Abstract-Under the framework of spectral clustering, the key of subspace clustering is building a similarity graph which describes the neighborhood relations among data points. Some recent works build the graph using sparse, low-rank, and ℓ2-norm-based representation, and have achieved state-of-the-art performance. However, these methods have suffered from the following two limitations. First, the time complexities of these methods are at least proportional to the cube of the data size, which make those methods inefficient for solving large-scale problems. Second, they cannot cope with out-of-sample data that are not used to construct the similarity graph. To cluster each out-of-sample datum, the methods have to recalculate the similarity graph and the cluster membership of the whole data set. In this paper, we propose a unified framework which makes representation-based subspace clustering algorithms feasible to cluster both out-of-sample and large-scale data. Under our framework, the large-scale problem is tackled by converting it as out-ofsample problem in the manner of "sampling, clustering, coding, and classifying". Furthermore, we give an estimation for the error bounds by treating each subspace as a point in a hyperspace. Extensive experimental results on various benchmark data sets show that our methods outperform several recently-proposed scalable methods in clustering large-scale data set.Index Terms-Scalable subspace clustering, out-of-sample problem, sparse subspace clustering, low-rank representation, least square regression, error bound analysis.

Social workers contributed significantly to the promotion of public and community health during the initial outbreak of COVID-19 in China. Based on a quasi-scoping review of articles on social work practice during that outbreak, this reflective article elucidates how social workers contributed in three chronological stages. In the early stage (late January and February 2020), social workers provided community services offered as part of the governmental structure (moderate information and resource provision); in the middle stage (March 2020), social workers provided services to vulnerable groups alongside supporting the quarantine strategy; and in the late stage (April 2020 onwards), their services were focused on recuperation and recovery after the national lockdown was lifted. In the meanwhile, several issues for public and community health social work as a profession in terms of how it was able to support anti-COVID-19 practices became clear, including a lack of independence and stability, the need for better flexibility and greater ability to act pragmatically and lack of professional agreement. This article aims to enlighten the development of a (re)emerging field—public health and community health social work in China in the wake of the COVID-19 pandemic.

High-performance air filters were prepared by a simple in situ ionic self-assembly process of amino acid salts.