91,207 research outputs found
Compressive Spectral Clustering
Spectral clustering has become a popular technique due to its high
performance in many contexts. It comprises three main steps: create a
similarity graph between N objects to cluster, compute the first k eigenvectors
of its Laplacian matrix to define a feature vector for each object, and run
k-means on these features to separate objects into k classes. Each of these
three steps becomes computationally intensive for large N and/or k. We propose
to speed up the last two steps based on recent results in the emerging field of
graph signal processing: graph filtering of random signals, and random sampling
of bandlimited graph signals. We prove that our method, with a gain in
computation time that can reach several orders of magnitude, is in fact an
approximation of spectral clustering, for which we are able to control the
error. We test the performance of our method on artificial and real-world
network data.Comment: 12 pages, 2 figure
IIR Adaptive Filters for Detection of Gravitational Waves from Coalescing Binaries
In this paper we propose a new strategy for gravitational waves detection
from coalescing binaries, using IIR Adaptive Line Enhancer (ALE) filters. This
strategy is a classical hierarchical strategy in which the ALE filters have the
role of triggers, used to select data chunks which may contain gravitational
events, to be further analyzed with more refined optimal techniques, like the
the classical Matched Filter Technique. After a direct comparison of the
performances of ALE filters with the Wiener-Komolgoroff optimum filters
(matched filters), necessary to discuss their performance and to evaluate the
statistical limitation in their use as triggers, we performed a series of
tests, demonstrating that these filters are quite promising both for the
relatively small computational power needed and for the robustness of the
algorithms used. The performed tests have shown a weak point of ALE filters,
that we fixed by introducing a further strategy, based on a dynamic bank of ALE
filters, running simultaneously, but started after fixed delay times. The
results of this global trigger strategy seems to be very promising, and can be
already used in the present interferometers, since it has the great advantage
of requiring a quite small computational power and can easily run in real-time,
in parallel with other data analysis algorithms.Comment: Accepted at SPIE: "Astronomical Telescopes and Instrumentation". 9
pages, 3 figure
Accelerated Spectral Clustering Using Graph Filtering Of Random Signals
We build upon recent advances in graph signal processing to propose a faster
spectral clustering algorithm. Indeed, classical spectral clustering is based
on the computation of the first k eigenvectors of the similarity matrix'
Laplacian, whose computation cost, even for sparse matrices, becomes
prohibitive for large datasets. We show that we can estimate the spectral
clustering distance matrix without computing these eigenvectors: by graph
filtering random signals. Also, we take advantage of the stochasticity of these
random vectors to estimate the number of clusters k. We compare our method to
classical spectral clustering on synthetic data, and show that it reaches equal
performance while being faster by a factor at least two for large datasets
Inference via low-dimensional couplings
We investigate the low-dimensional structure of deterministic transformations
between random variables, i.e., transport maps between probability measures. In
the context of statistics and machine learning, these transformations can be
used to couple a tractable "reference" measure (e.g., a standard Gaussian) with
a target measure of interest. Direct simulation from the desired measure can
then be achieved by pushing forward reference samples through the map. Yet
characterizing such a map---e.g., representing and evaluating it---grows
challenging in high dimensions. The central contribution of this paper is to
establish a link between the Markov properties of the target measure and the
existence of low-dimensional couplings, induced by transport maps that are
sparse and/or decomposable. Our analysis not only facilitates the construction
of transformations in high-dimensional settings, but also suggests new
inference methodologies for continuous non-Gaussian graphical models. For
instance, in the context of nonlinear state-space models, we describe new
variational algorithms for filtering, smoothing, and sequential parameter
inference. These algorithms can be understood as the natural
generalization---to the non-Gaussian case---of the square-root
Rauch-Tung-Striebel Gaussian smoother.Comment: 78 pages, 25 figure
Fog Computing in Medical Internet-of-Things: Architecture, Implementation, and Applications
In the era when the market segment of Internet of Things (IoT) tops the chart
in various business reports, it is apparently envisioned that the field of
medicine expects to gain a large benefit from the explosion of wearables and
internet-connected sensors that surround us to acquire and communicate
unprecedented data on symptoms, medication, food intake, and daily-life
activities impacting one's health and wellness. However, IoT-driven healthcare
would have to overcome many barriers, such as: 1) There is an increasing demand
for data storage on cloud servers where the analysis of the medical big data
becomes increasingly complex, 2) The data, when communicated, are vulnerable to
security and privacy issues, 3) The communication of the continuously collected
data is not only costly but also energy hungry, 4) Operating and maintaining
the sensors directly from the cloud servers are non-trial tasks. This book
chapter defined Fog Computing in the context of medical IoT. Conceptually, Fog
Computing is a service-oriented intermediate layer in IoT, providing the
interfaces between the sensors and cloud servers for facilitating connectivity,
data transfer, and queryable local database. The centerpiece of Fog computing
is a low-power, intelligent, wireless, embedded computing node that carries out
signal conditioning and data analytics on raw data collected from wearables or
other medical sensors and offers efficient means to serve telehealth
interventions. We implemented and tested an fog computing system using the
Intel Edison and Raspberry Pi that allows acquisition, computing, storage and
communication of the various medical data such as pathological speech data of
individuals with speech disorders, Phonocardiogram (PCG) signal for heart rate
estimation, and Electrocardiogram (ECG)-based Q, R, S detection.Comment: 29 pages, 30 figures, 5 tables. Keywords: Big Data, Body Area
Network, Body Sensor Network, Edge Computing, Fog Computing, Medical
Cyberphysical Systems, Medical Internet-of-Things, Telecare, Tele-treatment,
Wearable Devices, Chapter in Handbook of Large-Scale Distributed Computing in
Smart Healthcare (2017), Springe
Fast Approximate Spectral Clustering for Dynamic Networks
Spectral clustering is a widely studied problem, yet its complexity is
prohibitive for dynamic graphs of even modest size. We claim that it is
possible to reuse information of past cluster assignments to expedite
computation. Our approach builds on a recent idea of sidestepping the main
bottleneck of spectral clustering, i.e., computing the graph eigenvectors, by
using fast Chebyshev graph filtering of random signals. We show that the
proposed algorithm achieves clustering assignments with quality approximating
that of spectral clustering and that it can yield significant complexity
benefits when the graph dynamics are appropriately bounded
Chebyshev and Conjugate Gradient Filters for Graph Image Denoising
In 3D image/video acquisition, different views are often captured with
varying noise levels across the views. In this paper, we propose a graph-based
image enhancement technique that uses a higher quality view to enhance a
degraded view. A depth map is utilized as auxiliary information to match the
perspectives of the two views. Our method performs graph-based filtering of the
noisy image by directly computing a projection of the image to be filtered onto
a lower dimensional Krylov subspace of the graph Laplacian. We discuss two
graph spectral denoising methods: first using Chebyshev polynomials, and second
using iterations of the conjugate gradient algorithm. Our framework generalizes
previously known polynomial graph filters, and we demonstrate through numerical
simulations that our proposed technique produces subjectively cleaner images
with about 1-3 dB improvement in PSNR over existing polynomial graph filters.Comment: 6 pages, 6 figures, accepted to 2014 IEEE International Conference on
Multimedia and Expo Workshops (ICMEW
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