111 research outputs found
Distributed boundary tracking using alpha and Delaunay-Cech shapes
For a given point set in a plane, we develop a distributed algorithm to
compute the shape of . shapes are well known geometric
objects which generalize the idea of a convex hull, and provide a good
definition for the shape of . We assume that the distances between pairs of
points which are closer than a certain distance are provided, and we show
constructively that this information is sufficient to compute the alpha shapes
for a range of parameters, where the range depends on .
Such distributed algorithms are very useful in domains such as sensor
networks, where each point represents a sensing node, the location of which is
not necessarily known.
We also introduce a new geometric object called the Delaunay-\v{C}ech shape,
which is geometrically more appropriate than an shape for some cases,
and show that it is topologically equivalent to shapes
Persistent Homology of Delay Embeddings
The objective of this study is to detect and quantify the periodic behavior
of the signals using topological methods. We propose to use delay-coordinate
embeddings as a tool to measure the periodicity of signals. Moreover, we use
persistent homology for analyzing the structure of point clouds of
delay-coordinate embeddings. A method for finding the appropriate value of
delay is proposed based on the autocorrelation function of the signals. We
apply this topological approach to wheeze signals by introducing a model based
on their harmonic characteristics. Wheeze detection is performed using the
first Betti numbers of a few number of landmarks chosen from embeddings of the
signals.Comment: 16 pages, 8 figure
Demystifying Deep Learning: A Geometric Approach to Iterative Projections
Parametric approaches to Learning, such as deep learning (DL), are highly
popular in nonlinear regression, in spite of their extremely difficult training
with their increasing complexity (e.g. number of layers in DL). In this paper,
we present an alternative semi-parametric framework which foregoes the
ordinarily required feedback, by introducing the novel idea of geometric
regularization. We show that certain deep learning techniques such as residual
network (ResNet) architecture are closely related to our approach. Hence, our
technique can be used to analyze these types of deep learning. Moreover, we
present preliminary results which confirm that our approach can be easily
trained to obtain complex structures.Comment: To be appeared in the ICASSP 2018 proceeding
Deep Dictionary Learning: A PARametric NETwork Approach
Deep dictionary learning seeks multiple dictionaries at different image
scales to capture complementary coherent characteristics. We propose a method
for learning a hierarchy of synthesis dictionaries with an image classification
goal. The dictionaries and classification parameters are trained by a
classification objective, and the sparse features are extracted by reducing a
reconstruction loss in each layer. The reconstruction objectives in some sense
regularize the classification problem and inject source signal information in
the extracted features. The performance of the proposed hierarchical method
increases by adding more layers, which consequently makes this model easier to
tune and adapt. The proposed algorithm furthermore, shows remarkably lower
fooling rate in presence of adversarial perturbation. The validation of the
proposed approach is based on its classification performance using four
benchmark datasets and is compared to a CNN of similar size
Analysis Dictionary Learning: An Efficient and Discriminative Solution
Discriminative Dictionary Learning (DL) methods have been widely advocated
for image classification problems. To further sharpen their discriminative
capabilities, most state-of-the-art DL methods have additional constraints
included in the learning stages. These various constraints, however, lead to
additional computational complexity. We hence propose an efficient
Discriminative Convolutional Analysis Dictionary Learning (DCADL) method, as a
lower cost Discriminative DL framework, to both characterize the image
structures and refine the interclass structure representations. The proposed
DCADL jointly learns a convolutional analysis dictionary and a universal
classifier, while greatly reducing the time complexity in both training and
testing phases, and achieving a competitive accuracy, thus demonstrating great
performance in many experiments with standard databases.Comment: ICASSP 201
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