Compositional generative mapping for tree-structured data--part I: bottom-up probabilistic modeling of trees

A gentle introduction to deep learning for graphs

The adaptive processing of graph data is a long-standing research topic that has been lately consolidated as a theme of major interest in the deep learning community. The snap increase in the amount and breadth of related research has come at the price of little systematization of knowledge and attention to earlier literature. This work is a tutorial introduction to the field of deep learning for graphs. It favors a consistent and progressive presentation of the main concepts and architectural aspects over an exposition of the most recent literature, for which the reader is referred to available surveys. The paper takes a top-down view of the problem, introducing a generalized formulation of graph representation learning based on a local and iterative approach to structured information processing. Moreover, it introduces the basic building blocks that can be combined to design novel and effective neural models for graphs. We complement the methodological exposition with a discussion of interesting research challenges and applications in the field.

Applications of Artificial Intelligence in Transport: An Overview

The rapid pace of developments in Artificial Intelligence (AI) is providing unprecedented opportunities to enhance the performance of different industries and businesses, including the transport sector. The innovations introduced by AI include highly advanced computational methods that mimic the way the human brain works. The application of AI in the transport field is aimed at overcoming the challenges of an increasing travel demand, CO2 emissions, safety concerns, and environmental degradation. In light of the availability of a huge amount of quantitative and qualitative data and AI in this digital age, addressing these concerns in a more efficient and effective fashion has become more plausible. Examples of AI methods that are finding their way to the transport field include Artificial Neural Networks (ANN), Genetic algorithms (GA), Simulated Annealing (SA), Artificial Immune system (AIS), Ant Colony Optimiser (ACO) and Bee Colony Optimization (BCO) and Fuzzy Logic Model (FLM) The successful application of AI requires a good understanding of the relationships between AI and data on one hand, and transportation system characteristics and variables on the other hand. Moreover, it is promising for transport authorities to determine the way to use these technologies to create a rapid improvement in relieving congestion, making travel time more reliable to their customers and improve the economics and productivity of their vital assets. This paper provides an overview of the AI techniques applied worldwide to address transportation problems mainly in traffic management, traffic safety, public transportation, and urban mobility. The overview concludes by addressing the challenges and limitations of AI applications in transport.

Recursive Neural Networks for Density Estimation Over Generalized Random Graphs

Structured data in the form of labeled graphs (with variable order and topology) may be thought of as the outcomes of a random graph (RG) generating process characterized by an underlying probabilistic law. This paper formalizes the notions of generalized RG (GRG) and probability density function (pdf) for GRGs. Thence, a "universal" learning machine (combining the encoding module of a recursive neural network and a radial basis functions' network) is introduced for estimating the unknown pdf from an unsupervised sample of GRGs. A maximum likelihood training algorithm is presented and constrained so as to ensure that the resulting model satisfies the axioms of probability. Techniques for preventing the model from degenerate solutions are proposed, as well as variants of the algorithm suitable to the tasks of graphs classification and graphs clustering. The major properties of the machine are discussed. The approach is validated empirically through experimental investigations in the estimation of pdfs for synthetic and real-life GRGs, in the classification of images from the Caltech Benchmark data set and molecules from the Mutagenesis data set, and in clustering of images from the LabelMe data set.

Generative Kernels for Tree-Structured Data

This paper presents a family of methods for the design of adaptive kernels for tree-structured data that exploits the summarization properties of hidden states of hidden Markov models for trees. We introduce a compact and discriminative feature space based on the concept of hidden states multisets and we discuss different approaches to estimate such hidden state encoding. We show how it can be used to build an efficient and general tree kernel based on Jaccard similarity. Furthermore, we derive an unsupervised convolutional generative kernel using a topology induced on the Markov states by a tree topographic mapping. This paper provides an extensive empirical assessment on a variety of structured data learning tasks, comparing the predictive accuracy and computational efficiency of state-of-the-art generative, adaptive, and syntactical tree kernels. The results show that the proposed generative approach has a good tradeoff between computational complexity and predictive performance, in particular when considering the soft matching introduced by the topographic mapping.

Compositional generative mapping for tree-structured data--part II: topographic projection model

We introduce GTM-SD (Generative Topographic Mapping for Structured Data), which is the first compositional generative model for topographic mapping of tree-structured data. GTM-SD exploits a scalable bottom-up hidden-tree Markov model that was introduced in Part I of this paper to achieve a recursive topographic mapping of hierarchical information. The proposed model allows efficient exploitation of contextual information from shared substructures by a recursive upward propagation on the tree structure which distributes substructure information across the topographic map. Compared to its noncompositional generative counterpart, GTM-SD is shown to allow the topographic mapping of the full sample tree, which includes a projection onto the lattice of all the distinct subtrees rooted in each of its nodes. Experimental results show that the continuous projection space generated by the smooth topographic mapping of GTM-SD yields a finer grained discrimination of the sample structures with respect to the state-of-the-art recursive neural network approach.