1,173 research outputs found
Robust Localization from Incomplete Local Information
We consider the problem of localizing wireless devices in an ad-hoc network
embedded in a d-dimensional Euclidean space. Obtaining a good estimation of
where wireless devices are located is crucial in wireless network applications
including environment monitoring, geographic routing and topology control. When
the positions of the devices are unknown and only local distance information is
given, we need to infer the positions from these local distance measurements.
This problem is particularly challenging when we only have access to
measurements that have limited accuracy and are incomplete. We consider the
extreme case of this limitation on the available information, namely only the
connectivity information is available, i.e., we only know whether a pair of
nodes is within a fixed detection range of each other or not, and no
information is known about how far apart they are. Further, to account for
detection failures, we assume that even if a pair of devices is within the
detection range, it fails to detect the presence of one another with some
probability and this probability of failure depends on how far apart those
devices are. Given this limited information, we investigate the performance of
a centralized positioning algorithm MDS-MAP introduced by Shang et al., and a
distributed positioning algorithm, introduced by Savarese et al., called
HOP-TERRAIN. In particular, for a network consisting of n devices positioned
randomly, we provide a bound on the resulting error for both algorithms. We
show that the error is bounded, decreasing at a rate that is proportional to
R/Rc, where Rc is the critical detection range when the resulting random
network starts to be connected, and R is the detection range of each device.Comment: 40 pages, 13 figure
On Geometric Alignment in Low Doubling Dimension
In real-world, many problems can be formulated as the alignment between two
geometric patterns. Previously, a great amount of research focus on the
alignment of 2D or 3D patterns, especially in the field of computer vision.
Recently, the alignment of geometric patterns in high dimension finds several
novel applications, and has attracted more and more attentions. However, the
research is still rather limited in terms of algorithms. To the best of our
knowledge, most existing approaches for high dimensional alignment are just
simple extensions of their counterparts for 2D and 3D cases, and often suffer
from the issues such as high complexities. In this paper, we propose an
effective framework to compress the high dimensional geometric patterns and
approximately preserve the alignment quality. As a consequence, existing
alignment approach can be applied to the compressed geometric patterns and thus
the time complexity is significantly reduced. Our idea is inspired by the
observation that high dimensional data often has a low intrinsic dimension. We
adopt the widely used notion "doubling dimension" to measure the extents of our
compression and the resulting approximation. Finally, we test our method on
both random and real datasets, the experimental results reveal that running the
alignment algorithm on compressed patterns can achieve similar qualities,
comparing with the results on the original patterns, but the running times
(including the times cost for compression) are substantially lower
Communication aspects of parallel processing
Cover title.Includes bibliographical references.Supported in part by the Air Force Office of Scientific Research. AFOSR-88-0032Cüneyt Özveren
Maximum Entropy Linear Manifold for Learning Discriminative Low-dimensional Representation
Representation learning is currently a very hot topic in modern machine
learning, mostly due to the great success of the deep learning methods. In
particular low-dimensional representation which discriminates classes can not
only enhance the classification procedure, but also make it faster, while
contrary to the high-dimensional embeddings can be efficiently used for visual
based exploratory data analysis.
In this paper we propose Maximum Entropy Linear Manifold (MELM), a
multidimensional generalization of Multithreshold Entropy Linear Classifier
model which is able to find a low-dimensional linear data projection maximizing
discriminativeness of projected classes. As a result we obtain a linear
embedding which can be used for classification, class aware dimensionality
reduction and data visualization. MELM provides highly discriminative 2D
projections of the data which can be used as a method for constructing robust
classifiers.
We provide both empirical evaluation as well as some interesting theoretical
properties of our objective function such us scale and affine transformation
invariance, connections with PCA and bounding of the expected balanced accuracy
error.Comment: submitted to ECMLPKDD 201
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