PCA consistency in high dimension, low sample size context

Principal Component Analysis (PCA) is an important tool of dimension reduction especially when the dimension (or the number of variables) is very high. Asymptotic studies where the sample size is fixed, and the dimension grows [i.e., High Dimension, Low Sample Size (HDLSS)] are becoming increasingly relevant. We investigate the asymptotic behavior of the Principal Component (PC) directions. HDLSS asymptotics are used to study consistency, strong inconsistency and subspace consistency. We show that if the first few eigenvalues of a population covariance matrix are large enough compared to the others, then the corresponding estimated PC directions are consistent or converge to the appropriate subspace (subspace consistency) and most other PC directions are strongly inconsistent. Broad sets of sufficient conditions for each of these cases are specified and the main theorem gives a catalogue of possible combinations. In preparation for these results, we show that the geometric representation of HDLSS data holds under general conditions, which includes a $\rho$-mixing condition and a broad range of sphericity measures of the covariance matrix.Comment: Published in at http://dx.doi.org/10.1214/09-AOS709 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

On using gait to enhance frontal face extraction

Visual surveillance finds increasing deployment formonitoring urban environments. Operators need to be able to determine identity from surveillance images and often use face recognition for this purpose. In surveillance environments, it is necessary to handle pose variation of the human head, low frame rate, and low resolution input images. We describe the first use of gait to enable face acquisition and recognition, by analysis of 3-D head motion and gait trajectory, with super-resolution analysis. We use region- and distance-based refinement of head pose estimation. We develop a direct mapping to relate the 2-D image with a 3-D model. In gait trajectory analysis, we model the looming effect so as to obtain the correct face region. Based on head position and the gait trajectory, we can reconstruct high-quality frontal face images which are demonstrated to be suitable for face recognition. The contributions of this research include the construction of a 3-D model for pose estimation from planar imagery and the first use of gait information to enhance the face extraction process allowing for deployment in surveillance scenario

Hadroproduction of electroweak gauge boson plus jets and TMD parton density functions

If studies of electroweak gauge boson final states at the Large Hadron Collider, for Standard Model physics and beyond, are sensitive to effects of the initial state's transverse momentum distribution, appropriate generalizations of QCD shower evolution are required. We propose a method to do this based on QCD transverse momentum dependent (TMD) factorization at high energy. The method incorporates experimental information from the high-precision deep inelastic scattering (DIS) measurements, and includes experimental and theoretical uncertainties on TMD parton density functions. We illustrate the approach presenting results for production of W-boson + n jets at the LHC, including azimuthal correlations and subleading jet distributions.Comment: 9 pages, 4 figures. v2: comments and references added, typos corrected; results unchange

The CCFM uPDF evolution uPDFevolv

uPDFevolv is an evolution code for TMD parton densities using the CCFM evolution equation. A description of the underlying theoretical model and technical realization is given together with a detailed program description, with emphasis on parameters the user may want to changeComment: Code and description on https://updfevolv.hepforge.org Version to be published in EPJ

An Elliptic Curve-based Signcryption Scheme with Forward Secrecy

An elliptic curve-based signcryption scheme is introduced in this paper that effectively combines the functionalities of digital signature and encryption, and decreases the computational costs and communication overheads in comparison with the traditional signature-then-encryption schemes. It simultaneously provides the attributes of message confidentiality, authentication, integrity, unforgeability, non-repudiation, public verifiability, and forward secrecy of message confidentiality. Since it is based on elliptic curves and can use any fast and secure symmetric algorithm for encrypting messages, it has great advantages to be used for security establishments in store-and-forward applications and when dealing with resource-constrained devices.Comment: 13 Pages, 5 Figures, 2 Table

Principal arc analysis on direct product manifolds

We propose a new approach to analyze data that naturally lie on manifolds. We focus on a special class of manifolds, called direct product manifolds, whose intrinsic dimension could be very high. Our method finds a low-dimensional representation of the manifold that can be used to find and visualize the principal modes of variation of the data, as Principal Component Analysis (PCA) does in linear spaces. The proposed method improves upon earlier manifold extensions of PCA by more concisely capturing important nonlinear modes. For the special case of data on a sphere, variation following nongeodesic arcs is captured in a single mode, compared to the two modes needed by previous methods. Several computational and statistical challenges are resolved. The development on spheres forms the basis of principal arc analysis on more complicated manifolds. The benefits of the method are illustrated by a data example using medial representations in image analysis.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS370 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org