854 research outputs found
Changepoint Detection over Graphs with the Spectral Scan Statistic
We consider the change-point detection problem of deciding, based on noisy
measurements, whether an unknown signal over a given graph is constant or is
instead piecewise constant over two connected induced subgraphs of relatively
low cut size. We analyze the corresponding generalized likelihood ratio (GLR)
statistics and relate it to the problem of finding a sparsest cut in a graph.
We develop a tractable relaxation of the GLR statistic based on the
combinatorial Laplacian of the graph, which we call the spectral scan
statistic, and analyze its properties. We show how its performance as a testing
procedure depends directly on the spectrum of the graph, and use this result to
explicitly derive its asymptotic properties on few significant graph
topologies. Finally, we demonstrate both theoretically and by simulations that
the spectral scan statistic can outperform naive testing procedures based on
edge thresholding and testing
Connected subgraph detection with mirror descent on SDPs
We propose a novel, computationally efficient mirror-descent based optimization framework for subgraph detection in graph-structured data. Our aim is to discover anomalous patterns present in a connected subgraph of a given graph. This problem arises in many applications such as detection of network intrusions, community detection, detection of anomalous events in surveillance videos or disease outbreaks. Since optimization over connected subgraphs is a combinatorial and computationally difficult problem, we propose a convex relaxation that offers a principled approach to incorporating connectivity and conductance constraints on candidate subgraphs. We develop a novel efficient algorithm to solve the relaxed problem, establish convergence guarantees and demonstrate its feasibility and performance with experiments on real and very large simulated networks.http://proceedings.mlr.press/v70/aksoylar17a.htmlhttp://proceedings.mlr.press/v70/aksoylar17a/aksoylar17a.pdfhttp://proceedings.mlr.press/v70/aksoylar17a/aksoylar17a.pdfPublished versio
Graph Laplacian for Image Anomaly Detection
Reed-Xiaoli detector (RXD) is recognized as the benchmark algorithm for image
anomaly detection; however, it presents known limitations, namely the
dependence over the image following a multivariate Gaussian model, the
estimation and inversion of a high-dimensional covariance matrix, and the
inability to effectively include spatial awareness in its evaluation. In this
work, a novel graph-based solution to the image anomaly detection problem is
proposed; leveraging the graph Fourier transform, we are able to overcome some
of RXD's limitations while reducing computational cost at the same time. Tests
over both hyperspectral and medical images, using both synthetic and real
anomalies, prove the proposed technique is able to obtain significant gains
over performance by other algorithms in the state of the art.Comment: Published in Machine Vision and Applications (Springer
Online Graph-Based Change Point Detection in Multiband Image Sequences
The automatic detection of changes or anomalies between multispectral and
hyperspectral images collected at different time instants is an active and
challenging research topic. To effectively perform change-point detection in
multitemporal images, it is important to devise techniques that are
computationally efficient for processing large datasets, and that do not
require knowledge about the nature of the changes. In this paper, we introduce
a novel online framework for detecting changes in multitemporal remote sensing
images. Acting on neighboring spectra as adjacent vertices in a graph, this
algorithm focuses on anomalies concurrently activating groups of vertices
corresponding to compact, well-connected and spectrally homogeneous image
regions. It fully benefits from recent advances in graph signal processing to
exploit the characteristics of the data that lie on irregular supports.
Moreover, the graph is estimated directly from the images using superpixel
decomposition algorithms. The learning algorithm is scalable in the sense that
it is efficient and spatially distributed. Experiments illustrate the detection
and localization performance of the method
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