244,434 research outputs found
Multiclass Semi-Supervised Learning on Graphs using Ginzburg-Landau Functional Minimization
We present a graph-based variational algorithm for classification of
high-dimensional data, generalizing the binary diffuse interface model to the
case of multiple classes. Motivated by total variation techniques, the method
involves minimizing an energy functional made up of three terms. The first two
terms promote a stepwise continuous classification function with sharp
transitions between classes, while preserving symmetry among the class labels.
The third term is a data fidelity term, allowing us to incorporate prior
information into the model in a semi-supervised framework. The performance of
the algorithm on synthetic data, as well as on the COIL and MNIST benchmark
datasets, is competitive with state-of-the-art graph-based multiclass
segmentation methods.Comment: 16 pages, to appear in Springer's Lecture Notes in Computer Science
volume "Pattern Recognition Applications and Methods 2013", part of series on
Advances in Intelligent and Soft Computin
Applications of a Graph Theoretic Based Clustering Framework in Computer Vision and Pattern Recognition
Recently, several clustering algorithms have been used to solve variety of
problems from different discipline. This dissertation aims to address different
challenging tasks in computer vision and pattern recognition by casting the
problems as a clustering problem. We proposed novel approaches to solve
multi-target tracking, visual geo-localization and outlier detection problems
using a unified underlining clustering framework, i.e., dominant set clustering
and its extensions, and presented a superior result over several
state-of-the-art approaches.Comment: doctoral dissertatio
On the Von Neumann Entropy of Graphs
The von Neumann entropy of a graph is a spectral complexity measure that has
recently found applications in complex networks analysis and pattern
recognition. Two variants of the von Neumann entropy exist based on the graph
Laplacian and normalized graph Laplacian, respectively. Due to its
computational complexity, previous works have proposed to approximate the von
Neumann entropy, effectively reducing it to the computation of simple node
degree statistics. Unfortunately, a number of issues surrounding the von
Neumann entropy remain unsolved to date, including the interpretation of this
spectral measure in terms of structural patterns, understanding the relation
between its two variants, and evaluating the quality of the corresponding
approximations.
In this paper we aim to answer these questions by first analysing and
comparing the quadratic approximations of the two variants and then performing
an extensive set of experiments on both synthetic and real-world graphs. We
find that 1) the two entropies lead to the emergence of similar structures, but
with some significant differences; 2) the correlation between them ranges from
weakly positive to strongly negative, depending on the topology of the
underlying graph; 3) the quadratic approximations fail to capture the presence
of non-trivial structural patterns that seem to influence the value of the
exact entropies; 4) the quality of the approximations, as well as which variant
of the von Neumann entropy is better approximated, depends on the topology of
the underlying graph
Distilling Structure from Imagery : Graph-based Models for the Interpretation of Document Images
From its early stages, the community of Pattern Recognition and Computer Vision has considered the importance of leveraging the structural information when understanding images. Usually, graphs have been proposed as a suitable model to represent this kind of information due to their flexibility and representational power able to codify both, the components, objects, or entities and their pairwise relationship. Even though graphs have been successfully applied to a huge variety of tasks, as a result of their symbolic and relational nature, graphs have always suffered from some limitations compared to statistical approaches. Indeed, some trivial mathematical operations do not have an equivalence in the graph domain. For instance, in the core of many pattern recognition applications, there is a need to compare two objects. This operation, which is trivial when considering feature vectors defined in ℝn, is not properly defined for graphs. In this thesis, we have investigated the importance of the structural information from two perspectives, the traditional graph-based methods and the new advances on Geometric Deep Learning. On the one hand, we explore the problem of defining a graph representation and how to deal with it on a large scale and noisy scenario. On the other hand, Graph Neural Networks are proposed to first redefine a Graph Edit Distance methodologies as a metric learning problem, and second, to apply them in a real use case scenario for the detection of repetitive patterns which define tables in invoice documents. As experimental framework, we have validated the different methodological contributions in the domain of Document Image Analysis and Recognition
SAT-Based Algorithms for Regular Graph Pattern Matching
Graph matching is a fundamental problem in pattern recognition, with many
applications such as software analysis and computational biology. One
well-known type of graph matching problem is graph isomorphism, which consists
of deciding if two graphs are identical. Despite its usefulness, the properties
that one may check using graph isomorphism are rather limited, since it only
allows strict equality checks between two graphs. For example, it does not
allow one to check complex structural properties such as if the target graph is
an arbitrary length sequence followed by an arbitrary size loop.
We propose a generalization of graph isomorphism that allows one to check
such properties through a declarative specification. This specification is
given in the form of a Regular Graph Pattern (ReGaP), a special type of graph,
inspired by regular expressions, that may contain wildcard nodes that represent
arbitrary structures such as variable-sized sequences or subgraphs. We propose
a SAT-based algorithm for checking if a target graph matches a given ReGaP. We
also propose a preprocessing technique for improving the performance of the
algorithm and evaluate it through an extensive experimental evaluation on
benchmarks from the CodeSearchNet dataset.Comment: Shorter version accepted for publication at AAAI 202
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