Ekaterina Merkurjev

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We present two graph-based algorithms for multiclass segmentation of high-dimensional data on graphs. The algorithms use a diffuse interface model based on the Ginzburg-Landau functional, related to total variation and graph cuts. A multiclass extension is introduced using the Gibbs simplex, with the functional's double-well potential modified to handle the(More)
In this paper we present a computationally efficient algorithm utilizing a fully or semi nonlocal graph Laplacian for solving a wide range of learning problems in data clustering and image processing. Combining ideas from L1 compressive sensing, image processing and graph methods, the diffuse interface model based on the Ginzburg-Landau functional was(More)
In this paper we present a computationally efficient algorithm utilizing a fully or seminonlocal graph Laplacian for solving a wide range of learning problems in binary data classification and image processing. In their recent work [Multiscale Model. Simul., 10 (2012), pp. 1090–1118], Bertozzi and Flenner introduced a graph-based diffuse interface model(More)
We present two graph-based algorithms for multiclass segmentation of high-dimensional data. The algorithms use a diffuse interface model based on the Ginzburg-Landau functional, related to total variation compressed sensing and image processing. A multiclass extension is introduced using the Gibbs simplex, with the functional’s double-well potential(More)
This work develops a global minimization framework for segmentation of high-dimensional data into two classes. It combines recent convex optimization methods from imaging with recent graph- based variational models for data segmentation. Two convex splitting algorithms are proposed, where graph-based PDE techniques are used to solve some of the subproblems.(More)
We present two graph-based algorithms for multiclass segmentation of high-dimensional data,motivated by the binary diffuse interfacemodel. One algorithmgeneralizesGinzburg– Landau (GL) functional minimization on graphs to the Gibbs simplex. The other algorithm uses a reduction of GLminimization, based on theMerriman–Bence–Osher scheme formotion by mean(More)
We present a very efficient semi-supervised graph-based algorithm for classification of high-dimensional data that is motivated by the MBO method of Garcia-Cardona (2014) and derived using the similarity graph. Our procedure is an elegant combination of heat kernel pagerank and the MBO method applied to study semi-supervised problems. The timing of our(More)
We consider the challenge of detection of chemical plumes in hyperspectral image data. Segmentation of gas is difficult due to the diffusive nature of the cloud. The use of hyperspectral imagery provides non-visual data for this problem, allowing for the utilization of a richer array of sensing information. In this paper, we present a method to track and(More)
Automated detection of chemical plumes presents a segmentation challenge. The segmentation problem for gas plumes is difficult due to the diffusive nature of the cloud. The advantage of considering hyperspectral images in the gas plume detection problem over the conventional RGB imagery is the presence of non-visual data, allowing for a richer(More)
Graph-based variational methods have recently shown to be highly competitive for various classification problems of high-dimensional data, but are inherently difficult to handle from an optimization perspective. This paper proposes a convex relaxation for a certain set of graph-based multiclass data segmentation models involving a graph total variation(More)