63,162 research outputs found
Decorrelation of Neutral Vector Variables: Theory and Applications
In this paper, we propose novel strategies for neutral vector variable
decorrelation. Two fundamental invertible transformations, namely serial
nonlinear transformation and parallel nonlinear transformation, are proposed to
carry out the decorrelation. For a neutral vector variable, which is not
multivariate Gaussian distributed, the conventional principal component
analysis (PCA) cannot yield mutually independent scalar variables. With the two
proposed transformations, a highly negatively correlated neutral vector can be
transformed to a set of mutually independent scalar variables with the same
degrees of freedom. We also evaluate the decorrelation performances for the
vectors generated from a single Dirichlet distribution and a mixture of
Dirichlet distributions. The mutual independence is verified with the distance
correlation measurement. The advantages of the proposed decorrelation
strategies are intensively studied and demonstrated with synthesized data and
practical application evaluations
A Framework for Image Segmentation Using Shape Models and Kernel Space Shape Priors
©2008 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.DOI: 10.1109/TPAMI.2007.70774Segmentation involves separating an object from the background in a given image. The use of image information alone often leads to poor segmentation results due to the presence of noise, clutter or occlusion. The introduction of shape priors in the geometric active contour (GAC) framework has proved to be an effective way to ameliorate some of these problems. In this work, we propose a novel segmentation method combining image information with prior shape knowledge, using level-sets. Following the work of Leventon et al., we propose to revisit the use of PCA to introduce prior knowledge about shapes in a more robust manner. We utilize kernel PCA (KPCA) and show that this method outperforms linear PCA by allowing only those shapes that are close enough to the training data. In our segmentation framework, shape knowledge and image information are encoded into two energy functionals entirely described in terms of shapes. This consistent description permits to fully take advantage of the Kernel PCA methodology and leads to promising segmentation results. In particular, our shape-driven segmentation technique allows for the simultaneous encoding of multiple types of shapes, and offers a convincing level of robustness with respect to noise, occlusions, or smearing
Iterative graph cuts for image segmentation with a nonlinear statistical shape prior
Shape-based regularization has proven to be a useful method for delineating
objects within noisy images where one has prior knowledge of the shape of the
targeted object. When a collection of possible shapes is available, the
specification of a shape prior using kernel density estimation is a natural
technique. Unfortunately, energy functionals arising from kernel density
estimation are of a form that makes them impossible to directly minimize using
efficient optimization algorithms such as graph cuts. Our main contribution is
to show how one may recast the energy functional into a form that is
minimizable iteratively and efficiently using graph cuts.Comment: Revision submitted to JMIV (02/24/13
Support Vector Machines in Analysis of Top Quark Production
Multivariate data analysis techniques have the potential to improve physics
analyses in many ways. The common classification problem of signal/background
discrimination is one example. The Support Vector Machine learning algorithm is
a relatively new way to solve pattern recognition problems and has several
advantages over methods such as neural networks. The SVM approach is described
and compared to a conventional analysis for the case of identifying top quark
signal events in the dilepton decay channel amidst a large number of background
events.Comment: 8 pages, 8 figures, to be published in the proceedings of the
"Advanced Statistical Techniques in Particle Physics" conference in Durham,
UK (March, 2002
Non-Redundant Spectral Dimensionality Reduction
Spectral dimensionality reduction algorithms are widely used in numerous
domains, including for recognition, segmentation, tracking and visualization.
However, despite their popularity, these algorithms suffer from a major
limitation known as the "repeated Eigen-directions" phenomenon. That is, many
of the embedding coordinates they produce typically capture the same direction
along the data manifold. This leads to redundant and inefficient
representations that do not reveal the true intrinsic dimensionality of the
data. In this paper, we propose a general method for avoiding redundancy in
spectral algorithms. Our approach relies on replacing the orthogonality
constraints underlying those methods by unpredictability constraints.
Specifically, we require that each embedding coordinate be unpredictable (in
the statistical sense) from all previous ones. We prove that these constraints
necessarily prevent redundancy, and provide a simple technique to incorporate
them into existing methods. As we illustrate on challenging high-dimensional
scenarios, our approach produces significantly more informative and compact
representations, which improve visualization and classification tasks
Synergy and redundancy in the Granger causal analysis of dynamical networks
We analyze by means of Granger causality the effect of synergy and redundancy
in the inference (from time series data) of the information flow between
subsystems of a complex network. Whilst we show that fully conditioned Granger
causality is not affected by synergy, the pairwise analysis fails to put in
evidence synergetic effects.
In cases when the number of samples is low, thus making the fully conditioned
approach unfeasible, we show that partially conditioned Granger causality is an
effective approach if the set of conditioning variables is properly chosen. We
consider here two different strategies (based either on informational content
for the candidate driver or on selecting the variables with highest pairwise
influences) for partially conditioned Granger causality and show that depending
on the data structure either one or the other might be valid. On the other
hand, we observe that fully conditioned approaches do not work well in presence
of redundancy, thus suggesting the strategy of separating the pairwise links in
two subsets: those corresponding to indirect connections of the fully
conditioned Granger causality (which should thus be excluded) and links that
can be ascribed to redundancy effects and, together with the results from the
fully connected approach, provide a better description of the causality pattern
in presence of redundancy. We finally apply these methods to two different real
datasets. First, analyzing electrophysiological data from an epileptic brain,
we show that synergetic effects are dominant just before seizure occurrences.
Second, our analysis applied to gene expression time series from HeLa culture
shows that the underlying regulatory networks are characterized by both
redundancy and synergy
Supervised Classification: Quite a Brief Overview
The original problem of supervised classification considers the task of
automatically assigning objects to their respective classes on the basis of
numerical measurements derived from these objects. Classifiers are the tools
that implement the actual functional mapping from these measurements---also
called features or inputs---to the so-called class label---or output. The
fields of pattern recognition and machine learning study ways of constructing
such classifiers. The main idea behind supervised methods is that of learning
from examples: given a number of example input-output relations, to what extent
can the general mapping be learned that takes any new and unseen feature vector
to its correct class? This chapter provides a basic introduction to the
underlying ideas of how to come to a supervised classification problem. In
addition, it provides an overview of some specific classification techniques,
delves into the issues of object representation and classifier evaluation, and
(very) briefly covers some variations on the basic supervised classification
task that may also be of interest to the practitioner
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