9,206 research outputs found
Graph Kernels via Functional Embedding
We propose a representation of graph as a functional object derived from the
power iteration of the underlying adjacency matrix. The proposed functional
representation is a graph invariant, i.e., the functional remains unchanged
under any reordering of the vertices. This property eliminates the difficulty
of handling exponentially many isomorphic forms. Bhattacharyya kernel
constructed between these functionals significantly outperforms the
state-of-the-art graph kernels on 3 out of the 4 standard benchmark graph
classification datasets, demonstrating the superiority of our approach. The
proposed methodology is simple and runs in time linear in the number of edges,
which makes our kernel more efficient and scalable compared to many widely
adopted graph kernels with running time cubic in the number of vertices
A multi-species functional embedding integrating sequence and network structure
A key challenge to transferring knowledge between species is that different species have fundamentally different genetic architectures. Initial computational approaches to transfer knowledge across species have relied on measures of heredity such as genetic homology, but these approaches suffer from limitations. First, only a small subset of genes have homologs, limiting the amount of knowledge that can be transferred, and second, genes change or repurpose functions, complicating the transfer of knowledge. Many approaches address this problem by expanding the notion of homology by leveraging high-throughput genomic and proteomic measurements, such as through network alignment. In this work, we take a new approach to transferring knowledge across species by expanding the notion of homology through explicit measures of functional similarity between proteins in different species. Specifically, our kernel-based method, HANDL (Homology Assessment across Networks using Diffusion and Landmarks), integrates sequence and network structure to create a functional embedding in which proteins from different species are embedded in the same vector space. We show that inner products in this space and the vectors themselves capture functional similarity across species, and are useful for a variety of functional tasks. We perform the first whole-genome method for predicting phenologs, generating many that were previously identified, but also predicting new phenologs supported from the biological literature. We also demonstrate the HANDL embedding captures pairwise gene function, in that gene pairs with synthetic lethal interactions are significantly separated in HANDL space, and the direction of separation is conserved across species. Software for the HANDL algorithm is available at http://bit.ly/lrgr-handl.Published versio
A nonparametric two-sample hypothesis testing problem for random dot product graphs
We consider the problem of testing whether two finite-dimensional random dot
product graphs have generating latent positions that are independently drawn
from the same distribution, or distributions that are related via scaling or
projection. We propose a test statistic that is a kernel-based function of the
adjacency spectral embedding for each graph. We obtain a limiting distribution
for our test statistic under the null and we show that our test procedure is
consistent across a broad range of alternatives.Comment: 24 pages, 1 figure
A survey of kernel and spectral methods for clustering
Clustering algorithms are a useful tool to explore data structures and have been employed in many disciplines. The focus of this paper is the partitioning clustering problem with a special interest in two recent approaches: kernel and spectral methods. The aim of this paper is to present a survey of kernel and spectral clustering methods, two approaches able to produce nonlinear separating hypersurfaces between clusters. The presented kernel clustering methods are the kernel version of many classical clustering algorithms, e.g., K-means, SOM and neural gas. Spectral clustering arise from concepts in spectral graph theory and the clustering problem is configured as a graph cut problem where an appropriate objective function has to be optimized. An explicit proof of the fact that these two paradigms have the same objective is reported since it has been proven that these two seemingly different approaches have the same mathematical foundation. Besides, fuzzy kernel clustering methods are presented as extensions of kernel K-means clustering algorithm. (C) 2007 Pattem Recognition Society. Published by Elsevier Ltd. All rights reserved
Geometric deep learning: going beyond Euclidean data
Many scientific fields study data with an underlying structure that is a
non-Euclidean space. Some examples include social networks in computational
social sciences, sensor networks in communications, functional networks in
brain imaging, regulatory networks in genetics, and meshed surfaces in computer
graphics. In many applications, such geometric data are large and complex (in
the case of social networks, on the scale of billions), and are natural targets
for machine learning techniques. In particular, we would like to use deep
neural networks, which have recently proven to be powerful tools for a broad
range of problems from computer vision, natural language processing, and audio
analysis. However, these tools have been most successful on data with an
underlying Euclidean or grid-like structure, and in cases where the invariances
of these structures are built into networks used to model them. Geometric deep
learning is an umbrella term for emerging techniques attempting to generalize
(structured) deep neural models to non-Euclidean domains such as graphs and
manifolds. The purpose of this paper is to overview different examples of
geometric deep learning problems and present available solutions, key
difficulties, applications, and future research directions in this nascent
field
Efficient Deformable Shape Correspondence via Kernel Matching
We present a method to match three dimensional shapes under non-isometric
deformations, topology changes and partiality. We formulate the problem as
matching between a set of pair-wise and point-wise descriptors, imposing a
continuity prior on the mapping, and propose a projected descent optimization
procedure inspired by difference of convex functions (DC) programming.
Surprisingly, in spite of the highly non-convex nature of the resulting
quadratic assignment problem, our method converges to a semantically meaningful
and continuous mapping in most of our experiments, and scales well. We provide
preliminary theoretical analysis and several interpretations of the method.Comment: Accepted for oral presentation at 3DV 2017, including supplementary
materia
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