515 research outputs found
Optimizing Phylogenetic Supertrees Using Answer Set Programming
The supertree construction problem is about combining several phylogenetic
trees with possibly conflicting information into a single tree that has all the
leaves of the source trees as its leaves and the relationships between the
leaves are as consistent with the source trees as possible. This leads to an
optimization problem that is computationally challenging and typically
heuristic methods, such as matrix representation with parsimony (MRP), are
used. In this paper we consider the use of answer set programming to solve the
supertree construction problem in terms of two alternative encodings. The first
is based on an existing encoding of trees using substructures known as
quartets, while the other novel encoding captures the relationships present in
trees through direct projections. We use these encodings to compute a
genus-level supertree for the family of cats (Felidae). Furthermore, we compare
our results to recent supertrees obtained by the MRP method.Comment: To appear in Theory and Practice of Logic Programming (TPLP),
Proceedings of ICLP 201
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
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
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
Reconstructing phylogenies from noisy quartets in polynomial time with a high success probability
<p>Abstract</p> <p>Background</p> <p>In recent years, quartet-based phylogeny reconstruction methods have received considerable attentions in the computational biology community. Traditionally, the accuracy of a phylogeny reconstruction method is measured by simulations on synthetic datasets with known "true" phylogenies, while little theoretical analysis has been done. In this paper, we present a new model-based approach to measuring the accuracy of a quartet-based phylogeny reconstruction method. Under this model, we propose three efficient algorithms to reconstruct the "true" phylogeny with a high success probability.</p> <p>Results</p> <p>The first algorithm can reconstruct the "true" phylogeny from the input quartet topology set without quartet errors in <it>O</it>(<it>n</it><sup>2</sup>) time by querying at most (<it>n </it>- 4) log(<it>n </it>- 1) quartet topologies, where <it>n </it>is the number of the taxa. When the input quartet topology set contains errors, the second algorithm can reconstruct the "true" phylogeny with a probability approximately 1 - <it>p </it>in <it>O</it>(<it>n</it><sup>4 </sup>log <it>n</it>) time, where <it>p </it>is the probability for a quartet topology being an error. This probability is improved by the third algorithm to approximately <inline-formula><m:math name="1748-7188-3-1-i1" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:semantics><m:mrow><m:mfrac><m:mn>1</m:mn><m:mrow><m:mn>1</m:mn><m:mo>+</m:mo><m:msup><m:mi>q</m:mi><m:mn>2</m:mn></m:msup><m:mo>+</m:mo><m:mfrac><m:mn>1</m:mn><m:mn>2</m:mn></m:mfrac><m:msup><m:mi>q</m:mi><m:mn>4</m:mn></m:msup><m:mo>+</m:mo><m:mfrac><m:mn>1</m:mn><m:mrow><m:mn>16</m:mn></m:mrow></m:mfrac><m:msup><m:mi>q</m:mi><m:mn>5</m:mn></m:msup></m:mrow></m:mfrac></m:mrow><m:annotation encoding="MathType-MTEF"> MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGacaGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSaaaeaacqaIXaqmaeaacqaIXaqmcqGHRaWkcqWGXbqCdaahaaqabeaacqaIYaGmaaGaey4kaSYaaSaaaeaacqaIXaqmaeaacqaIYaGmaaGaemyCae3aaWbaaeqabaGaeGinaqdaaiabgUcaRmaalaaabaGaeGymaedabaGaeGymaeJaeGOnaydaaiabdghaXnaaCaaabeqaaiabiwda1aaaaaaaaa@3D5A@</m:annotation></m:semantics></m:math></inline-formula>, where <inline-formula><m:math name="1748-7188-3-1-i2" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:semantics><m:mrow><m:mi>q</m:mi><m:mo>=</m:mo><m:mfrac><m:mi>p</m:mi><m:mrow><m:mn>1</m:mn><m:mo>β</m:mo><m:mi>p</m:mi></m:mrow></m:mfrac></m:mrow><m:annotation encoding="MathType-MTEF"> MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGacaGaaiaabeqaaeqabiWaaaGcbaGaemyCaeNaeyypa0tcfa4aaSaaaeaacqWGWbaCaeaacqaIXaqmcqGHsislcqWGWbaCaaaaaa@3391@</m:annotation></m:semantics></m:math></inline-formula>, with running time of <it>O</it>(<it>n</it><sup>5</sup>), which is at least 0.984 when <it>p </it>< 0.05.</p> <p>Conclusion</p> <p>The three proposed algorithms are mathematically guaranteed to reconstruct the "true" phylogeny with a high success probability. The experimental results showed that the third algorithm produced phylogenies with a higher probability than its aforementioned theoretical lower bound and outperformed some existing phylogeny reconstruction methods in both speed and accuracy.</p
Algorithmic Clustering of Music
We present a fully automatic method for music classification, based only on
compression of strings that represent the music pieces. The method uses no
background knowledge about music whatsoever: it is completely general and can,
without change, be used in different areas like linguistic classification and
genomics. It is based on an ideal theory of the information content in
individual objects (Kolmogorov complexity), information distance, and a
universal similarity metric. Experiments show that the method distinguishes
reasonably well between various musical genres and can even cluster pieces by
composer.Comment: 17 pages, 11 figure
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