4,479 research outputs found
Propagation Kernels
We introduce propagation kernels, a general graph-kernel framework for
efficiently measuring the similarity of structured data. Propagation kernels
are based on monitoring how information spreads through a set of given graphs.
They leverage early-stage distributions from propagation schemes such as random
walks to capture structural information encoded in node labels, attributes, and
edge information. This has two benefits. First, off-the-shelf propagation
schemes can be used to naturally construct kernels for many graph types,
including labeled, partially labeled, unlabeled, directed, and attributed
graphs. Second, by leveraging existing efficient and informative propagation
schemes, propagation kernels can be considerably faster than state-of-the-art
approaches without sacrificing predictive performance. We will also show that
if the graphs at hand have a regular structure, for instance when modeling
image or video data, one can exploit this regularity to scale the kernel
computation to large databases of graphs with thousands of nodes. We support
our contributions by exhaustive experiments on a number of real-world graphs
from a variety of application domains
Reconstruction of biological networks by supervised machine learning approaches
We review a recent trend in computational systems biology which aims at using
pattern recognition algorithms to infer the structure of large-scale biological
networks from heterogeneous genomic data. We present several strategies that
have been proposed and that lead to different pattern recognition problems and
algorithms. The strenght of these approaches is illustrated on the
reconstruction of metabolic, protein-protein and regulatory networks of model
organisms. In all cases, state-of-the-art performance is reported
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 simple yet effective baseline for non-attributed graph classification
Graphs are complex objects that do not lend themselves easily to typical
learning tasks. Recently, a range of approaches based on graph kernels or graph
neural networks have been developed for graph classification and for
representation learning on graphs in general. As the developed methodologies
become more sophisticated, it is important to understand which components of
the increasingly complex methods are necessary or most effective.
As a first step, we develop a simple yet meaningful graph representation, and
explore its effectiveness in graph classification. We test our baseline
representation for the graph classification task on a range of graph datasets.
Interestingly, this simple representation achieves similar performance as the
state-of-the-art graph kernels and graph neural networks for non-attributed
graph classification. Its performance on classifying attributed graphs is
slightly weaker as it does not incorporate attributes. However, given its
simplicity and efficiency, we believe that it still serves as an effective
baseline for attributed graph classification. Our graph representation is
efficient (linear-time) to compute. We also provide a simple connection with
the graph neural networks.
Note that these observations are only for the task of graph classification
while existing methods are often designed for a broader scope including node
embedding and link prediction. The results are also likely biased due to the
limited amount of benchmark datasets available. Nevertheless, the good
performance of our simple baseline calls for the development of new, more
comprehensive benchmark datasets so as to better evaluate and analyze different
graph learning methods. Furthermore, given the computational efficiency of our
graph summary, we believe that it is a good candidate as a baseline method for
future graph classification (or even other graph learning) studies.Comment: 13 pages. Shorter version appears at 2019 ICLR Workshop:
Representation Learning on Graphs and Manifolds. arXiv admin note: text
overlap with arXiv:1810.00826 by other author
Learning with Graphs using Kernels from Propagated Information
Traditional machine learning approaches are designed to learn from independent vector-valued data points. The assumption that instances are independent, however, is not always true. On the contrary, there are numerous domains where data points are cross-linked, for example social networks, where persons are linked by friendship relations. These relations among data points make traditional machine learning diffcult and often insuffcient. Furthermore, data points themselves can have complex structure, for example molecules or proteins constructed from various bindings of different atoms. Networked and structured data are naturally represented by graphs, and for learning we aimto exploit their structure to improve upon non-graph-based methods. However, graphs encountered in real-world applications often come with rich additional information. This naturally implies many challenges for representation and learning: node information is likely to be incomplete leading to partially labeled graphs, information can be aggregated from multiple sources and can therefore be uncertain, or additional information on nodes and edges can be derived from complex sensor measurements, thus being naturally continuous. Although learning with graphs is an active research area, learning with structured data, substantially modeling structural similarities of graphs, mostly assumes fully labeled graphs of reasonable sizes with discrete and certain node and edge information, and learning with networked data, naturally dealing with missing information and huge graphs, mostly assumes homophily and forgets about structural similarity. To close these gaps, we present a novel paradigm for learning with graphs, that exploits the intermediate results of iterative information propagation schemes on graphs. Originally developed for within-network relational and semi-supervised learning, these propagation schemes have two desirable properties: they capture structural information and they can naturally adapt to the aforementioned issues of real-world graph data. Additionally, information propagation can be efficiently realized by random walks leading to fast, flexible, and scalable feature and kernel computations. Further, by considering intermediate random walk distributions, we can model structural similarity for learning with structured and networked data. We develop several approaches based on this paradigm. In particular, we introduce propagation kernels for learning on the graph level and coinciding walk kernels and Markov logic sets for learning on the node level. Finally, we present two application domains where kernels from propagated information successfully tackle real-world problems
kLog: A Language for Logical and Relational Learning with Kernels
We introduce kLog, a novel approach to statistical relational learning.
Unlike standard approaches, kLog does not represent a probability distribution
directly. It is rather a language to perform kernel-based learning on
expressive logical and relational representations. kLog allows users to specify
learning problems declaratively. It builds on simple but powerful concepts:
learning from interpretations, entity/relationship data modeling, logic
programming, and deductive databases. Access by the kernel to the rich
representation is mediated by a technique we call graphicalization: the
relational representation is first transformed into a graph --- in particular,
a grounded entity/relationship diagram. Subsequently, a choice of graph kernel
defines the feature space. kLog supports mixed numerical and symbolic data, as
well as background knowledge in the form of Prolog or Datalog programs as in
inductive logic programming systems. The kLog framework can be applied to
tackle the same range of tasks that has made statistical relational learning so
popular, including classification, regression, multitask learning, and
collective classification. We also report about empirical comparisons, showing
that kLog can be either more accurate, or much faster at the same level of
accuracy, than Tilde and Alchemy. kLog is GPLv3 licensed and is available at
http://klog.dinfo.unifi.it along with tutorials
A kernel-based framework for learning graded relations from data
Driven by a large number of potential applications in areas like
bioinformatics, information retrieval and social network analysis, the problem
setting of inferring relations between pairs of data objects has recently been
investigated quite intensively in the machine learning community. To this end,
current approaches typically consider datasets containing crisp relations, so
that standard classification methods can be adopted. However, relations between
objects like similarities and preferences are often expressed in a graded
manner in real-world applications. A general kernel-based framework for
learning relations from data is introduced here. It extends existing approaches
because both crisp and graded relations are considered, and it unifies existing
approaches because different types of graded relations can be modeled,
including symmetric and reciprocal relations. This framework establishes
important links between recent developments in fuzzy set theory and machine
learning. Its usefulness is demonstrated through various experiments on
synthetic and real-world data.Comment: This work has been submitted to the IEEE for possible publication.
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