You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
The vast increase in amount and complexity of digital content led to a wide interest in ad-hoc retrieval systems in recent years. Complementary, the existence of heterogeneous data sources and retrieval models stimulated the proliferation of increasingly ingenious and effective rank aggregation functions. Although recently proposed rank aggregation functions are promising with respect to effectiveness, existing proposals in the area usually overlook efficiency aspects. We propose an innovative rank aggregation function that is unsupervised, intrinsically multimodal, and targeted for fast retrieval and top effectiveness performance. We introduce the concepts of embedding and indexing of graph-based rank-aggregation representation models, and their application for search tasks. Embedding formulations are also proposed for graph-based rank representations. We introduce the concept of fusion vectors, a late-fusion representation of objects based on ranks, from which an intrinsically rank-aggregation retrieval model is defined. Next, we present an approach for fast retrieval based on fusion vectors, thus promoting an efficient rank aggregation system. Our method presents top effectiveness performance among state-of-the-art related work, while bringing novel aspects of multimodality and effectiveness. Consistent speedups are achieved against the recent baselines in all datasets considered.

Cited Abstract(s):
[1]: Graph-based representations are of broad use and applicability in pattern recognition. They exhibit, however, a major drawback with regards to the processing tools that are available in their domain. Graph embedding into vector spaces is a growing field among the structural pattern recognition community which aims at providing a feature vector representation for every graph, and thus enables classical statistical learning machinery to be used on graph-based input patterns. In this work, we propose a novel embedding methodology for graphs with continuous node attributes and unattributed edges. The approach presented in this paper is based on statistics of the node labels and the edges between them, based on their similarity to a set of representatives. We specifically deal with an important issue of this methodology, namely, the selection of a suitable set of representatives. In an experimental evaluation, we empirically show the advantages of this novel approach in the context of different classification problems using several databases of graphs.

[2]: 

[3]: Abstract This paper introduces the Bag of Graphs (BoG) , a Bag-of-Words model that encodes in graphs the local structures of a digital object. We present a formal definition, introducing concepts and rules that make this model flexible and adaptable for different applications. We define two BoG-based methods – Bag of Singleton Graphs (BoSG) and Bag of Visual Graphs (BoVG) , which create vector representations for graphs and images, respectively. We evaluate the Bag of Singleton Graphs (BoSG) for graph classification on four datasets of the IAM repository, obtaining significant results in accuracy and execution time. The method Bag of Visual Graphs (BoVG) is evaluated for image classification on Caltech and ALOI datasets, and for remote sensing image classification on images of Monte Santo and Campinas datasets. This framework opens possibilities for retrieval, classification, and clustering tasks on large datasets that use graph-based representations impractical before due to the complexity of inexact graph matching.

[4]: Graph based pattern representation offers a versatile alternative to vectorial data structures. Therefore, a growing interest in graphs can be observed in various fields. However, a serious limitation in the use of graphs is the lack of elementary mathematical operations in the graph domain, actually required in many pattern recognition algorithms. In order to overcome this limitation, the present paper proposes an embedding of a given graph population in a vector space R^n. The key idea of this embedding approach is to interpret the distances of a graph g to a number of prototype graphs as numerical features of g. In previous works, the prototypes were selected beforehand with heuristic selection algorithms. In the present paper we take a more fundamental approach and regard the problem of prototype selection as a feature selection or dimensionality reduction problem, for which many methods are available. With several experiments we show the feasibility of graph embedding based on prototypes obtained from such feature selection algorithms and demonstrate their potential to outperform previous approaches.
Graph embedding approaches have been effective in multiple scenarios involving graph databases, because vector representations from graphs usually promote better scalability, and they also have more existing mining and search functions at disposal. An embedding acts as a mapping function from a graph domain to a multidimensional vector space. proposed a map that roughly preserves distances between those domains, but to spaces of high dimensionality. This map can also be based on statistics of vertex attributes and edge attributes [1] , prototypes [4] , or graph kernels [3] . Among these initiatives, Bag of Graphs (BoG) [3] was introduced as a general unsupervised framework for graph embedding that allows graphs to be represented as vectors based on common local graph patterns. Despite BoG is targeted for any graph scenario, it requires some functions to explicitly defined concerning the target scenario. BoG has been extended for some scenarios already, such as for text classification and retrieval [2] . proposed a learning method for embedding representations of entities and relations previously modeled by graphs.