratory in Bangui between 2003 and 2015 and 348 age-matched controls. Data collection tools included a questionnaire, interviews and a review of medical records of patients. Data were analysed using SPSS software version 20. Odd ratios and 95% confidence intervals (CI) for the likelihood of developing breast Ca were obtained using unconditional logistic regression.ResultsIn total, 522 women with a mean age of 45.8 (SD = 13.4) years were enrolled. Women with breast Ca were more likely to have attained little or no education (AOR = 11.23, CI: 4.65–27.14 and AOR = 2.40, CI: 1.15–4.99), to be married (AOR = 2.09, CI: 1.18–3.71), to have had an abortion (AOR = 5.41, CI: 3.47–8.44), and to be nulliparous (AOR = 1.98, CI: 1.12–3.49). Decreased odds of breast Ca were associated with being employed (AOR = 0.32, CI: 0.19–0.56), living in urban areas (AOR = 0.16, CI: 0.07–0.37), late menarche (AOR = 0.18, CI: 0.07–0.44), regular menstrual cycles (AOR = 0.44, CI: 0.23–0.81), term pregnancy (AOR = 0.26, CI: 0.13–0.50) and hormonal contraceptive use (AOR = 0.62, CI: 0.41–0.93).ConclusionBreast Ca risk factors in CAR did not appear to be significantly different from that observed in other populations. This study highlighted the risk factors of breast Ca in women living in Bangui to inform appropriate control measures.

Low-rank representation (LRR) has received considerable attention in subspace segmentation due to its effectiveness in exploring low-dimensional subspace structures embedded in data. To preserve the intrinsic geometrical structure of data, a graph regularizer has been introduced into LRR framework for learning the locality and similarity information within data. However, it is often the case that not only the high-dimensional data reside on a non-linear low-dimensional manifold in the ambient space, but also their features lie on a manifold in feature space. In this paper, we propose a dual graph regularized LRR model (DGLRR) by enforcing preservation of geometric information in both the ambient space and the feature space. The proposed method aims for simultaneously considering the geometric structures of the data manifold and the feature manifold. Furthermore, we extend the DGLRR model to include non-negative constraint, leading to a parts-based representation of data. Experiments are conducted on several image data sets to demonstrate that the proposed method outperforms the state-of-the-art approaches in image clustering.

The ubiquitous information from multiple-view data, as well as the complementary information among different views, is usually beneficial for various tasks, for example, clustering, classification, denoising, and so on. Multiview subspace clustering is based on the fact that multiview data are generated from a latent subspace. To recover the underlying subspace structure, a successful approach adopted recently has been sparse and/or low-rank subspace clustering. Despite the fact that existing subspace clustering approaches may numerically handle multiview data, by exploring all possible pairwise correlation within views, high-order statistics that can only be captured by simultaneously utilizing all views are often overlooked. As a consequence, the clustering performance of the multiview data is compromised. To address this issue, in this paper, a novel multiview clustering method is proposed by using t-product in the third-order tensor space. First, we propose a novel tensor construction method to organize multiview tensorial data, to which the tensor-tensor product can be applied. Second, based on the circular convolution operation, multiview data can be effectively represented by a t-linear combination with sparse and low-rank penalty using ``self-expressiveness.'' Our extensive experimental results on face, object, digital image, and text data demonstrate that the proposed method outperforms the state-of-the-art methods for a range of criteria.

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