Optimising decision trees using multi-objective particle swarm optimisation

Copyright © 2009 Springer-Verlag Berlin Heidelberg. The final publication is available at link.springer.comBook title: Swarm Intelligence for Multi-objective Problems in Data MiningSummary. Although conceptually quite simple, decision trees are still among the most popular classifiers applied to real-world problems. Their popularity is due to a number of factors – core among these is their ease of comprehension, robust performance and fast data processing capabilities. Additionally feature selection is implicit within the decision tree structure. This chapter introduces the basic ideas behind decision trees, focusing on decision trees which only consider a rule relating to a single feature at a node (therefore making recursive axis-parallel slices in feature space to form their classification boundaries). The use of particle swarm optimization (PSO) to train near optimal decision trees is discussed, and PSO is applied both in a single objective formulation (minimizing misclassification cost), and multi-objective formulation (trading off misclassification rates across classes). Empirical results are presented on popular classification data sets from the well-known UCI machine learning repository, and PSO is demonstrated as being fully capable of acting as an optimizer for trees on these problems. Results additionally support the argument that multi-objectification of a problem can improve uni-objective search in classification problems

Grasslands - more important for ecosystem services than you might think

Extensively managed grasslands are recognized globally for their high biodiversity and their social and cultural values. However, their capacity to deliver multiple ecosystem services (ES) as parts of agricultural systems is surprisingly understudied compared to other production systems. We undertook a comprehensive overview of ES provided by natural and semi‐natural grasslands, using southern Africa (SA) and northwest Europe as case studies, respectively. We show that these grasslands can supply additional non‐agricultural services, such as water supply and flow regulation, carbon storage, erosion control, climate mitigation, pollination, and cultural ES. While demand for ecosystems services seems to balance supply in natural grasslands of SA, the smaller areas of semi‐natural grasslands in Europe appear to not meet the demand for many services. We identified three bundles of related ES from grasslands: water ES including fodder production, cultural ES connected to livestock production, and population‐based regulating services (e.g., pollination and biological control), which also linked to biodiversity. Greenhouse gas emission mitigation seemed unrelated to the three bundles. The similarities among the bundles in SA and northwestern Europe suggest that there are generalities in ES relations among natural and semi‐natural grassland areas. We assessed trade‐offs and synergies among services in relation to management practices and found that although some trade‐offs are inevitable, appropriate management may create synergies and avoid trade‐offs among many services. We argue that ecosystem service and food security research and policy should give higher priority to how grasslands can be managed for fodder and meat production alongside other ES. By integrating grasslands into agricultural production systems and land‐use decisions locally and regionally, their potential to contribute to functional landscapes and to food security and sustainable livelihoods can be greatly enhanced

Closed-Form Bayesian Inferences for the Logit Model via Polynomial Expansions

Articles in Marketing and choice literatures have demonstrated the need for incorporating person-level heterogeneity into behavioral models (e.g., logit models for multiple binary outcomes as studied here). However, the logit likelihood extended with a population distribution of heterogeneity doesn't yield closed-form inferences, and therefore numerical integration techniques are relied upon (e.g., MCMC methods). We present here an alternative, closed-form Bayesian inferences for the logit model, which we obtain by approximating the logit likelihood via a polynomial expansion, and then positing a distribution of heterogeneity from a flexible family that is now conjugate and integrable. For problems where the response coefficients are independent, choosing the Gamma distribution leads to rapidly convergent closed-form expansions; if there are correlations among the coefficients one can still obtain rapidly convergent closed-form expansions by positing a distribution of heterogeneity from a Multivariate Gamma distribution. The solution then comes from the moment generating function of the Multivariate Gamma distribution or in general from the multivariate heterogeneity distribution assumed. Closed-form Bayesian inferences, derivatives (useful for elasticity calculations), population distribution parameter estimates (useful for summarization) and starting values (useful for complicated algorithms) are hence directly available. Two simulation studies demonstrate the efficacy of our approach.Comment: 30 pages, 2 figures, corrected some typos. Appears in Quantitative Marketing and Economics vol 4 (2006), no. 2, 173--20

Turbulent spectrum of the Earth's ozone field

The Total Ozone Mapping Spectrometer (TOMS) database is subjected to an analysis in terms of the Karhunen-Loeve (KL) empirical eigenfunctions. The concentration variance spectrum is transformed into a wavenumber spectrum, $E_c(k)$. In terms of wavenumber $E_c(k)$ is shown to be $O(k^{-2/3})$ in the inverse cascade regime, $O(k^{-2})$ in the enstrophy cascade regime with the spectral {\it knee} at the wavenumber of barotropic instability.The spectrum is related to known geophysical phenomena and shown to be consistent with physical dimensional reasoning for the problem. The appropriate Reynolds number for the phenomena is $Re\approx 10^{10}$.Comment: RevTeX file, 4 pages, 4 postscript figures available upon request from Richard Everson <[email protected]