Exploiting Unsupervised and Supervised Constraints for Subspace Clustering

3D Rigid Motion Segmentation with Mixed and Unknown Number of Models

Many real-world video sequences cannot be conveniently categorized as general or degenerate; in such cases, imposing a false dichotomy in using the fundamental matrix or homography model for motion segmentation on video sequences would lead to difficulty. Even when we are confronted with a general scene-motion, the fundamental matrix approach as a model for motion segmentation still suffers from several defects, which we discuss in this paper. The full potential of the fundamental matrix approach could only be realized if we judiciously harness information from the simpler homography model. From these considerations, we propose a multi-model spectral clustering framework that synergistically combines multiple models (homography and fundamental matrix) together. We show that the performance can be substantially improved in this way. For general motion segmentation tasks, the number of independently moving objects is often unknown a priori and needs to be estimated from the observations. This is referred to as model selection and it is essentially still an open research problem. In this work, we propose a set of model selection criteria balancing data fidelity and model complexity. We perform extensive testing on existing motion segmentation datasets with both segmentation and model selection tasks, achieving state-of-the-art performance on all of them; we also put forth a more realistic and challenging dataset adapted from the KITTI benchmark, containing real-world effects such as strong perspectives and strong forward translations not seen in the traditional datasets.

Trajectory Data Classification

This article comprehensively surveys the development of trajectory data classification. Considering the critical role of trajectory data classification in modern intelligent systems for surveillance security, abnormal behavior detection, crowd behavior analysis, and traffic control, trajectory data classification has attracted growing attention. According to the availability of manual labels, which is critical to the classification performances, the methods can be classified into three categories, i.e., unsupervised, semi-supervised, and supervised. Furthermore, classification methods are divided into some sub-categories according to what extracted features are used. We provide a holistic understanding and deep insight into three types of trajectory data classification methods and present some promising future directions.

Robust Structured Nonnegative Matrix Factorization for Image Representation

Dimensionality reduction has attracted increasing attention, because high-dimensional data have arisen naturally in numerous domains in recent years. As one popular dimensionality reduction method, nonnegative matrix factorization (NMF), whose goal is to learn parts-based representations, has been widely studied and applied to various applications. In contrast to the previous approaches, this paper proposes a novel semisupervised NMF learning framework, called robust structured NMF, that learns a robust discriminative representation by leveraging the block-diagonal structure and the -norm (especially when ) loss function. Specifically, the problems of noise and outliers are well addressed by the -norm ( ) loss function, while the discriminative representations of both the labeled and unlabeled data are simultaneously learned by explicitly exploring the block-diagonal structure. The proposed problem is formulated as an optimization problem with a well-defined objective function solved by the proposed iterative algorithm. The convergence of the proposed optimization algorithm is analyzed both theoretically and empirically. In addition, we also discuss the relationships between the proposed method and some previous methods. Extensive experiments on both the synthetic and real-world data sets are conducted, and the experimental results demonstrate the effectiveness of the proposed method in comparison to the state-of-the-art methods.