Hierarchical stochastic graphlet embedding for graph-based pattern recognition

This is the final version. Available on open access from Springer via the DOI in this recordDespite being very successful within the pattern recognition and machine learning community, graph-based methods are often unusable with many machine learning tools. This is because of the incompatibility of most of the mathematical operations in graph domain. Graph embedding has been proposed as a way to tackle these difficulties, which maps graphs to a vector space and makes the standard machine learning techniques applicable for them. However, it is well known that graph embedding techniques usually suffer from the loss of structural information. In this paper, given a graph, we consider its hierarchical structure for mapping it into a vector space. The hierarchical structure is constructed by topologically clustering the graph nodes, and considering each cluster as a node in the upper hierarchical level. Once this hierarchical structure of graph is constructed, we consider its various configurations of its parts, and use stochastic graphlet embedding (SGE) for mapping them into vector space. Broadly speaking, SGE produces a distribution of uniformly sampled low to high order graphlets as a way to embed graphs into the vector space. In what follows, the coarse-to-fine structure of a graph hierarchy and the statistics fetched through the distribution of low to high order stochastic graphlets complements each other and include important structural information with varied contexts. Altogether, these two techniques substantially cope with the usual information loss involved in graph embedding techniques, and it is not a surprise that we obtain more robust vector space embedding of graphs. This fact has been corroborated through a detailed experimental evaluation on various benchmark graph datasets, where we outperform the state-of-the-art methods.European Union Horizon 2020Ministerio de Educación, Cultura y Deporte, SpainGeneralitat de Cataluny

Frequent subgraph mining algorithms on weighted graphs

This thesis describes research work undertaken in the field of graph-based knowledge discovery (or graph mining). The objective of the research is to investigate the benefits that the concept of weighted frequent subgraph mining can offer in the context of the graph model based classification. Weighted subgraphs are graphs where some of the vertexes/edges are considered to be more significant than others. How to discover frequent sub-structures with different strengths is the main issue to be resolved in this thesis. The main approach to addressing this issue is to integrate weight constraints into the frequent subgraph mining process. It is suggested that the utilization of weighted frequent subgraph mining generates more discriminate and significant subgraphs, which will have application in, for example, the classification and clustering of graph data

Distributed Robotic Vision for Calibration, Localisation, and Mapping

This dissertation explores distributed algorithms for calibration, localisation, and mapping in the context of a multi-robot network equipped with cameras and onboard processing, comparing against centralised alternatives where all data is transmitted to a singular external node on which processing occurs. With the rise of large-scale camera networks, and as low-cost on-board processing becomes increasingly feasible in robotics networks, distributed algorithms are becoming important for robustness and scalability. Standard solutions to multi-camera computer vision require the data from all nodes to be processed at a central node which represents a significant single point of failure and incurs infeasible communication costs. Distributed solutions solve these issues by spreading the work over the entire network, operating only on local calculations and direct communication with nearby neighbours. This research considers a framework for a distributed robotic vision platform for calibration, localisation, mapping tasks where three main stages are identified: an initialisation stage where calibration and localisation are performed in a distributed manner, a local tracking stage where visual odometry is performed without inter-robot communication, and a global mapping stage where global alignment and optimisation strategies are applied. In consideration of this framework, this research investigates how algorithms can be developed to produce fundamentally distributed solutions, designed to minimise computational complexity whilst maintaining excellent performance, and designed to operate effectively in the long term. Therefore, three primary objectives are sought aligning with these three stages

GENERIC FRAMEWORKS FOR INTERACTIVE PERSONALIZED INTERESTING PATTERN DISCOVERY

The traditional frequent pattern mining algorithms generate an exponentially large number of patterns of which a substantial portion are not much significant for many data analysis endeavours. Due to this, the discovery of a small number of interesting patterns from the exponentially large number of frequent patterns according to a particular user\u27s interest is an important task. Existing works on patter

Convex relaxation methods for graphical models : Lagrangian and maximum entropy approaches

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.Includes bibliographical references (p. 241-257).Graphical models provide compact representations of complex probability distributions of many random variables through a collection of potential functions defined on small subsets of these variables. This representation is defined with respect to a graph in which nodes represent random variables and edges represent the interactions among those random variables. Graphical models provide a powerful and flexible approach to many problems in science and engineering, but also present serious challenges owing to the intractability of optimal inference and estimation over general graphs. In this thesis, we consider convex optimization methods to address two central problems that commonly arise for graphical models. First, we consider the problem of determining the most probable configuration-also known as the maximum a posteriori (MAP) estimate-of all variables in a graphical model, conditioned on (possibly noisy) measurements of some variables. This general problem is intractable, so we consider a Lagrangian relaxation (LR) approach to obtain a tractable dual problem. This involves using the Lagrangian decomposition technique to break up an intractable graph into tractable subgraphs, such as small "blocks" of nodes, embedded trees or thin subgraphs. We develop a distributed, iterative algorithm that minimizes the Lagrangian dual function by block coordinate descent. This results in an iterative marginal-matching procedure that enforces consistency among the subgraphs using an adaptation of the well-known iterative scaling algorithm. This approach is developed both for discrete variable and Gaussian graphical models. In discrete models, we also introduce a deterministic annealing procedure, which introduces a temperature parameter to define a smoothed dual function and then gradually reduces the temperature to recover the (non-differentiable) Lagrangian dual. When strong duality holds, we recover the optimal MAP estimate. We show that this occurs for a broad class of "convex decomposable" Gaussian graphical models, which generalizes the "pairwise normalizable" condition known to be important for iterative estimation in Gaussian models.(cont.) In certain "frustrated" discrete models a duality gap can occur using simple versions of our approach. We consider methods that adaptively enhance the dual formulation, by including more complex subgraphs, so as to reduce the duality gap. In many cases we are able to eliminate the duality gap and obtain the optimal MAP estimate in a tractable manner. We also propose a heuristic method to obtain approximate solutions in cases where there is a duality gap. Second, we consider the problem of learning a graphical model (both the graph and its potential functions) from sample data. We propose the maximum entropy relaxation (MER) method, which is the convex optimization problem of selecting the least informative (maximum entropy) model over an exponential family of graphical models subject to constraints that small subsets of variables should have marginal distributions that are close to the distribution of sample data. We use relative entropy to measure the divergence between marginal probability distributions. We find that MER leads naturally to selection of sparse graphical models. To identify this sparse graph efficiently, we use a "bootstrap" method that constructs the MER solution by solving a sequence of tractable subproblems defined over thin graphs, including new edges at each step to correct for large marginal divergences that violate the MER constraint. The MER problem on each of these subgraphs is efficiently solved using the primaldual interior point method (implemented so as to take advantage of efficient inference methods for thin graphical models). We also consider a dual formulation of MER that minimizes a convex function of the potentials of the graphical model. This MER dual problem can be interpreted as a robust version of maximum-likelihood parameter estimation, where the MER constraints specify the uncertainty in the sufficient statistics of the model. This also corresponds to a regularized maximum-likelihood approach, in which an information-geometric regularization term favors selection of sparse potential representations. We develop a relaxed version of the iterative scaling method to solve this MER dual problem.by Jason K. Johnson.Ph.D

Beyond Flatland : exploring graphs in many dimensions

Societies, technologies, economies, ecosystems, organisms, . . . Our world is composed of complex networks—systems with many elements that interact in nontrivial ways. Graphs are natural models of these systems, and scientists have made tremendous progress in developing tools for their analysis. However, research has long focused on relatively simple graph representations and problem specifications, often discarding valuable real-world information in the process. In recent years, the limitations of this approach have become increasingly apparent, but we are just starting to comprehend how more intricate data representations and problem formulations might benefit our understanding of relational phenomena. Against this background, our thesis sets out to explore graphs in five dimensions: descriptivity, multiplicity, complexity, expressivity, and responsibility. Leveraging tools from graph theory, information theory, probability theory, geometry, and topology, we develop methods to (1) descriptively compare individual graphs, (2) characterize similarities and differences between groups of multiple graphs, (3) critically assess the complexity of relational data representations and their associated scientific culture, (4) extract expressive features from and for hypergraphs, and (5) responsibly mitigate the risks induced by graph-structured content recommendations. Thus, our thesis is naturally situated at the intersection of graph mining, graph learning, and network analysis.Gesellschaften, Technologien, Volkswirtschaften, Ökosysteme, Organismen, . . . Unsere Welt besteht aus komplexen Netzwerken—Systemen mit vielen Elementen, die auf nichttriviale Weise interagieren. Graphen sind natürliche Modelle dieser Systeme, und die Wissenschaft hat bei der Entwicklung von Methoden zu ihrer Analyse große Fortschritte gemacht. Allerdings hat sich die Forschung lange auf relativ einfache Graphrepräsentationen und Problemspezifikationen beschränkt, oft unter Vernachlässigung wertvoller Informationen aus der realen Welt. In den vergangenen Jahren sind die Grenzen dieser Herangehensweise zunehmend deutlich geworden, aber wir beginnen gerade erst zu erfassen, wie unser Verständnis relationaler Phänomene von intrikateren Datenrepräsentationen und Problemstellungen profitieren kann. Vor diesem Hintergrund erkundet unsere Dissertation Graphen in fünf Dimensionen: Deskriptivität, Multiplizität, Komplexität, Expressivität, und Verantwortung. Mithilfe von Graphentheorie, Informationstheorie, Wahrscheinlichkeitstheorie, Geometrie und Topologie entwickeln wir Methoden, welche (1) einzelne Graphen deskriptiv vergleichen, (2) Gemeinsamkeiten und Unterschiede zwischen Gruppen multipler Graphen charakterisieren, (3) die Komplexität relationaler Datenrepräsentationen und der mit ihnen verbundenen Wissenschaftskultur kritisch beleuchten, (4) expressive Merkmale von und für Hypergraphen extrahieren, und (5) verantwortungsvoll den Risiken begegnen, welche die Graphstruktur von Inhaltsempfehlungen mit sich bringt. Damit liegt unsere Dissertation naturgemäß an der Schnittstelle zwischen Graph Mining, Graph Learning und Netzwerkanalyse