An Algebra of Hierarchical Graphs

We define an algebraic theory of hierarchical graphs, whose axioms characterise graph isomorphism: two terms are equated exactly when they represent the same graph. Our algebra can be understood as a high-level language for describing graphs with a node-sharing, embedding structure, and it is then well suited for defining graphical representations of software models where nesting and linking are key aspects

An Algebra of Hierarchical Graphs and its Application to Structural Encoding

We define an algebraic theory of hierarchical graphs, whose axioms characterise graph isomorphism: two terms are equated exactly when they represent the same graph. Our algebra can be understood as a high-level language for describing graphs with a node-sharing, embedding structure, and it is then well suited for defining graphical representations of software models where nesting and linking are key aspects. In particular, we propose the use of our graph formalism as a convenient way to describe configurations in process calculi equipped with inherently hierarchical features such as sessions, locations, transactions, membranes or ambients. The graph syntax can be seen as an intermediate representation language, that facilitates the encodings of algebraic specifications, since it provides primitives for nesting, name restriction and parallel composition. In addition, proving soundness and correctness of an encoding (i.e. proving that structurally equivalent processes are mapped to isomorphic graphs) becomes easier as it can be done by induction over the graph syntax

Modelos Bayesianos gráficos jerárquicos en psicología

El mejoramiento de los métodos gráficos en la investigación en psicología puede promover su uso y una mejor compresión de su poder de expresión. La aplicación de modelos Bayesianos gráficos jerárquicos se ha vuelto más frecuente en la investigación en psicología. El objetivo de este trabajo es introducir sugerencias para el mejoramiento de los modelos Bayesianos gráficos jerárquicos en psicología. Este conjunto de sugerencias se apoya en la descripción y comparación entre los dos enfoques principales con el uso de notación y pictogramas de distribución. Se concluye que la combinación de los aspectos relevantes de ambos puede mejorar el uso de los modelos Bayesianos gráficos jerárquicos en psicología.The improvement of graphical methods in psychological research can promote their use and a better comprehension of their expressive power. The application of hierarchical Bayesian graphical models has recently become more frequent in psychological research. The aim of this contribution is to introduce suggestions for the improvement of hierarchical Bayesian graphical models in psychology. This novel set of suggestions stems from the description and comparison between two main approaches concerned with the use of plate notation and distribution pictograms. It is concluded that the combination of relevant aspects of both models might improve the use of powerful hierarchical Bayesian graphical models in psychology.Fil: Campitelli, Guillermo Jorge. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Edith Cowan University; AustraliaFil: Macbeth, Guillermo Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Entre Ríos. Facultad de Ciencias de la Educación; Argentin

Hierarchical models for service-oriented systems

We present our approach to the denotation and representation of hierarchical graphs: a suitable algebra of hierarchical graphs and two domains of interpretations. Each domain of interpretation focuses on a particular perspective of the graph hierarchy: the top view (nested boxes) is based on a notion of embedded graphs while the side view (tree hierarchy) is based on gs-graphs. Our algebra can be understood as a high-level language for describing such graphical models, which are well suited for defining graphical representations of service-oriented systems where nesting (e.g. sessions, transactions, locations) and linking (e.g. shared channels, resources, names) are key aspects

Hierarchically Clustered Representation Learning

The joint optimization of representation learning and clustering in the embedding space has experienced a breakthrough in recent years. In spite of the advance, clustering with representation learning has been limited to flat-level categories, which often involves cohesive clustering with a focus on instance relations. To overcome the limitations of flat clustering, we introduce hierarchically-clustered representation learning (HCRL), which simultaneously optimizes representation learning and hierarchical clustering in the embedding space. Compared with a few prior works, HCRL firstly attempts to consider a generation of deep embeddings from every component of the hierarchy, not just leaf components. In addition to obtaining hierarchically clustered embeddings, we can reconstruct data by the various abstraction levels, infer the intrinsic hierarchical structure, and learn the level-proportion features. We conducted evaluations with image and text domains, and our quantitative analyses showed competent likelihoods and the best accuracies compared with the baselines.Comment: 10 pages, 7 figures, Under review as a conference pape