67 research outputs found
Extremal Optimization: Methods derived from Co-Evolution
We describe a general-purpose method for finding high-quality solutions to
hard optimization problems, inspired by self-organized critical models of
co-evolution such as the Bak-Sneppen model. The method, called Extremal
Optimization, successively eliminates extremely undesirable components of
sub-optimal solutions, rather than ``breeding'' better components. In contrast
to Genetic Algorithms which operate on an entire ``gene-pool'' of possible
solutions, Extremal Optimization improves on a single candidate solution by
treating each of its components as species co-evolving according to Darwinian
principles. Unlike Simulated Annealing, its non-equilibrium approach effects an
algorithm requiring few parameters to tune. With only one adjustable parameter,
its performance proves competitive with, and often superior to, more elaborate
stochastic optimization procedures. We demonstrate it here on two classic hard
optimization problems: graph partitioning and the traveling salesman problem.Comment: 8 pages, Latex, 5 ps-figures included. To appear in ``GECCO-99:
Proceedings of the Genetic and Evolutionary Computation Conference,'' (Morgan
Kaufmann, San Francisco, 1999
Multiclass Data Segmentation using Diffuse Interface Methods on Graphs
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 modified to handle the
multiclass case. The first algorithm minimizes the functional using a convex
splitting numerical scheme. The second algorithm is a uses a graph adaptation
of the classical numerical Merriman-Bence-Osher (MBO) scheme, which alternates
between diffusion and thresholding. We demonstrate the performance of both
algorithms experimentally on synthetic data, grayscale and color images, and
several benchmark data sets such as MNIST, COIL and WebKB. We also make use of
fast numerical solvers for finding the eigenvectors and eigenvalues of the
graph Laplacian, and take advantage of the sparsity of the matrix. Experiments
indicate that the results are competitive with or better than the current
state-of-the-art multiclass segmentation algorithms.Comment: 14 page
Improving Image Clustering using Sparse Text and the Wisdom of the Crowds
We propose a method to improve image clustering using sparse text and the wisdom of the crowds. In particular, we present a method to fuse two different kinds of document features, image and text features, and use a common dictionary or “wisdom of the crowds” as the connection between the two different kinds of documents. With the proposed fusion matrix, we use topic modeling via non-negative matrix factorization to cluster documents
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