Face recognition has received significant attention in the past decades due to its potential applications in biometrics, information security, law enforcement, etc. Numerous methods have been suggested to address this problem [1]. Among appearance-based holistic approaches, principal component analysis (PCA) turns out to be very effective. As a classical unsupervised learning and data analysis ...

A proper circular-arc (PCA) model is a pairM = (C,A) where C is a circle and A is a family of inclusion-free arcs on C in which no two arcs of A cover C. A PCA model U is a (c, `, d, ds)-CA model when C has circumference c, all the arcs in A have length `, all the extremes of the arcs in A are at a distance at least d, and all the beginning points of the arcs in A are at a distance at least d+ ...

Principal component analysis (PCA) is a popular tool for linear dimensionality reduction and feature extraction. Kernel PCA is the nonlinear form of PCA, which better exploits the complicated spatial structure of high-dimensional features. In this paper, we first review the basic ideas of PCA and kernel PCA. Then we focus on the reconstruction of pre-images for kernel PCA. We also give an intro...

Principal components analysis (PCA) is a popular descriptive multivariate method for handling quantitative data. In PCA of a mixture of quantitative and qualitative data, it requires quantification of qualitative data to obtain optimal scaling data and use ordinary PCA. The extended PCA including such quantification is called nonlinear PCA, see Gifi [Gifi, 1990]. The existing algorithms for non...

There are several cutting edge applications needing PCA methods for data on tori and we propose a novel torus-PCA method with important properties that can be generally applied. There are two existing general methods: tangent space PCA and geodesic PCA. However, unlike tangent space PCA, our torus-PCA honors the cyclic topology of the data space whereas, unlike geodesic PCA, our torus-PCA produ...