A stochastic approach to handle resource constraints as knapsack problems in ensemble pruning

Ensemble-based methods are highly popular approaches that increase the accuracy of a decision by aggregating the opinions of individual voters. The common point is to maximize accuracy; however, a natural limitation occurs if incremental costs are also assigned to the individual voters. Consequently, we investigate creating ensembles under an additional constraint on the total cost of the members. This task can be formulated as a knapsack problem, where the energy is the ensemble accuracy formed by some aggregation rules. However, the generally applied aggregation rules lead to a nonseparable energy function, which takes the common solution tools—such as dynamic programming—out of action. We introduce a novel stochastic approach that considers the energy as the joint probability function of the member accuracies. This type of knowledge can be efficiently incorporated in a stochastic search process as a stopping rule, since we have the information on the expected accuracy or, alternatively, the probability of finding more accurate ensembles. Experimental analyses of the created ensembles of pattern classifiers and object detectors confirm the efficiency of our approach over other pruning ones. Moreover, we propose a novel stochastic search method that better fits the energy, which can be incorporated in other stochastic strategies as well.

The nested structure of urban business clusters

Although the cluster theory literature is bountiful in economics and regional science, there is still a lack of understanding of how the geographical scales of analysis (neighbourhood, city, region) relate to one another and impact the observed phenomenon, and to which extent the clusters are industrially coherent or geographically consistent. In this paper, we cluster spatial economic activities through a multi-scalar approach making use of percolation theory. We consider both the industrial similarity and the geographical proximity between firms, through their joint probability function which is constructed as a copula. This gives rise to an emergent nested hierarchy of geoindustrial clusters, which enables us to analyse the relationships between the different scales, and specific industrial sectors. Using longitudinal business microdata from the Office for National Statistics, we look at the evolution of clusters which spans from very local groups of businesses to the metropolitan level, in 2007 and in 2014, so that the changes stemming from the financial crisis can be observed.