414 research outputs found
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
Clustering by compression
We present a new method for clustering based on compression. The method
doesn't use subject-specific features or background knowledge, and works as
follows: First, we determine a universal similarity distance, the normalized
compression distance or NCD, computed from the lengths of compressed data files
(singly and in pairwise concatenation). Second, we apply a hierarchical
clustering method. The NCD is universal in that it is not restricted to a
specific application area, and works across application area boundaries. A
theoretical precursor, the normalized information distance, co-developed by one
of the authors, is provably optimal but uses the non-computable notion of
Kolmogorov complexity. We propose precise notions of similarity metric, normal
compressor, and show that the NCD based on a normal compressor is a similarity
metric that approximates universality. To extract a hierarchy of clusters from
the distance matrix, we determine a dendrogram (binary tree) by a new quartet
method and a fast heuristic to implement it. The method is implemented and
available as public software, and is robust under choice of different
compressors. To substantiate our claims of universality and robustness, we
report evidence of successful application in areas as diverse as genomics,
virology, languages, literature, music, handwritten digits, astronomy, and
combinations of objects from completely different domains, using statistical,
dictionary, and block sorting compressors. In genomics we presented new
evidence for major questions in Mammalian evolution, based on
whole-mitochondrial genomic analysis: the Eutherian orders and the Marsupionta
hypothesis against the Theria hypothesis.Comment: LaTeX, 27 pages, 20 figure
A Fast Quartet Tree Heuristic for Hierarchical Clustering
The Minimum Quartet Tree Cost problem is to construct an optimal weight tree
from the weighted quartet topologies on objects, where
optimality means that the summed weight of the embedded quartet topologies is
optimal (so it can be the case that the optimal tree embeds all quartets as
nonoptimal topologies). We present a Monte Carlo heuristic, based on randomized
hill climbing, for approximating the optimal weight tree, given the quartet
topology weights. The method repeatedly transforms a dendrogram, with all
objects involved as leaves, achieving a monotonic approximation to the exact
single globally optimal tree. The problem and the solution heuristic has been
extensively used for general hierarchical clustering of nontree-like
(non-phylogeny) data in various domains and across domains with heterogeneous
data. We also present a greatly improved heuristic, reducing the running time
by a factor of order a thousand to ten thousand. All this is implemented and
available, as part of the CompLearn package. We compare performance and running
time of the original and improved versions with those of UPGMA, BioNJ, and NJ,
as implemented in the SplitsTree package on genomic data for which the latter
are optimized.
Keywords: Data and knowledge visualization, Pattern
matching--Clustering--Algorithms/Similarity measures, Hierarchical clustering,
Global optimization, Quartet tree, Randomized hill-climbing,Comment: LaTeX, 40 pages, 11 figures; this paper has substantial overlap with
arXiv:cs/0606048 in cs.D
Topology Discovery of Sparse Random Graphs With Few Participants
We consider the task of topology discovery of sparse random graphs using
end-to-end random measurements (e.g., delay) between a subset of nodes,
referred to as the participants. The rest of the nodes are hidden, and do not
provide any information for topology discovery. We consider topology discovery
under two routing models: (a) the participants exchange messages along the
shortest paths and obtain end-to-end measurements, and (b) additionally, the
participants exchange messages along the second shortest path. For scenario
(a), our proposed algorithm results in a sub-linear edit-distance guarantee
using a sub-linear number of uniformly selected participants. For scenario (b),
we obtain a much stronger result, and show that we can achieve consistent
reconstruction when a sub-linear number of uniformly selected nodes
participate. This implies that accurate discovery of sparse random graphs is
tractable using an extremely small number of participants. We finally obtain a
lower bound on the number of participants required by any algorithm to
reconstruct the original random graph up to a given edit distance. We also
demonstrate that while consistent discovery is tractable for sparse random
graphs using a small number of participants, in general, there are graphs which
cannot be discovered by any algorithm even with a significant number of
participants, and with the availability of end-to-end information along all the
paths between the participants.Comment: A shorter version appears in ACM SIGMETRICS 2011. This version is
scheduled to appear in J. on Random Structures and Algorithm
Testing for polytomies in phylogenetic species trees using quartet frequencies
Phylogenetic species trees typically represent the speciation history as a
bifurcating tree. Speciation events that simultaneously create more than two
descendants, thereby creating polytomies in the phylogeny, are possible.
Moreover, the inability to resolve relationships is often shown as a (soft)
polytomy. Both types of polytomies have been traditionally studied in the
context of gene tree reconstruction from sequence data. However, polytomies in
the species tree cannot be detected or ruled out without considering gene tree
discordance. In this paper, we describe a statistical test based on properties
of the multi-species coalescent model to test the null hypothesis that a branch
in an estimated species tree should be replaced by a polytomy. On both
simulated and biological datasets, we show that the null hypothesis is rejected
for all but the shortest branches, and in most cases, it is retained for true
polytomies. The test, available as part of the ASTRAL package, can help
systematists decide whether their datasets are sufficient to resolve specific
relationships of interest
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