Under the framework of graph-based learning, the key to robust subspace clustering and subspace learning is to obtain a good similarity graph that eliminates the effects of errors and retains only connections between the data points from the same subspace (i.e., intrasubspace data points). Recent works achieve good performance by modeling errors into their objective functions to remove the errors from the inputs. However, these approaches face the limitations that the structure of errors should be known prior and a complex convex problem must be solved. In this paper, we present a novel method to eliminate the effects of the errors from the projection space (representation) rather than from the input space. We first prove that l -, l -, l -, and nuclear-norm-based linear projection spaces share the property of intrasubspace projection dominance, i.e., the coefficients over intrasubspace data points are larger than those over intersubspace data points. Based on this property, we introduce a method to construct a sparse similarity graph, called L2-graph. The subspace clustering and subspace learning algorithms are developed upon L2-graph. We conduct comprehensive experiment on subspace learning, image clustering, and motion segmentation and consider several quantitative benchmarks classification/clustering accuracy, normalized mutual information, and running time. Results show that L2-graph outperforms many state-of-the-art methods in our experiments, including L1-graph, low rank representation (LRR), and latent LRR, least square regression, sparse subspace clustering, and locally linear representation.

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.

s a bio-inspired and emerging sensor, an event-based neuromorphic vision sensor has a different working principle compared to the standard frame-based cameras, which leads to promising properties of low energy consumption, low latency, high dynamic range (HDR), and high temporal resolution. It poses a paradigm shift to sense and perceive the environment by capturing local pixel-level light intensity changes and producing asynchronous event streams. Advanced technologies for the visual sensing system of autonomous vehicles from standard computer vision to event-based neuromorphic vision have been developed. In this tutorial-like article, a comprehensive review of the emerging technology is given. First, the course of the development of the neuromorphic vision sensor that is derived from the understanding of biological retina is introduced. The signal processing techniques for event noise processing and event data representation are then discussed. Next, the signal processing algorithms and applications for event-based neuromorphic vision in autonomous driving and various assistance systems are reviewed. Finally, challenges and future research directions are pointed out. It is expected that this article will serve as a starting point for new researchers and engineers in the autonomous driving field and provide a bird's-eye view to both neuromorphic vision and autonomous driving research communities.