Robust PCA as Bilinear Decomposition with Outlier-Sparsity Regularization

Principal component analysis (PCA) is widely used for dimensionality reduction, with well-documented merits in various applications involving high-dimensional data, including computer vision, preference measurement, and bioinformatics. In this context, the fresh look advocated here permeates benefits from variable selection and compressive sampling, to robustify PCA against outliers. A least-trimmed squares estimator of a low-rank bilinear factor analysis model is shown closely related to that obtained from an $\ell_0$-(pseudo)norm-regularized criterion encouraging sparsity in a matrix explicitly modeling the outliers. This connection suggests robust PCA schemes based on convex relaxation, which lead naturally to a family of robust estimators encompassing Huber's optimal M-class as a special case. Outliers are identified by tuning a regularization parameter, which amounts to controlling sparsity of the outlier matrix along the whole robustification path of (group) least-absolute shrinkage and selection operator (Lasso) solutions. Beyond its neat ties to robust statistics, the developed outlier-aware PCA framework is versatile to accommodate novel and scalable algorithms to: i) track the low-rank signal subspace robustly, as new data are acquired in real time; and ii) determine principal components robustly in (possibly) infinite-dimensional feature spaces. Synthetic and real data tests corroborate the effectiveness of the proposed robust PCA schemes, when used to identify aberrant responses in personality assessment surveys, as well as unveil communities in social networks, and intruders from video surveillance data.Comment: 30 pages, submitted to IEEE Transactions on Signal Processin

A Fusion Framework for Camouflaged Moving Foreground Detection in the Wavelet Domain

Detecting camouflaged moving foreground objects has been known to be difficult due to the similarity between the foreground objects and the background. Conventional methods cannot distinguish the foreground from background due to the small differences between them and thus suffer from under-detection of the camouflaged foreground objects. In this paper, we present a fusion framework to address this problem in the wavelet domain. We first show that the small differences in the image domain can be highlighted in certain wavelet bands. Then the likelihood of each wavelet coefficient being foreground is estimated by formulating foreground and background models for each wavelet band. The proposed framework effectively aggregates the likelihoods from different wavelet bands based on the characteristics of the wavelet transform. Experimental results demonstrated that the proposed method significantly outperformed existing methods in detecting camouflaged foreground objects. Specifically, the average F-measure for the proposed algorithm was 0.87, compared to 0.71 to 0.8 for the other state-of-the-art methods.Comment: 13 pages, accepted by IEEE TI

On landmark selection and sampling in high-dimensional data analysis

In recent years, the spectral analysis of appropriately defined kernel matrices has emerged as a principled way to extract the low-dimensional structure often prevalent in high-dimensional data. Here we provide an introduction to spectral methods for linear and nonlinear dimension reduction, emphasizing ways to overcome the computational limitations currently faced by practitioners with massive datasets. In particular, a data subsampling or landmark selection process is often employed to construct a kernel based on partial information, followed by an approximate spectral analysis termed the Nystrom extension. We provide a quantitative framework to analyse this procedure, and use it to demonstrate algorithmic performance bounds on a range of practical approaches designed to optimize the landmark selection process. We compare the practical implications of these bounds by way of real-world examples drawn from the field of computer vision, whereby low-dimensional manifold structure is shown to emerge from high-dimensional video data streams.Comment: 18 pages, 6 figures, submitted for publicatio

Vision-Based Production of Personalized Video

In this paper we present a novel vision-based system for the automated production of personalised video souvenirs for visitors in leisure and cultural heritage venues. Visitors are visually identified and tracked through a camera network. The system produces a personalized DVD souvenir at the end of a visitor’s stay allowing visitors to relive their experiences. We analyze how we identify visitors by fusing facial and body features, how we track visitors, how the tracker recovers from failures due to occlusions, as well as how we annotate and compile the final product. Our experiments demonstrate the feasibility of the proposed approach

Scheduling Dimension Reduction of LPV Models -- A Deep Neural Network Approach

In this paper, the existing Scheduling Dimension Reduction (SDR) methods for Linear Parameter-Varying (LPV) models are reviewed and a Deep Neural Network (DNN) approach is developed that achieves higher model accuracy under scheduling dimension reduction. The proposed DNN method and existing SDR methods are compared on a two-link robotic manipulator, both in terms of model accuracy and performance of controllers synthesized with the reduced models. The methods compared include SDR for state-space models using Principal Component Analysis (PCA), Kernel PCA (KPCA) and Autoencoders (AE). On the robotic manipulator example, the DNN method achieves improved representation of the matrix variations of the original LPV model in terms of the Frobenius norm compared to the current methods. Moreover, when the resulting model is used to accommodate synthesis, improved closed-loop performance is obtained compared to the current methods.Comment: Accepted to American Control Conference (ACC) 2020, Denve

Bags of Affine Subspaces for Robust Object Tracking

We propose an adaptive tracking algorithm where the object is modelled as a continuously updated bag of affine subspaces, with each subspace constructed from the object's appearance over several consecutive frames. In contrast to linear subspaces, affine subspaces explicitly model the origin of subspaces. Furthermore, instead of using a brittle point-to-subspace distance during the search for the object in a new frame, we propose to use a subspace-to-subspace distance by representing candidate image areas also as affine subspaces. Distances between subspaces are then obtained by exploiting the non-Euclidean geometry of Grassmann manifolds. Experiments on challenging videos (containing object occlusions, deformations, as well as variations in pose and illumination) indicate that the proposed method achieves higher tracking accuracy than several recent discriminative trackers.Comment: in International Conference on Digital Image Computing: Techniques and Applications, 201