Abstract: Graphs are the most powerful, expressive and convenient data structures but there is a lack of efficient computational tools and algorithms for processing them. The embedding of graphs into numeric vector spaces permits them to access the state-of-the-art computational efficient statistical models and tools. In this paper we take forward our work on explicit graph embedding and present an improvement to our earlier proposed method, named “fuzzy multilevel graph embedding – FMGE”, through feature selection technique. FMGE achieves the embedding of attributed graphs into low dimensional vector spaces by performing a multilevel analysis of graphs and extracting a set of global, structural and elementary level features. Feature selection permits FMGE to select the subset of most discriminating features and to discard the confusing ones for underlying graph dataset. Experimental results for graph classification experimentation on IAM letter, GREC and fingerprint graph databases, show improvement in the performance of FMGE.

Abstract: To recognise objects is perhaps the most important task an autonomous system, either biological or artificial needs to perform. In the context of human vision, this is partly achieved by recognizing the colour of surfaces despite changes in the wavelength distribution of the illumination, a property called colour constancy. Correct surface colour recognition may be adequately accomplished by colour category matching without the need to match colours precisely, therefore categorical colour constancy is likely to play an important role for object identification to be successful. The main aim of this work is to study the relationship between colour constancy and categorical colour perception. Previous studies of colour constancy have shown the influence of factors such the spatio-chromatic properties of the background, individual observer's performance, semantics, etc. However there is very little systematic study of these influences. To this end, we developed a new approach to colour constancy which includes both individual observers' categorical perception, the categorical structure of the background, and their interrelations resulting in a more comprehensive characterization of the phenomenon. In our study, we first developed a new method to analyse the categorical structure of 3D colour space, which allowed us to characterize individual categorical colour perception as well as quantify inter-individual variations in terms of shape and centroid location of 3D categorical regions. Second, we developed a new colour constancy paradigm, termed chromatic setting, which allows measuring the precise location of nine categorically-relevant points in colour space under immersive illumination. Additionally, we derived from these measurements a new colour constancy index which takes into account the magnitude and orientation of the chromatic shift, memory effects and the interrelations among colours and a model of colour naming tuned to each observer/adaptation state. Our results lead to the following conclusions: (1) There exists large inter-individual variations in the categorical structure of colour space, and thus colour naming ability varies significantly but this is not well predicted by low-level chromatic discrimination ability; (2) Analysis of the average colour naming space suggested the need for an additional three basic colour terms (turquoise, lilac and lime) for optimal colour communication; (3) Chromatic setting improved the precision of more complex linear colour constancy models and suggested that mechanisms other than cone gain might be best suited to explain colour constancy; (4) The categorical structure of colour space is broadly stable under illuminant changes for categorically balanced backgrounds; (5) Categorical inconstancy exists for categorically unbalanced backgrounds thus indicating that categorical information perceived in the initial stages of adaptation may constrain further categorical perception.