Davide Eynard

Shape-from-Operator: Recovering Shapes from Intrinsic Operators

We formulate the problem of shape‐from‐operator (SfO), recovering an embedding of a mesh from intrinsic operators defined through the discrete metric (edge lengths). Particularly interesting instances of our SfO problem include: shape‐from‐Laplacian, allowing to transfer style between shapes; shape‐from‐difference operator, used to synthesize shape analogies; and shape‐from‐eigenvectors, allowing to generate ‘intrinsic averages’ of shape collections. Numerically, we approach the SfO problem by splitting it into two optimization sub‐problems: metric‐from‐operator (reconstruction of the discrete metric from the intrinsic operator) and embedding‐from‐metric (finding a shape embedding that would realize a given metric, a setting of the multidimensional scaling problem). We study numerical properties of our problem, exemplify it on several applications, and discuss its imitations.

Multimodal Manifold Analysis by Simultaneous Diagonalization of Laplacians

We construct an extension of spectral and diffusion geometry to multiple modalities through simultaneous diagonalization of Laplacian matrices. This naturally extends classical data analysis tools based on spectral geometry, such as diffusion maps and spectral clustering. We provide several synthetic and real examples of manifold learning, object classification, and clustering, showing that the joint spectral geometry better captures the inherent structure of multi-modal data. We also show the relation of many previous approaches for multimodal manifold analysis to our framework.

An integrated approach to discover tag semantics

Tag-based systems have become very common for online classification thanks to their intrinsic advantages such as self-organization and rapid evolution. However, they are still affected by some issues that limit their utility, mainly due to the inherent ambiguity in the semantics of tags. Synonyms, homonyms, and polysemous words, while not harmful for the casual user, strongly affect the quality of search results and the performances of tag-based recommendation systems. In this paper we rely on the concept of tag relatedness in order to study small groups of similar tags and detect relationships between them. This approach is grounded on a model that builds upon an edge-colored multigraph of users, tags, and resources. To put our thoughts in practice, we present a modular and extensible framework of analysis for discovering synonyms, homonyms and hierarchical relationships amongst sets of tags. Some initial results of its application to the delicious database are presented, showing that such an approach could be useful to solve some of the well known problems of folksonomies.

Laplacian colormaps: a framework for structure-preserving color transformations

Mappings between color spaces are ubiquitous in image processing problems such as gamut mapping, decolorization, and image optimization for color‐blind people. Simple color transformations often result in information loss and ambiguities, and one wishes to find an image‐specific transformation that would preserve as much as possible the structure of the original image in the target color space. In this paper, we propose Laplacian colormaps, a generic framework for structure‐preserving color transformations between images. We use the image Laplacian to capture the structural information, and show that if the color transformation between two images preserves the structure, the respective Laplacians have similar eigenvectors, or in other words, are approximately jointly diagonalizable. Employing the relation between joint diagonalizability and commutativity of matrices, we use Laplacians commutativity as a criterion of color mapping quality and minimize it w.r.t. the parameters of a color transformation to achieve optimal structure preservation. We show numerous applications of our approach, including color‐to‐gray conversion, gamut mapping, multispectral image fusion, and image optimization for color deficient viewers.

Improving Search and Navigation by Combining Ontologies and Social Tags

The Semantic Web has the ambitious goal of enabling complex autonomous applications to reason on a machine-processable version of the World Wide Web. This, however, would require a coordinated effort not easily achievable in practice. On the other hand, spontaneous communities, based on social tagging, recently achieved noticeable consensus and diffusion. The goal of the TagOnto system is to bridge between these two realities by automatically mapping (social) tags to more structured domain ontologies, thus, providing assistive, navigational features typical of the Semantic Web. These novel searching and navigational capabilities are complementary to more traditional search engine functionalities. The system, and its intuitive AJAX interface, are released and demonstrated on-line.

A semantic tool to support navigation in a folksonomy

We propose a new approach to integrate the navigation interface of a folksonomy adding explicit semantics provided by an ontology. We describe a tool that uses WordNet to build a semantic hierarchy of related tags that helps users find related resources in del.icio.us. In this way it is possible to combine the advantages of the traditional approach to classification with the ones of the collaborative paradigm that is emerging on the Web, dealing with some of the main limitations to which folksonomies are prone.

The Uses of Norms

This chapter presents a variety of applications of norms. These applications include governance in sociotechnical systems, data licensing and data collection, understanding software development teams, requirements engineering, assurance, natural resource allocation, wireless grids, autonomous vehicles, serious games, and virtual worlds.

Harvesting Online Contents: An Analysis of Hotel Reviews Websites

Hotel Reviews Websites (HRWs) are the most used online sources to evaluate accommodation alternatives. However, they often present an overwhelming amount of unstructured or only semi-structured information which is not shared between all the systems and which cannot be easily analyzed in an automatic way. This study aims to automatically analyse hotel evaluations for a given number of Swiss hotels by comparing hotel reviews. Furthermore, the consistency of users’ countries of origin in their evaluations has been studied. The results show that there is an overall agreement on considered HRWs and a general consistency among reviewers with different countries of origin.

Exploiting tag similarities to discover synonyms and homonyms in folksonomies

Tag‐based systems are widely available, thanks to their intrinsic advantages, such as self‐organization, currency, and ease of use. Although they represent a precious source of semantic metadata, their utility is still limited. The inherent lexical ambiguities of tags strongly affect the extraction of structured knowledge and the quality of tag‐based recommendation systems. In this paper, we propose a methodology for the analysis of tag‐based systems, addressing tag synonymy and homonymy at the same time in a holistic approach: in more detail, we exploit a tripartite graph to reduce the problem of synonyms and homonyms; we apply a customized version of Tag Context Similarity to detect them, overcoming the limitations of current similarity metrics; finally, we propose the application of an overlapping clustering algorithm to detect contexts and homonymies, then evaluate its performances, and introduce a methodology for the interpretation of its results. Copyright

Coupled Functional Maps

Classical formulations of the shape matching problem involve the definition of a matching cost that directly depends on the action of the desired map when applied to some input data. Such formulations are typically one-sided - they seek for a mapping from one shape to the other, but not vice versa. In this paper we consider an unbiased formulation of this problem, in which we solve simultaneously for a low-distortion map relating the two given shapes and its inverse. We phrase the problem in the spectral domain using the language of functional maps, resulting in an especially compact and efficient optimization problem. The benefits of our proposed regularization are especially evident in the scarce data setting, where we demonstrate highly competitive results with respect to the state of the art.