<div>Graph-structured data is pervasive. Modeling large-scale network-structured datasets require graph processing and management systems such as graph databases. Further, the analysis of graph-structured data often necessitates bulk downloads/uploads from/to the cloud or edge nodes. Unfortunately, experience has shown that malicious actors can compromise the confidentiality of highly-sensitive data stored in the cloud or shared nodes, even in an encrypted form. For particular use cases —multi-modal knowledge graphs, electronic health records, finance— network-structured datasets can be highly sensitive and require auditability, authentication, integrity protection, and privacy-preserving computation in a controlled and trusted environment, i.e., the traditional cloud computation is not suitable for these use cases. Similarly, many modern applications utilize a "shared, replicated database" approach to provide accountability and traceability. Those applications often suffer from significant privacy issues because every node in the network can access a copy of relevant contract code and data to guarantee the integrity of transactions and reach consensus, even in the presence of malicious actors.</div><div><br></div><div>This dissertation proposes breaking from the traditional cloud computation model, and instead ship certified pre-approved trusted code closer to the data to protect graph-structured data confidentiality. Further, our technique runs in a controlled environment in a trusted data owner node and provides proof of correct code execution. This computation can be audited in the future and provides the building block to automate a variety of real use cases that require preserving data ownership. This project utilizes trusted execution environments (TEEs) but does not rely solely on TEE's architecture to provide privacy for data and code. We thoughtfully examine the drawbacks of using trusted execution environments in cloud environments. Similarly, we analyze the privacy challenges exposed by the use of blockchain technologies to provide accountability and traceability.</div><div><br></div><div>First, we propose AGAPECert, an Auditable, Generalized, Automated, Privacy-Enabling, Certification framework capable of performing auditable computation on private graph-structured data and reporting real-time aggregate certification status without disclosing underlying private graph-structured data. AGAPECert utilizes a novel mix of trusted execution environments, blockchain technologies, and a real-time graph-based API standard to provide automated, oblivious, and auditable certification. This dissertation includes the invention of two core concepts that provide accountability, data provenance, and automation for the certification process: Oblivious Smart Contracts and Private Automated Certifications. Second, we contribute an auditable and integrity-preserving graph processing model called AuditGraph.io. AuditGraph.io utilizes a unique block-based layout and a multi-modal knowledge graph, potentially improving access locality, encryption, and integrity of highly-sensitive graph-structured data. Third, we contribute a unique data store and compute engine that facilitates the analysis and presentation of graph-structured data, i.e., TruenoDB. TruenoDB offers better throughput than the state-of-the-art. Finally, this dissertation proposes integrity-preserving streaming frameworks at the edge of the network with a personalized graph-based object lookup.</div>

O presente texto descreve a tese de doutorado intitulada Análise de Formas usando Wavelets em Grafos. O tema está relacionado à área de Visão Computacional, particularmente aos tópicos de Caracterização, Descrição e Classificação de Formas. Dentre os métodos da extensa literatura em Análise de Formas 2D, percebe-se uma presença menor daqueles baseados em grafos com topologia arbitrária e irregular. As contribuições desta tese procuram preencher esta lacuna. É proposta uma metodologia baseada no seguinte pipeline : (i) Amostragem da forma, (ii) Estruturação das amostras em grafos, (iii) Função-base definida nos vértices, (iv) Análise multiescala de grafos por meio da Transformada Wavelet Espectral em grafos, (v) Extração de Características da Transformada Wavelet e (vi) Discriminação. Para cada uma das etapas (i), (ii), (iii), (v) e (vi), são inúmeras as abordagens possíveis. Um dos desafios é encontrar uma combinação de abordagens, dentre as muitas alternativas, que resulte em um pipeline eficaz para nossos propósitos. Em particular, para a etapa (iii), dado um grafo que representa uma forma, o desafio é identificar uma característica associada às amostras que possa ser definida sobre os vértices do grafo. Esta característica deve capturar a influência subjacente da estrutura combinatória de toda a rede sobre cada vértice, em diversas escalas. A Transformada Wavelet Espectral sobre os Grafos revelará esta influência subjacente em cada vértice. São apresentados resultados obtidos de experimentos usando formas 2D de benchmarks conhecidos na literatura, bem como de experimentos de aplicações em astronomia para análise de formas de galáxias do Sloan Digital Sky Survey não-rotuladas e rotuladas pelo projeto Galaxy Zoo 2 , demonstrando o sucesso da técnica proposta, comparada a abordagens clássicas como Transformada de Fourier e Transformada Wavelet Contínua 2D. / This document describes the PhD thesis entitled Shape Analysis by using Wavelets on Graphs. The addressed theme is related to Computer Vision, particularly to the Characterization, Description and Classication topics. Amongst the methods presented in an extensive literature on Shape Analysis 2D, it is perceived a smaller presence of graph-based methods with arbitrary and irregular topologies. The contributions of this thesis aim at fullling this gap. A methodology based on the following pipeline is proposed: (i) Shape sampling, (ii) Samples structuring in graphs, (iii) Function dened on vertices, (iv) Multiscale analysis of graphs through the Spectral Wavelet Transform, (v) Features extraction from the Wavelet Transforms and (vi) Classication. For the stages (i), (ii), (iii), (v) and (vi), there are numerous possible approaches. One great challenge is to nd a proper combination of approaches from the several available alternatives, which may be able to yield an eective pipeline for our purposes. In particular, for the stage (iii), given a graph representing a shape, the challenge is to identify a feature, which may be dened over the graph vertices. This feature should capture the underlying inuence from the combinatorial structure of the entire network over each vertex, in multiple scales. The Spectral Graph Wavelet Transform will reveal such an underpining inuence over each vertex. Yielded results from experiments on 2D benchmarks shapes widely known in literature, as well as results from astronomy applications to the analysis of unlabeled galaxies shapes from the Sloan Digital Sky Survey and labeled galaxies shapes by the Galaxy Zoo 2 Project are presented, demonstrating the achievements of the proposed technique, in comparison to classic approaches such as the 2D Fourier Transform and the 2D Continuous Wavelet Transform.

O presente texto descreve a tese de doutorado intitulada Análise de Formas usando Wavelets em Grafos. O tema está relacionado à área de Visão Computacional, particularmente aos tópicos de Caracterização, Descrição e Classificação de Formas. Dentre os métodos da extensa literatura em Análise de Formas 2D, percebe-se uma presença menor daqueles baseados em grafos com topologia arbitrária e irregular. As contribuições desta tese procuram preencher esta lacuna. É proposta uma metodologia baseada no seguinte pipeline : (i) Amostragem da forma, (ii) Estruturação das amostras em grafos, (iii) Função-base definida nos vértices, (iv) Análise multiescala de grafos por meio da Transformada Wavelet Espectral em grafos, (v) Extração de Características da Transformada Wavelet e (vi) Discriminação. Para cada uma das etapas (i), (ii), (iii), (v) e (vi), são inúmeras as abordagens possíveis. Um dos desafios é encontrar uma combinação de abordagens, dentre as muitas alternativas, que resulte em um pipeline eficaz para nossos propósitos. Em particular, para a etapa (iii), dado um grafo que representa uma forma, o desafio é identificar uma característica associada às amostras que possa ser definida sobre os vértices do grafo. Esta característica deve capturar a influência subjacente da estrutura combinatória de toda a rede sobre cada vértice, em diversas escalas. A Transformada Wavelet Espectral sobre os Grafos revelará esta influência subjacente em cada vértice. São apresentados resultados obtidos de experimentos usando formas 2D de benchmarks conhecidos na literatura, bem como de experimentos de aplicações em astronomia para análise de formas de galáxias do Sloan Digital Sky Survey não-rotuladas e rotuladas pelo projeto Galaxy Zoo 2 , demonstrando o sucesso da técnica proposta, comparada a abordagens clássicas como Transformada de Fourier e Transformada Wavelet Contínua 2D. / This document describes the PhD thesis entitled Shape Analysis by using Wavelets on Graphs. The addressed theme is related to Computer Vision, particularly to the Characterization, Description and Classication topics. Amongst the methods presented in an extensive literature on Shape Analysis 2D, it is perceived a smaller presence of graph-based methods with arbitrary and irregular topologies. The contributions of this thesis aim at fullling this gap. A methodology based on the following pipeline is proposed: (i) Shape sampling, (ii) Samples structuring in graphs, (iii) Function dened on vertices, (iv) Multiscale analysis of graphs through the Spectral Wavelet Transform, (v) Features extraction from the Wavelet Transforms and (vi) Classication. For the stages (i), (ii), (iii), (v) and (vi), there are numerous possible approaches. One great challenge is to nd a proper combination of approaches from the several available alternatives, which may be able to yield an eective pipeline for our purposes. In particular, for the stage (iii), given a graph representing a shape, the challenge is to identify a feature, which may be dened over the graph vertices. This feature should capture the underlying inuence from the combinatorial structure of the entire network over each vertex, in multiple scales. The Spectral Graph Wavelet Transform will reveal such an underpining inuence over each vertex. Yielded results from experiments on 2D benchmarks shapes widely known in literature, as well as results from astronomy applications to the analysis of unlabeled galaxies shapes from the Sloan Digital Sky Survey and labeled galaxies shapes by the Galaxy Zoo 2 Project are presented, demonstrating the achievements of the proposed technique, in comparison to classic approaches such as the 2D Fourier Transform and the 2D Continuous Wavelet Transform.