30,547 research outputs found
Fast Approximate -Means via Cluster Closures
-means, a simple and effective clustering algorithm, is one of the most
widely used algorithms in multimedia and computer vision community. Traditional
-means is an iterative algorithm---in each iteration new cluster centers are
computed and each data point is re-assigned to its nearest center. The cluster
re-assignment step becomes prohibitively expensive when the number of data
points and cluster centers are large.
In this paper, we propose a novel approximate -means algorithm to greatly
reduce the computational complexity in the assignment step. Our approach is
motivated by the observation that most active points changing their cluster
assignments at each iteration are located on or near cluster boundaries. The
idea is to efficiently identify those active points by pre-assembling the data
into groups of neighboring points using multiple random spatial partition
trees, and to use the neighborhood information to construct a closure for each
cluster, in such a way only a small number of cluster candidates need to be
considered when assigning a data point to its nearest cluster. Using complexity
analysis, image data clustering, and applications to image retrieval, we show
that our approach out-performs state-of-the-art approximate -means
algorithms in terms of clustering quality and efficiency
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Metaheuristic approaches for the quartet method of hierarchical clustering
Given a set of objects and their pairwise distances, we wish to determine a visual representation of the data. We use the quartet paradigm to compute a hierarchy of clusters of the objects. The method is based on an NP-hard graph optimization problem called the Minimum Quartet Tree Cost problem. This paper presents and compares several metaheuristic approaches to approximate the optimal hierarchy. The performance of the algorithms is tested through extensive computational experiments and it is shown that the Reduced Variable Neighbourhood Search metaheuristic is the most effective approach to the problem, obtaining high quality solutions in short computational running times
A New Quartet Tree Heuristic for Hierarchical Clustering
We consider the problem of constructing an an optimal-weight tree from the
3*(n choose 4) weighted quartet topologies on n objects, where optimality means
that the summed weight of the embedded quartet topologiesis optimal (so it can
be the case that the optimal tree embeds all quartets as non-optimal
topologies). We present a heuristic for reconstructing the optimal-weight tree,
and a canonical manner to derive the quartet-topology weights from a given
distance matrix. The method repeatedly transforms a bifurcating tree, with all
objects involved as leaves, achieving a monotonic approximation to the exact
single globally optimal tree. This contrasts to other heuristic search methods
from biological phylogeny, like DNAML or quartet puzzling, which, repeatedly,
incrementally construct a solution from a random order of objects, and
subsequently add agreement values.Comment: 22 pages, 14 figure
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