Abstract: Graph embeddings in vector spaces aim at assigning a pattern vector to every graph so that the problems of graph classification and clustering can be solved by using data processing algorithms originally developed for statistical feature vectors. An important requirement graph features should fulfil is that they reproduce as much as possible the properties among objects in the graph domain. In particular, it is usually desired that distances between pairs of graphs in the graph domain closely resemble those between their corresponding vectorial representations. In this work, we analyse relations between the edit distance in the graph domain and the L1 distance of the attribute statistics based embedding, for which good classification performance has been reported on various datasets. We show that there is actually a high correlation between the two kinds of distances provided that the corresponding parameter values that account for balancing the weight between node and edge based features are properly selected.

Abstract: Pattern recognition is the task that aims at distinguishing objects among different classes. When such a task wants to be solved in an automatic way a crucial step is how to formally represent such patterns to the computer. Based on the different representational formalisms, we may distinguish between statistical and structural pattern recognition. The former describes objects as a set of measurements arranged in the form of what is called a feature vector. The latter assumes that relations between parts of the underlying objects need to be explicitly represented and thus it uses relational structures such as graphs for encoding their inherent information. Vector spaces are a very flexible mathematical structure that has allowed to come up with several efficient ways for the analysis of patterns under the form of feature vectors. Nevertheless, such a representation cannot explicitly cope with binary relations between parts of the objects and it is restricted to measure the exact same number of features for each pattern under study regardless of their complexity. Graph-based representations present the contrary situation. They can easily adapt to the inherent complexity of the patterns but introduce a problem of high computational complexity, hindering the design of efficient tools to process and analyse patterns.
Solving this paradox is the main goal of this thesis. The ideal situation for solving pattern recognition problems would be to represent the patterns using relational structures such as graphs, and to be able to use the wealthy repository of data processing tools from the statistical pattern recognition domain. An elegant solution to this problem is to transform the graph domain into a vector domain where any processing algorithm can be applied. In other words, by mapping each graph to a point in a vector space we automatically get access to the rich set of algorithms from the statistical domain to be applied in the graph domain. Such methodology is called graph embedding.
In this thesis we propose to associate feature vectors to graphs in a simple and very efficient way by just putting attention on the labelling information that graphs store. In particular, we count frequencies of node labels and of edges between labels. Although their locality, these features are able to robustly represent structurally global properties of graphs, when considered together in the form of a vector. We initially deal with the case of discrete attributed graphs, where features are easy to compute. The continuous case is tackled as a natural generalization of the discrete one, where rather than counting node and edge labelling instances, we count statistics of some representatives of them. We encounter how the proposed vectorial representations of graphs suffer from high dimensionality and correlation among components and we face these problems by feature selection algorithms. We also explore how the diversity of different embedding representations can be exploited in order to boost the performance of base classifiers in a multiple classifier systems framework. An extensive experimental evaluation finally shows how the methodology we propose can be efficiently computed and compete with other graph matching and embedding methodologies.

Abstract: In this paper we present some conclusions about the advantages of having an efficient task formulation when a crowdsourcing platform is used. In particular we show how the task atomization and distribution can help to obtain results in an efficient way. Our proposal is based on a recursive splitting of the original task into a set of smaller and simpler tasks. As a result both more accurate and faster solutions are obtained. Our evaluation is performed on a set of ancient documents that need to be digitized.

Abstract: This paper deals with a subgraph matching problem in Region Adjacency Graph (RAG) applied to symbol spotting in graphical documents. RAG is a very important, efficient and natural way of representing graphical information with a graph but this is limited to cases where the information is well defined with perfectly delineated regions. What if the information we are interested in is not confined within well defined regions? This paper addresses this particular problem and solves it by defining near convex grouping of oriented line segments which results in near convex regions. Pure convexity imposes hard constraints and can not handle all the cases efficiently. Hence to solve this problem we have defined a new type of convexity of regions, which allows convex regions to have concavity to some extend. We call this kind of regions Near Convex Regions (NCRs). These NCRs are then used to create the Near Convex Region Adjacency Graph (NCRAG) and with this representation we have formulated the problem of symbol spotting in graphical documents as a subgraph matching problem. For subgraph matching we have used the Approximate Edit Distance Algorithm (AEDA) on the neighborhood string, which starts working after finding a key node in the input or target graph and iteratively identifies similar nodes of the query graph in the neighborhood of the key node. The experiments are performed on artificial, real and distorted datasets.

Abstract: Unique hue settings of 185 observers under three room-lighting conditions were used to evaluate the accuracy of full and mixed chromatic adaptation transform models of CIECAM02 in terms of unique hue reproduction. Perceptual hue shifts in CIECAM02 were evaluated for both models with no clear difference using the current Commission Internationale de l'Éclairage (CIE) recommendation for mixed chromatic adaptation ratio. Using our large dataset of unique hue data as a benchmark, an optimised parameter is proposed for chromatic adaptation under mixed illumination conditions that produces more accurate results in unique hue reproduction. © 2011 Wiley Periodicals, Inc. Col Res Appl, 2013