108,920 research outputs found
High Dimensional Semiparametric Scale-Invariant Principal Component Analysis
We propose a new high dimensional semiparametric principal component analysis
(PCA) method, named Copula Component Analysis (COCA). The semiparametric model
assumes that, after unspecified marginally monotone transformations, the
distributions are multivariate Gaussian. COCA improves upon PCA and sparse PCA
in three aspects: (i) It is robust to modeling assumptions; (ii) It is robust
to outliers and data contamination; (iii) It is scale-invariant and yields more
interpretable results. We prove that the COCA estimators obtain fast estimation
rates and are feature selection consistent when the dimension is nearly
exponentially large relative to the sample size. Careful experiments confirm
that COCA outperforms sparse PCA on both synthetic and real-world datasets.Comment: Accepted in IEEE Transactions on Pattern Analysis and Machine
Intelligence (TPMAI
Resonances and Twist in Volume-Preserving Mappings
The phase space of an integrable, volume-preserving map with one action and
angles is foliated by a one-parameter family of -dimensional invariant
tori. Perturbations of such a system may lead to chaotic dynamics and
transport. We show that near a rank-one, resonant torus these mappings can be
reduced to volume-preserving "standard maps." These have twist only when the
image of the frequency map crosses the resonance curve transversely. We show
that these maps can be approximated---using averaging theory---by the usual
area-preserving twist or nontwist standard maps. The twist condition
appropriate for the volume-preserving setting is shown to be distinct from the
nondegeneracy condition used in (volume-preserving) KAM theory.Comment: Many typos fixed and notation simplified. New order
averaging theorem and volume-preserving variant. Numerical comparison with
averaging adde
An iterative method for the approximation of fibers in slow-fast systems
In this paper we extend a method for iteratively improving slow manifolds so
that it also can be used to approximate the fiber directions. The extended
method is applied to general finite dimensional real analytic systems where we
obtain exponential estimates of the tangent spaces to the fibers. The method is
demonstrated on the Michaelis-Menten-Henri model and the Lindemann mechanism.
The latter example also serves to demonstrate the method on a slow-fast system
in non-standard slow-fast form. Finally, we extend the method further so that
it also approximates the curvature of the fibers.Comment: To appear in SIAD
Initial Conditions for Models of Dynamical Systems
The long-time behaviour of many dynamical systems may be effectively
predicted by a low-dimensional model that describes the evolution of a reduced
set of variables. We consider the question of how to equip such a
low-dimensional model with appropriate initial conditions, so that it
faithfully reproduces the long-term behaviour of the original high-dimensional
dynamical system. Our method involves putting the dynamical system into normal
form, which not only generates the low-dimensional model, but also provides the
correct initial conditions for the model. We illustrate the method with several
examples.
Keywords: normal form, isochrons, initialisation, centre manifoldComment: 24 pages in standard LaTeX, 66K, no figure
Affine Subspace Representation for Feature Description
This paper proposes a novel Affine Subspace Representation (ASR) descriptor
to deal with affine distortions induced by viewpoint changes. Unlike the
traditional local descriptors such as SIFT, ASR inherently encodes local
information of multi-view patches, making it robust to affine distortions while
maintaining a high discriminative ability. To this end, PCA is used to
represent affine-warped patches as PCA-patch vectors for its compactness and
efficiency. Then according to the subspace assumption, which implies that the
PCA-patch vectors of various affine-warped patches of the same keypoint can be
represented by a low-dimensional linear subspace, the ASR descriptor is
obtained by using a simple subspace-to-point mapping. Such a linear subspace
representation could accurately capture the underlying information of a
keypoint (local structure) under multiple views without sacrificing its
distinctiveness. To accelerate the computation of ASR descriptor, a fast
approximate algorithm is proposed by moving the most computational part (ie,
warp patch under various affine transformations) to an offline training stage.
Experimental results show that ASR is not only better than the state-of-the-art
descriptors under various image transformations, but also performs well without
a dedicated affine invariant detector when dealing with viewpoint changes.Comment: To Appear in the 2014 European Conference on Computer Visio
Perturbation analysis of trapped-particle dynamics in axisymmetric dipole geometry
The perturbation analysis of the bounce action-angle coordinates
for charged particles trapped in an axisymmetric dipole magnetic field is
presented. First, the lowest-order bounce action-angle coordinates are derived
for deeply-trapped particles in the harmonic-oscillator approximation. Next,
the Lie-transform perturbation method is used to derive higher-order anharmonic
action-angle corrections. Explicit expressions (with anharmonic corrections)
for the canonical parallel coordinates and are
presented, which satisfy the canonical identity . Lastly, analytical expressions for the bounce and drift frequencies
(which include anharmonic corrections) yield excellent agreement with exact
numerical results.Comment: 16 pages, 3 figure
Gait recognition based on shape and motion analysis of silhouette contours
This paper presents a three-phase gait recognition method that analyses the spatio-temporal shape and dynamic motion (STS-DM) characteristics of a human subject’s silhouettes to identify the subject in the presence of most of the challenging factors that affect existing gait recognition systems. In phase 1, phase-weighted magnitude spectra of the Fourier descriptor of the silhouette contours at ten phases of a gait period are used to analyse the spatio-temporal changes of the subject’s shape. A component-based Fourier descriptor based on anatomical studies of human body is used to achieve robustness against shape variations caused by all common types of small carrying conditions with folded hands, at the subject’s back and in upright position. In phase 2, a full-body shape and motion analysis is performed by fitting ellipses to contour segments of ten phases of a gait period and using a histogram matching with Bhattacharyya distance of parameters of the ellipses as dissimilarity scores. In phase 3, dynamic time warping is used to analyse the angular rotation pattern of the subject’s leading knee with a consideration of arm-swing over a gait period to achieve identification that is invariant to walking speed, limited clothing variations, hair style changes and shadows under feet. The match scores generated in the three phases are fused using weight-based score-level fusion for robust identification in the presence of missing and distorted frames, and occlusion in the scene. Experimental analyses on various publicly available data sets show that STS-DM outperforms several state-of-the-art gait recognition methods
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