Defining Geographical Rating Territories in Auto Insurance Regulation by Spatially Constrained Clustering

Territory design and analysis using geographical loss cost are a key aspect in auto insurance rate regulation. The major objective of this work is to study the design of geographical rating territories by maximizing the within-group homogeneity, as well as maximizing the among-group heterogeneity from statistical perspectives, while maximizing the actuarial equity of pure premium, as required by insurance regulation. To achieve this goal, the spatially-constrained clustering of industry level loss cost was investigated. Within this study, in order to meet the contiguity, which is a legal requirement on the design of geographical rating territories, a clustering approach based on Delaunay triangulation is proposed. Furthermore, an entropy-based approach was introduced to quantify the homogeneity of clusters, while both the elbow method and the gap statistic are used to determine the initial number of clusters. This study illustrated the usefulness of the spatially-constrained clustering approach in defining geographical rating territories for insurance rate regulation purposes. The significance of this work is to provide a new solution for better designing geographical rating territories. The proposed method can be useful for other demographical data analysis because of the similar nature of the spatial constraint.

Optimal distributed interconnectivity of multi-robot systems by spatially-constrained clustering

A spatially-constrained clustering algorithm is presented in this paper. This algorithm is a distributed clustering approach to fine-tune the optimal distances between agents of the system to strengthen the data passing among them using a set of spatial constraints. In fact, this method will increase interconnectivity among agents and clusters, leading to improvement of the overall communicative functionality of the multi-robot system. This strategy will lead to the establishment of loosely-coupled connections among the clusters. These implicit interconnections will mobilize the clusters to receive and transmit information within the multi-agent system. In other words, this algorithm classifies each agent into the clusters with the lowest cost of local communication with its peers. This research demonstrates that the presented decentralized method will actually boost the communicative agility of the swarm by probabilistic proof of the acquired optimality. Hence, the common assumption regarding the full-knowledge of the agents’ primary locations has been fully relaxed compared to former methods. Consequently, the algorithm’s reliability and efficiency is confirmed. Furthermore, the method’s efficacy in passing information will improve the functionality of higher-level swarm operations, such as task assignment and swarm flocking. Analytical investigations and simulated accomplishments, corresponding to highly-populated swarms, prove the claimed efficiency and coherence.

An alternative fire regime zonation for Canada

The ability of national and multipurpose ecological classification systems to provide an optimal zonation for a fire regime is questionable. Using wildfire (>1 ha) point data for the 1980–99 period, we defined zones with a homogeneous fire regime (HFR) across Canada and we assessed how these differ from the National Ecological Framework for Canada (NEFC) units of corresponding scale, i.e. ecoprovinces. Two HFR zonations were produced through spatially constrained clustering of (i) 1600-km2 cells and (ii) the smallest units of the NEFC system, i.e. ecodistricts, using attributes for natural and anthropogenic fires. Thirty-three HFR zones were identified. HFR zonations showed smaller differences among each other than with NEFC ecoprovinces. Comparisons with ecoprovinces suggested general agreement of generalised fire regime values with HFR zones but with poor zone boundary correspondence. Ecoprovince zonation led to an overgeneralisation of fire regime estimates with less variation captured than by the HFR zonations, especially that using gridded fixed-area cells. Estimates of fire-return interval strongly differed between a priori and HFR zonations. The use of large-scale NEFC units or a zonation using its smallest units may constrain our ability to accurately quantify and portray fire regime variability across the country. The alternative empirical HFR zonation using gridded cells refines the location and nature of fire risk.