70,022 research outputs found
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 -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
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
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
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