Local Geometry Processing for Deformations of Non-Rigid 3D Shapes

Geometry processing and in particular spectral geometry processing deal with many different deformations that complicate shape analysis problems for non-rigid 3D objects. Furthermore, pointwise description of surfaces has increased relevance for several applications such as shape correspondences and matching, shape representation, shape modelling and many others. In this thesis we propose four local approaches to face the problems generated by the deformations of real objects and improving the pointwise characterization of surfaces. Differently from global approaches that work simultaneously on the entire shape we focus on the properties of each point and its local neighborhood. Global analysis of shapes is not negative in itself. However, having to deal with local variations, distortions and deformations, it is often challenging to relate two real objects globally. For this reason, in the last decades, several instruments have been introduced for the local analysis of images, graphs, shapes and surfaces. Starting from this idea of localized analysis, we propose both theoretical insights and application tools within the local geometry processing domain. In more detail, we extend the windowed Fourier transform from the standard Euclidean signal processing to different versions specifically designed for spectral geometry processing. Moreover, from the spectral geometry processing perspective, we define a new family of localized basis for the functional space defined on surfaces that improve the spatial localization for standard applications in this field. Finally, we introduce the discrete time evolution process as a framework that characterizes a point through its pairwise relationship with the other points on the surface in an increasing scale of locality. The main contribute of this thesis is a set of tools for local geometry processing and local spectral geometry processing that could be used in standard useful applications. The overall observation of our analysis is that localization around points could factually improve the geometry processing in many different applications

Novel Directions for Multiagent Trust Modeling in Online Social Networks

This thesis presents two works with the shared goal of improving the capacity of multiagent trust modeling to be applied to social networks. The first demonstrates how analyzing the responses to content on a discussion forum can be used to detect certain types of undesirable behaviour. This technique can be used to extract quantified representations of the impact agents are having on the community, a critical component for trust modeling. The second work expands on the technique of multi-faceted trust modeling, determining whether a clustering step designed to group agents by similarity can improve the performance of trust link predictors. Specifically, we hypothesize that learning a distinct model for each cluster of similar users will result in more personalized, and therefore more accurate, predictions. Online social networks have exploded in popularity over the course of the last decade, becoming a central source of information and entertainment for millions of users. This radical democratization of the flow of information, while purporting many benefits, also raises a raft of new issues. These networks have proven to be a potent medium for the spread of misinformation and rumors, may contribute to the radicalization of communities, and are vulnerable to deliberate manipulation by bad actors. In this thesis, our primary aim is to examine content recommendation on social media through the lens of trust modeling. The central supposition along this path is that the behaviors of content creators and the consumers of their content can be fit into the trust modeling framework, supporting recommendations of content from creators who not only are popular, but have the support of trustworthy users and are trustworthy themselves. This research direction shows promise for tackling many of the issues we've mentioned. Our works show that a machine learning model can predict certain types of anti-social behaviour in a discussion starting comment solely on the basis of analyzing replies to that comment with accuracy in the range of 70% to 80%. Further, we show that a clustering based approach to personalization for multi-faceted trust models can increase accuracy on a down-stream trust aware item recommendation task, evaluated on a large data set of Yelp users