54,020 research outputs found
Fast Hierarchical Clustering and Other Applications of Dynamic Closest Pairs
We develop data structures for dynamic closest pair problems with arbitrary
distance functions, that do not necessarily come from any geometric structure
on the objects. Based on a technique previously used by the author for
Euclidean closest pairs, we show how to insert and delete objects from an
n-object set, maintaining the closest pair, in O(n log^2 n) time per update and
O(n) space. With quadratic space, we can instead use a quadtree-like structure
to achieve an optimal time bound, O(n) per update. We apply these data
structures to hierarchical clustering, greedy matching, and TSP heuristics, and
discuss other potential applications in machine learning, Groebner bases, and
local improvement algorithms for partition and placement problems. Experiments
show our new methods to be faster in practice than previously used heuristics.Comment: 20 pages, 9 figures. A preliminary version of this paper appeared at
the 9th ACM-SIAM Symp. on Discrete Algorithms, San Francisco, 1998, pp.
619-628. For source code and experimental results, see
http://www.ics.uci.edu/~eppstein/projects/pairs
An Efficient Index for Visual Search in Appearance-based SLAM
Vector-quantization can be a computationally expensive step in visual
bag-of-words (BoW) search when the vocabulary is large. A BoW-based appearance
SLAM needs to tackle this problem for an efficient real-time operation. We
propose an effective method to speed up the vector-quantization process in
BoW-based visual SLAM. We employ a graph-based nearest neighbor search (GNNS)
algorithm to this aim, and experimentally show that it can outperform the
state-of-the-art. The graph-based search structure used in GNNS can efficiently
be integrated into the BoW model and the SLAM framework. The graph-based index,
which is a k-NN graph, is built over the vocabulary words and can be extracted
from the BoW's vocabulary construction procedure, by adding one iteration to
the k-means clustering, which adds small extra cost. Moreover, exploiting the
fact that images acquired for appearance-based SLAM are sequential, GNNS search
can be initiated judiciously which helps increase the speedup of the
quantization process considerably
Planar Ultrametric Rounding for Image Segmentation
We study the problem of hierarchical clustering on planar graphs. We
formulate this in terms of an LP relaxation of ultrametric rounding. To solve
this LP efficiently we introduce a dual cutting plane scheme that uses minimum
cost perfect matching as a subroutine in order to efficiently explore the space
of planar partitions. We apply our algorithm to the problem of hierarchical
image segmentation
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