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1. Curado, Manuel. Structural Similarity: Applications to Object Recognition and Clustering .

Degree: 2018, University of Alicante

In this thesis, we propose many developments in the context of Structural Similarity. We address both node (local) similarity and graph (global) similarity. Concerning node similarity, we focus on improving the diffusive process leading to compute this similarity (e.g. Commute Times) by means of modifying or rewiring the structure of the graph (Graph Densification), although some advances in Laplacian-based ranking are also included in this document. Graph Densification is a particular case of what we call graph rewiring, i.e. a novel field (similar to image processing) where input graphs are rewired to be better conditioned for the subsequent pattern recognition tasks (e.g. clustering). In the thesis, we contribute with an scalable an effective method driven by Dirichlet processes. We propose both a completely unsupervised and a semi-supervised approach for Dirichlet densification. We also contribute with new random walkers (Return Random Walks) that are useful structural filters as well as asymmetry detectors in directed brain networks used to make early predictions of Alzheimer's disease (AD). Graph similarity is addressed by means of designing structural information channels as a means of measuring the Mutual Information between graphs. To this end, we first embed the graphs by means of Commute Times. Commute times embeddings have good properties for Delaunay triangulations (the typical representation for Graph Matching in computer vision). This means that these embeddings can act as encoders in the channel as well as decoders (since they are invertible). Consequently, structural noise can be modelled by the deformation introduced in one of the manifolds to fit the other one. This methodology leads to a very high discriminative similarity measure, since the Mutual Information is measured on the manifolds (vectorial domain) through copulas and bypass entropy estimators. This is consistent with the methodology of decoupling the measurement of graph similarity in two steps: a) linearizing the Quadratic Assignment Problem (QAP) by means of the embedding trick, and b) measuring similarity in vector spaces. The QAP problem is also investigated in this thesis. More precisely, we analyze the behaviour of m-best Graph Matching methods. These methods usually start by a couple of best solutions and then expand locally the search space by excluding previous clamped variables. The next variable to clamp is usually selected randomly, but we show that this reduces the performance when structural noise arises (outliers). Alternatively, we propose several heuristics for spanning the search space and evaluate all of them, showing that they are usually better than random selection. These heuristics are particularly interesting because they exploit the structure of the affinity matrix. Efficiency is improved as well. Concerning the application domains explored in this thesis we focus on object recognition (graph similarity), clustering (rewiring), compression/decompression of graphs (links with Extremal Graph Theory), 3D shape… Advisors/Committee Members: Escolano, Francisco (advisor), Sáez Martínez, Juan Manuel (advisor).

Subjects/Keywords: Graph densification; Cut similarity; Spectral clustering; Dirichlet problems; Random walkers; Commute Times; Graph algorithms; Regular Partition; Szemeredi; Alzheimer's disease; Graphs; Return Random Walk; Net4lap; Directed graphs; Spectral graph theory; Graph entropy; Mutual information; Manifold alignment; m-Best Graph Matching; Binary-Tree Partitions; QAP; Graph sparsification; Shape simplification; Alpha shapes

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APA (6th Edition):

Curado, M. (2018). Structural Similarity: Applications to Object Recognition and Clustering . (Thesis). University of Alicante. Retrieved from http://hdl.handle.net/10045/98110

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Curado, Manuel. “Structural Similarity: Applications to Object Recognition and Clustering .” 2018. Thesis, University of Alicante. Accessed July 11, 2020. http://hdl.handle.net/10045/98110.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Curado, Manuel. “Structural Similarity: Applications to Object Recognition and Clustering .” 2018. Web. 11 Jul 2020.

Vancouver:

Curado M. Structural Similarity: Applications to Object Recognition and Clustering . [Internet] [Thesis]. University of Alicante; 2018. [cited 2020 Jul 11]. Available from: http://hdl.handle.net/10045/98110.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Curado M. Structural Similarity: Applications to Object Recognition and Clustering . [Thesis]. University of Alicante; 2018. Available from: http://hdl.handle.net/10045/98110

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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