Possibilistic classifiers for numerical data

International audienceNaive Bayesian Classifiers, which rely on independence hypotheses, together with a normality assumption to estimate densities for numerical data, are known for their simplicity and their effectiveness. However, estimating densities, even under the normality assumption, may be problematic in case of poor data. In such a situation, possibility distributions may provide a more faithful representation of these data. Naive Possibilistic Classifiers (NPC), based on possibility theory, have been recently proposed as a counterpart of Bayesian classifiers to deal with classification tasks. There are only few works that treat possibilistic classification and most of existing NPC deal only with categorical attributes. This work focuses on the estimation of possibility distributions for continuous data. In this paper we investigate two kinds of possibilistic classifiers. The first one is derived from classical or flexible Bayesian classifiers by applying a probability–possibility transformation to Gaussian distributions, which introduces some further tolerance in the description of classes. The second one is based on a direct interpretation of data in possibilistic formats that exploit an idea of proximity between data values in different ways, which provides a less constrained representation of them. We show that possibilistic classifiers have a better capability to detect new instances for which the classification is ambiguous than Bayesian classifiers, where probabilities may be poorly estimated and illusorily precise. Moreover, we propose, in this case, an hybrid possibilistic classification approach based on a nearest-neighbour heuristics to improve the accuracy of the proposed possibilistic classifiers when the available information is insufficient to choose between classes. Possibilistic classifiers are compared with classical or flexible Bayesian classifiers on a collection of benchmarks databases. The experiments reported show the interest of possibilistic classifiers. In particular, flexible possibilistic classifiers perform well for data agreeing with the normality assumption, while proximity-based possibilistic classifiers outperform others in the other cases. The hybrid possibilistic classification exhibits a good ability for improving accuracy

Molybdenum (Mo) increases endogenous phenolics, proline and photosynthetic pigments and the phytoremediation potential of the industrially important plant Ricinus communis L. for removal of cadmium from contaminated soil.

Cadmium (Cd) in agricultural soil negatively affects crops yield and compromises food safety. Remediation of polluted soil is necessary for the re-establishment of sustainable agriculture and to prevent hazards to human health and environmental pollution. Phytoremediation is a promising technology for decontamination of polluted soil. The present study investigated the effect of molybdenum (Mo) (0.5, 1.0 and 2.0 ppm) on endogenous production of total phenolics and free proline, plant biomass and photosynthetic pigments in Ricinus communis plants grown in Cd (25, 50 and 100 ppm) contaminated soils and the potential for Cd phytoextraction. Mo was applied via seed soaking, soil addition and foliar spray. Foliar sprays significantly increased plant biomass, Cd accumulation and bioconcentration. Phenolic concentrations showed significantly positive correlations with Cd accumulation in roots (R 2 = 0.793, 0.807 and 0.739) and leaves (R 2 = 0.707, 721 and 0.866). Similarly, proline was significantly positively correlated with Cd accumulation in roots (R 2 = 0.668, 0.694 and 0.673) and leaves (R 2 = 0.831, 0.964 and 0.930). Foliar application was found to be the most effective way to deliver Mo in terms of increase in plant growth, Cd accumulation and production of phenolics and proline

Solving the steiner tree problem with revenues, budget and hop constraints to optimality

Due to copyright restrictions, the access to the full text of this article is only available via subscription.We investigate the Steiner tree problem with revenues, budget and hop constraints (STPRBH) on graph, which is a generalization of the well-known Steiner tree problem. Given a root node, edge costs, nodes revenues, as well as a preset budget and hop, the STPRBH seeks to find a subtree that includes the root node and maximizes the sum of the total edge revenues respecting the budget and hop constraints. These constraints impose limits on the total cost of the network and the number of edges between any vertex and the root. Not surprisingly, the STPRBH is NP-hard. For this challenging network design problem that arises in telecommunication settings and multicast routing, we present several polynomial size formulations. We propose an enhanced formulation based on the classical work of Miller, Tucker, and Zemlin by using additional set of variables representing the rank-order of visiting the nodes. Also, we investigate a new formulation for the STPRBH by tailoring a partial rank-1 of the Reformulation-Linearization Technique. Extensive results are exhibited using a set of benchmark instances to compare the proposed formulations by using a general purpose MIP solver

Strength of three MIP formulations for the prize collecting steiner tree problem with a quota constraint

Due to copyright restrictions, the access to the full text of this article is only available via subscription.This paper investigates the quota version of the Prize Collecting Steiner Tree Problem (PCSTP) on a graph as a generalization of the well-known Steiner tree problem. For this challenging network design problem that arises in telecommunication settings, we present three MIP formulations: (a) the first one is a compact Miller-Tucker-Zemlin (MTZ-) based formulation, (b) the second one is derived through lifting the MTZ constraints, and (c) the third one is based on the RLT technique. We report the results of extensive computational experiments on large PCSTP instances, having up to 2500 nodes using a general-purpose MIP solver