32,451 research outputs found
On multi-view learning with additive models
In many scientific settings data can be naturally partitioned into variable
groupings called views. Common examples include environmental (1st view) and
genetic information (2nd view) in ecological applications, chemical (1st view)
and biological (2nd view) data in drug discovery. Multi-view data also occur in
text analysis and proteomics applications where one view consists of a graph
with observations as the vertices and a weighted measure of pairwise similarity
between observations as the edges. Further, in several of these applications
the observations can be partitioned into two sets, one where the response is
observed (labeled) and the other where the response is not (unlabeled). The
problem for simultaneously addressing viewed data and incorporating unlabeled
observations in training is referred to as multi-view transductive learning. In
this work we introduce and study a comprehensive generalized fixed point
additive modeling framework for multi-view transductive learning, where any
view is represented by a linear smoother. The problem of view selection is
discussed using a generalized Akaike Information Criterion, which provides an
approach for testing the contribution of each view. An efficient implementation
is provided for fitting these models with both backfitting and local-scoring
type algorithms adjusted to semi-supervised graph-based learning. The proposed
technique is assessed on both synthetic and real data sets and is shown to be
competitive to state-of-the-art co-training and graph-based techniques.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS202 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Combinatorial approaches to Hopf bifurcations in systems of interacting elements
We describe combinatorial approaches to the question of whether families of
real matrices admit pairs of nonreal eigenvalues passing through the imaginary
axis. When the matrices arise as Jacobian matrices in the study of dynamical
systems, these conditions provide necessary conditions for Hopf bifurcations to
occur in parameterised families of such systems. The techniques depend on the
spectral properties of additive compound matrices: in particular, we associate
with a product of matrices a signed, labelled digraph termed a DSR^[2] graph,
which encodes information about the second additive compound of this product. A
condition on the cycle structure of this digraph is shown to rule out the
possibility of nonreal eigenvalues with positive real part. The techniques
developed are applied to systems of interacting elements termed "interaction
networks", of which networks of chemical reactions are a special case.Comment: A number of minor errors and typos corrected, and some results
slightly improve
Compound Node-Kayles on Paths
In his celebrated book "On Number and Games" (Academic Press, New-York,
1976), J.H. Conway introduced twelve versions of compound games. We analyze
these twelve versions for the Node-Kayles game on paths. For usual disjunctive
compound, Node-Kayles has been solved for a long time under normal play, while
it is still unsolved under mis\`ere play. We thus focus on the ten remaining
versions, leaving only one of them unsolved.Comment: Theoretical Computer Science (2009) to appea
Spiders for rank 2 Lie algebras
A spider is an axiomatization of the representation theory of a group,
quantum group, Lie algebra, or other group or group-like object. We define
certain combinatorial spiders by generators and relations that are isomorphic
to the representation theories of the three rank two simple Lie algebras,
namely A2, B2, and G2. They generalize the widely-used Temperley-Lieb spider
for A1. Among other things, they yield bases for invariant spaces which are
probably related to Lusztig's canonical bases, and they are useful for
computing quantities such as generalized 6j-symbols and quantum link
invariants.Comment: 33 pages. Has color figure
Effectiveness of graph-based and fingerprint-based similarity measures for virtual screening of 2D chemical structure databases
This paper reports an evaluation of both graph-based and fingerprint-based measures of structural similarity, when used for virtual screening of sets of 2D molecules drawn from the MDDR and ID Alert databases. The graph-based measures employ a new maximum common edge subgraph isomorphism algorithm, called RASCAL, with several similarity coefficients described previously for quantifying the similarity between pairs of graphs. The effectiveness of these graph-based searches is compared with that resulting from similarity searches using BCI, Daylight and Unity 2D fingerprints. Our results suggest that graph-based approaches provide an effective complement to existing fingerprint-based approaches to virtual screening
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