88,490 research outputs found
Extension of One-Dimensional Proximity Regions to Higher Dimensions
Proximity maps and regions are defined based on the relative allocation of
points from two or more classes in an area of interest and are used to
construct random graphs called proximity catch digraphs (PCDs) which have
applications in various fields. The simplest of such maps is the spherical
proximity map which maps a point from the class of interest to a disk centered
at the same point with radius being the distance to the closest point from the
other class in the region. The spherical proximity map gave rise to class cover
catch digraph (CCCD) which was applied to pattern classification. Furthermore
for uniform data on the real line, the exact and asymptotic distribution of the
domination number of CCCDs were analytically available. In this article, we
determine some appealing properties of the spherical proximity map in compact
intervals on the real line and use these properties as a guideline for defining
new proximity maps in higher dimensions. Delaunay triangulation is used to
partition the region of interest in higher dimensions. Furthermore, we
introduce the auxiliary tools used for the construction of the new proximity
maps, as well as some related concepts that will be used in the investigation
and comparison of them and the resulting graphs. We characterize the geometry
invariance of PCDs for uniform data. We also provide some newly defined
proximity maps in higher dimensions as illustrative examples
Random Feature Maps via a Layered Random Projection (LaRP) Framework for Object Classification
The approximation of nonlinear kernels via linear feature maps has recently
gained interest due to their applications in reducing the training and testing
time of kernel-based learning algorithms. Current random projection methods
avoid the curse of dimensionality by embedding the nonlinear feature space into
a low dimensional Euclidean space to create nonlinear kernels. We introduce a
Layered Random Projection (LaRP) framework, where we model the linear kernels
and nonlinearity separately for increased training efficiency. The proposed
LaRP framework was assessed using the MNIST hand-written digits database and
the COIL-100 object database, and showed notable improvement in object
classification performance relative to other state-of-the-art random projection
methods.Comment: 5 page
Compact Random Feature Maps
Kernel approximation using randomized feature maps has recently gained a lot
of interest. In this work, we identify that previous approaches for polynomial
kernel approximation create maps that are rank deficient, and therefore do not
utilize the capacity of the projected feature space effectively. To address
this challenge, we propose compact random feature maps (CRAFTMaps) to
approximate polynomial kernels more concisely and accurately. We prove the
error bounds of CRAFTMaps demonstrating their superior kernel reconstruction
performance compared to the previous approximation schemes. We show how
structured random matrices can be used to efficiently generate CRAFTMaps, and
present a single-pass algorithm using CRAFTMaps to learn non-linear multi-class
classifiers. We present experiments on multiple standard data-sets with
performance competitive with state-of-the-art results.Comment: 9 page
Automated detection of extended sources in radio maps: progress from the SCORPIO survey
Automated source extraction and parameterization represents a crucial
challenge for the next-generation radio interferometer surveys, such as those
performed with the Square Kilometre Array (SKA) and its precursors. In this
paper we present a new algorithm, dubbed CAESAR (Compact And Extended Source
Automated Recognition), to detect and parametrize extended sources in radio
interferometric maps. It is based on a pre-filtering stage, allowing image
denoising, compact source suppression and enhancement of diffuse emission,
followed by an adaptive superpixel clustering stage for final source
segmentation. A parameterization stage provides source flux information and a
wide range of morphology estimators for post-processing analysis. We developed
CAESAR in a modular software library, including also different methods for
local background estimation and image filtering, along with alternative
algorithms for both compact and diffuse source extraction. The method was
applied to real radio continuum data collected at the Australian Telescope
Compact Array (ATCA) within the SCORPIO project, a pathfinder of the ASKAP-EMU
survey. The source reconstruction capabilities were studied over different test
fields in the presence of compact sources, imaging artefacts and diffuse
emission from the Galactic plane and compared with existing algorithms. When
compared to a human-driven analysis, the designed algorithm was found capable
of detecting known target sources and regions of diffuse emission,
outperforming alternative approaches over the considered fields.Comment: 15 pages, 9 figure
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