Stochastic Graphlet Embedding

Abstract--Graph-based methods are known to be successful in many machine learning and pattern classification tasks. These methods consider semi-structured data as graphs where nodes correspond to primitives (parts, interest points, segments, etc.) and edges characterize the relationships between these primitives. However, these non-vectorial graph data cannot be straightforwardly plugged into off-the-shelf machine learning algorithms without a preliminary step of - explicit/implicit - graph vectorization and embedding. This embedding process should be resilient to intra-class graph variations while being highly discriminant. In this paper, we propose a novel high-order stochastic graphlet embedding (SGE) that maps graphs into vector spaces. Our main contribution includes a new stochastic search procedure that efficiently parses a given graph and extracts/samples unlimitedly high-order graphlets. We consider these graphlets, with increasing orders, to model local primitives as well as their increasingly complex interactions. In order to build our graph representation, we measure the distribution ofthese graphlets into a given graph, using particular hash functions that efficiently assign sampled graphlets into isomorphic sets with a very low probability of collision. When combined with maximum margin classifiers, these graphlet-based representations have positive impact on the performance of pattern comparison and recognition as corroborated through extensive experiments using standard benchmark databases. I. INTRODUCTION In this paper, we consider the problem of graph-based classification: given a pattern (image, shape, handwritten character, documentetc.) Most of the early pattern classification methods were designed using numerical feature vectors resulting from statistical analysis [12], [29]. Other more successful extensions of these methods also integrate structural information (see for instance [27]). These extensions were built upon the assumption that parts, in patterns, do not appear independently and structural relationships among these parts are crucial in order to achieve effective description and classification [20].