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The existence of a macroscopic fundamental diagram (MFD) in a network/subnetwork allows one to formulate hierarchical traffic management strategies. In order to achieve this, a robust and efficient network partitioning algorithm is needed. This research aims to create such an algorithm, where distinct MFD properties exist for each respective partition. The proposed four-step network partition approach utilizes the concept of lambda-connectedness and the technique of region growing and, unlike prior studies, can work with partial traffic data. This research brings forth the following contributions: 1) an algorithmic approach that allows for incomplete traffic datasets as an input and 2) an approach that does not require the user to arbitrarily pre-determine the number of necessary subnetworks. The proposed algorithmic approach can intuitively decide on the number of partitions based on the network connectivity and traffic congestion patterns. The proposed approach was implemented and tested on the regional planning network of Tucson/Pima County Arizona, USA. The MFD related statistics for each subnetwork are presented and discussed. Numerical analysis on lambda choice and algorithm sensitivity regarding different data missing ratios were also performed and elaborated.

Our work aims at developing or expliciting bridges between Bayesian networks (BNs) and Natural Exponential Families, by proposing discrete exponential Bayesian networks as a generalization of usual discrete ones. We introduce a family of prior distributions which generalizes the Dirichlet prior applied on discrete Bayesian networks, and then we determine the overall posterior distribution. Subsequently, we develop the Bayesian estimators of the parameters, and a new score function that extends the Bayesian Dirichlet score for BN structure learning. Our goal is to determine empirically in which contexts some of our discrete exponential BNs (Poisson deBNs) can be an effective alternative to usual BNs for density estimation.

This paper proposes a general formalism for representation, inference and learning with general hybrid Bayesian networks in which continuous and discrete variables may appear anywhere in a directed acyclic graph. The formalism fuzzifies a hybrid Bayesian network into two alternative forms: the first form replaces each continuous variable in the given directed acyclic graph (DAG) by a partner discrete variable and adds a directed link from the partner discrete variable to the continuous one. The mapping between two variables is not crisp quantization but is approximated (fuzzified) by a conditional Gaussian (CG) distribution. The CG model is equivalent to a fuzzy set but no fuzzy logic formalism is employed. The conditional distribution of a discrete variable given its discrete parents is still assumed to be multinomial as in discrete Bayesian networks. The second form only replaces each continuous variable whose descendants include discrete variables by a partner discrete variable and adds a directed link from that partner discrete variable to the continuous one. The dependence between the partner discrete variable and the original continuous variable is approximated by a CG distribution, but the dependence between a continuous variable and its continuous and discrete parents is approximated by a conditional Gaussian regression (CGR) distribution. Obviously, the second form is a finer approximation, but restricted to CGR models, and requires more complicated inference and learning algorithms. This results in two general approximate representations of a general hybrid Bayesian networks, which are called here the fuzzy Bayesian network (FBN) form-I and form-II. For the two forms of FBN, general exact inference algorithms exists, which are extensions of the junction tree inference algorithm for discrete Bayesian networks. Learning fuzzy Bayesian networks from data is different from learning purely discrete Bayesian networks because not only all the newly converted discrete variables are latent in the data, but also the number of discrete states for each of these variables and the CG or CGR distribution of each continuous variable given its partner discrete parents or both continuous and discrete parents have to be determined.

We consider estimation of Bayesian network structures given a finite number of examples when both discrete and continuous random variables are present in a Bayesian network.

Structure-variable Discrete Dynamic Bayesian Networks can model under the situation n of the process of mutation and the change of discrete network structure and parameters, but can't model and reason the system containing both continuous variables and discrete variables. Focusing on this question the concept of Structure-variable Hybrid Dynamic Bayesian Networks is proposed, introduce the algorithm of the discrete forward-backward into Discrete Dynamic Bayesian Network inference to get inference algorithm of more hidden nodes in Structure-variable Discrete Dynamic Bayesian Networks, and combine with the forward-backward reasoning algorithm of continuous variables, propose inference algorithm for Structure-variable Hybrid Dynamic Bayesian Networks. The simulation background is the assessment of UAV under dynamic environment situation and validates the algorithm .The results of simulation demonstrates the validity of the proposed concepts and reasoning algorithm for Variable Structure Hybrid Dynamic Bayesian Networks.

In this paper, we develop the notion of discrete exponential Bayesian network, parametrization of Bayesian networks (BNs) using more general discrete quadratic exponential families instead of usual multinomial ones. We then introduce a family of prior distributions which generalizes the Dirichlet prior classically used with discrete Bayesian network. We develop the posterior distribution for our discrete exponential BNs leading to bayesian estimations of the parameters of our models and one new scoring function extending the Bayesian Dirichlet score used for structure learning. These theoretical results are finally illustrated for Poisson and Negative Binomial BNs.

International audience; We propose in this paper a segmentation process that can deal with noisy discrete objects. A flexible approach considering arithmetic discrete planes with a variable width is used to avoid the over-segmentation that might happen when classical segmentation algorithms based on regular discrete planes are used to decompose the surface of the object. A method to choose a seed and different segmentation strategies according to the shape of the surface are also proposed.

The classical connectivity is typically used to capture the robustness of networks. Robustness, however, encompasses more than this simple definition of being connected. A spectral metric, referred to as the algebraic connectivity, plays a special role for the robustness since it measures the extent to which it is difficult to cut the network into independent components. We rely on the algebraic connectivity to study the robustness to random node and link failures in three important network models: the random graph of Erdos-Renyi, the small-world graph of Watts and Strogatz and the scale-free graph of Barabasi-Albert. We show that the robustness to random node and link failures significantly differs between the three models. This points to explicit influence of the network structure on the robustness. The homogeneous structure of the random graph of Erdos-Renyi implies an invariant robustness under random node failures. The heterogeneous structure of the small-world graph of Watts and Strogatz and scale-free graph of Barabasi-Albert, on the other hand, implies a non-trivial robustness to random node and link failures.

The complexity of finding local optima is an open problem for many neighborhood structures. We show how to derive close lower and upper bounds on the minimum number of function evaluations needed to find a local optimum in an arbitrary graph. When these bounding techniques are applied to the hypercube, the results give insights into the class PLS and the gap between the average and worst-case behavior of local search.

A newly developed classification scheme for samples with discrete valued features is presented in this paper. In it, we first map the discrete feature space into a Euclidean space called logarithm of likelihood ratio (LLR) space. The likelihood ratios are formed from the estimated distributions based on the dependence tree structure obtained through minimizing the error probability. By discriminant analysis, we then transform the LLR space into one-dimensional space on which classification is conducted. We have applied this new scheme to several sets of biomedical data and have obtained significantly high classification rates.