Current local density-based anomaly detection methods are limited in that the local density estimation and the neighborhood density estimation are not accurate enough for complex and large databases, and the detection performance depends on the size parameter of the neighborhood. In this paper, we propose a new kernel function to estimate samples' local densities and propose a weighted neighborhood density estimation to increase the robustness to changes in the neighborhood size. We further propose a local kernel regression estimator and a hierarchical strategy for combining information from the multiple scale neighborhoods to refine anomaly factors of samples. We apply our general anomaly detection method to image saliency detection by regarding salient pixels in objects as anomalies to the background regions. Local density estimation in the visual feature space and kernel-based saliency score propagation in the image enable the assignment of similar saliency values to homogenous object regions. Experimental results on several benchmark datasets demonstrate that our anomaly detection methods overall outperform several state-of-art anomaly detection methods. The effectiveness of our image saliency detection method is validated by comparison with several state-of-art saliency detection methods.

Effectively modeling a collection of three-dimensional (3-D) faces is an important task in various applications, especially facial expression-driven ones, e.g., expression generation, retargeting, and synthesis. These 3-D faces naturally form a set of second-order tensors-one modality for identity and the other for expression. The number of these second-order tensors is three times of that of the vertices for 3-D face modeling. As for algorithms, Bayesian data modeling, which is a natural data analysis tool, has been widely applied with great success; however, it works only for vector data. Therefore, there is a gap between tensor-based representation and vector-based data analysis tools. Aiming at bridging this gap and generalizing conventional statistical tools over tensors, this paper proposes a decoupled probabilistic algorithm, which is named Bayesian tensor analysis (BTA). Theoretically, BTA can automatically and suitably determine dimensionality for different modalities of tensor data. With BTA, a collection of 3-D faces can be well modeled. Empirical studies on expression retargeting also justify the advantages of BTA.