2,442 research outputs found
Clustering Time Series from Mixture Polynomial Models with Discretised Data
Clustering time series is an active research area with applications in many fields. One common feature of time series is the likely presence of outliers. These uncharacteristic data can significantly effect the quality of clusters formed. This paper evaluates a method of over-coming the detrimental effects of outliers. We describe some of the alternative approaches to clustering time series, then specify a particular class of model for experimentation with k-means clustering and a correlation based distance metric. For data derived from this class of model we demonstrate that discretising the data into a binary series of above and below the median improves the clustering when the data has outliers. More specifically, we show that firstly discretisation does not significantly effect the accuracy of the clusters when there are no outliers and secondly it significantly increases the accuracy in the presence of outliers, even when the probability of outlier is very low
The EM Algorithm and the Rise of Computational Biology
In the past decade computational biology has grown from a cottage industry
with a handful of researchers to an attractive interdisciplinary field,
catching the attention and imagination of many quantitatively-minded
scientists. Of interest to us is the key role played by the EM algorithm during
this transformation. We survey the use of the EM algorithm in a few important
computational biology problems surrounding the "central dogma"; of molecular
biology: from DNA to RNA and then to proteins. Topics of this article include
sequence motif discovery, protein sequence alignment, population genetics,
evolutionary models and mRNA expression microarray data analysis.Comment: Published in at http://dx.doi.org/10.1214/09-STS312 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Generalized Species Sampling Priors with Latent Beta reinforcements
Many popular Bayesian nonparametric priors can be characterized in terms of
exchangeable species sampling sequences. However, in some applications,
exchangeability may not be appropriate. We introduce a {novel and
probabilistically coherent family of non-exchangeable species sampling
sequences characterized by a tractable predictive probability function with
weights driven by a sequence of independent Beta random variables. We compare
their theoretical clustering properties with those of the Dirichlet Process and
the two parameters Poisson-Dirichlet process. The proposed construction
provides a complete characterization of the joint process, differently from
existing work. We then propose the use of such process as prior distribution in
a hierarchical Bayes modeling framework, and we describe a Markov Chain Monte
Carlo sampler for posterior inference. We evaluate the performance of the prior
and the robustness of the resulting inference in a simulation study, providing
a comparison with popular Dirichlet Processes mixtures and Hidden Markov
Models. Finally, we develop an application to the detection of chromosomal
aberrations in breast cancer by leveraging array CGH data.Comment: For correspondence purposes, Edoardo M. Airoldi's email is
[email protected]; Federico Bassetti's email is
[email protected]; Michele Guindani's email is
[email protected] ; Fabrizo Leisen's email is
[email protected]. To appear in the Journal of the American
Statistical Associatio
Sequence-based Multiscale Model (SeqMM) for High-throughput chromosome conformation capture (Hi-C) data analysis
In this paper, I introduce a Sequence-based Multiscale Model (SeqMM) for the
biomolecular data analysis. With the combination of spectral graph method, I
reveal the essential difference between the global scale models and local scale
ones in structure clustering, i.e., different optimization on Euclidean (or
spatial) distances and sequential (or genomic) distances. More specifically,
clusters from global scale models optimize Euclidean distance relations. Local
scale models, on the other hand, result in clusters that optimize the genomic
distance relations. For a biomolecular data, Euclidean distances and sequential
distances are two independent variables, which can never be optimized
simultaneously in data clustering. However, sequence scale in my SeqMM can work
as a tuning parameter that balances these two variables and deliver different
clusterings based on my purposes. Further, my SeqMM is used to explore the
hierarchical structures of chromosomes. I find that in global scale, the
Fiedler vector from my SeqMM bears a great similarity with the principal vector
from principal component analysis, and can be used to study genomic
compartments. In TAD analysis, I find that TADs evaluated from different scales
are not consistent and vary a lot. Particularly when the sequence scale is
small, the calculated TAD boundaries are dramatically different. Even for
regions with high contact frequencies, TAD regions show no obvious consistence.
However, when the scale value increases further, although TADs are still quite
different, TAD boundaries in these high contact frequency regions become more
and more consistent. Finally, I find that for a fixed local scale, my method
can deliver very robust TAD boundaries in different cluster numbers.Comment: 22 PAGES, 13 FIGURE
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