9,161 research outputs found
Incremental spectral clustering and its application to topological mapping
This paper presents a novel use of spectral clustering algorithms to support cases where the entries in the affinity matrix are costly to compute. The method is incremental – the
spectral clustering algorithm is applied to the affinity matrix after each row/column is added – which makes it possible to inspect the clusters as new data points are added. The method is well suited to the problem of appearance-based, on-line topological mapping for mobile robots. In this problem domain, we show that we can reduce environment-dependent parameters of the clustering algorithm to just a single, intuitive parameter. Experimental results in large outdoor and indoor environments
show that we can close loops correctly by computing only a fraction of the entries in the affinity matrix. The accompanying video clip shows how an example map is produced by the
algorithm
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
Topological structures in the equities market network
We present a new method for articulating scale-dependent topological
descriptions of the network structure inherent in many complex systems. The
technique is based on "Partition Decoupled Null Models,'' a new class of null
models that incorporate the interaction of clustered partitions into a random
model and generalize the Gaussian ensemble. As an application we analyze a
correlation matrix derived from four years of close prices of equities in the
NYSE and NASDAQ. In this example we expose (1) a natural structure composed of
two interacting partitions of the market that both agrees with and generalizes
standard notions of scale (eg., sector and industry) and (2) structure in the
first partition that is a topological manifestation of a well-known pattern of
capital flow called "sector rotation.'' Our approach gives rise to a natural
form of multiresolution analysis of the underlying time series that naturally
decomposes the basic data in terms of the effects of the different scales at
which it clusters. The equities market is a prototypical complex system and we
expect that our approach will be of use in understanding a broad class of
complex systems in which correlation structures are resident.Comment: 17 pages, 4 figures, 3 table
ASPECT: A spectra clustering tool for exploration of large spectral surveys
We present the novel, semi-automated clustering tool ASPECT for analysing
voluminous archives of spectra. The heart of the program is a neural network in
form of Kohonen's self-organizing map. The resulting map is designed as an icon
map suitable for the inspection by eye. The visual analysis is supported by the
option to blend in individual object properties such as redshift, apparent
magnitude, or signal-to-noise ratio. In addition, the package provides several
tools for the selection of special spectral types, e.g. local difference maps
which reflect the deviations of all spectra from one given input spectrum (real
or artificial). ASPECT is able to produce a two-dimensional topological map of
a huge number of spectra. The software package enables the user to browse and
navigate through a huge data pool and helps him to gain an insight into
underlying relationships between the spectra and other physical properties and
to get the big picture of the entire data set. We demonstrate the capability of
ASPECT by clustering the entire data pool of 0.6 million spectra from the Data
Release 4 of the Sloan Digital Sky Survey (SDSS). To illustrate the results
regarding quality and completeness we track objects from existing catalogues of
quasars and carbon stars, respectively, and connect the SDSS spectra with
morphological information from the GalaxyZoo project.Comment: 15 pages, 14 figures; accepted for publication in Astronomy and
Astrophysic
Fair Evaluation of Global Network Aligners
Biological network alignment identifies topologically and functionally
conserved regions between networks of different species. It encompasses two
algorithmic steps: node cost function (NCF), which measures similarities
between nodes in different networks, and alignment strategy (AS), which uses
these similarities to rapidly identify high-scoring alignments. Different
methods use both different NCFs and different ASs. Thus, it is unclear whether
the superiority of a method comes from its NCF, its AS, or both. We already
showed on MI-GRAAL and IsoRankN that combining NCF of one method and AS of
another method can lead to a new superior method. Here, we evaluate MI-GRAAL
against newer GHOST to potentially further improve alignment quality. Also, we
approach several important questions that have not been asked systematically
thus far. First, we ask how much of the node similarity information in NCF
should come from sequence data compared to topology data. Existing methods
determine this more-less arbitrarily, which could affect the resulting
alignment(s). Second, when topology is used in NCF, we ask how large the size
of the neighborhoods of the compared nodes should be. Existing methods assume
that larger neighborhood sizes are better.
We find that MI-GRAAL's NCF is superior to GHOST's NCF, while the performance
of the methods' ASs is data-dependent. Thus, the combination of MI-GRAAL's NCF
and GHOST's AS could be a new superior method for certain data. Also, which
amount of sequence information is used within NCF does not affect alignment
quality, while the inclusion of topological information is crucial. Finally,
larger neighborhood sizes are preferred, but often, it is the second largest
size that is superior, and using this size would decrease computational
complexity.
Together, our results give several general recommendations for a fair
evaluation of network alignment methods.Comment: 19 pages. 10 figures. Presented at the 2014 ISMB Conference, July
13-15, Boston, M
- …