PULSE, progressive upper level set scan statistic for geospatial hotspot detection

Abstract

This paper presents a scan statistic, progressive upper level set (PULSE) scan statistic, for geospatial hotspot detection and its software implementation. Like ULS, the PULSE scan statistic is based on the arbitrarily shaped scan window and can be adapted for a network setting. PULSE is a refinement of the upper level set (ULS) scan statistic. Like some other likelihood based scanning devices, the ULS scan statistic identifies maximum likelihood estimate (MLE) zones that tend to be 'stringy' and sprawling. Its search path increases possibility of inclusion of extraneous cells in its MLE zones and, to a smaller extent, of exclusion of cells that belong to a true hotspot from its MLE zone. The PULSE scan statistic achieves improvement over the ULS scan statistic in two ways. First, it begins its search for a most likely zone with a large population of candidate zones obtained by modifying the ULS tree structure and continues its search using a genetic algorithm. Secondly, to reduce chances of generating an MLE that is excessively stringy and that includes extraneous cells in the MLE zone, PULSE uses cardinality and compactness of zones along with their 123 150 Environ Ecol Stat (2010) 17:149-182 likelihoods as the fitness function in the genetic algorithm and uses several pertinent criteria including evenness of intra-zone cellular response ratios to determine the MLE zone. To reduce computation, Gumbel distribution of extreme values is used to determine the p-value of the MLE zone. Better results come at the cost of increased processing time. An evaluative performance study is presented.

Novel evaluation metrics for sparse spatio-temporal point process hotspot predictions - a crime case study

“…By defining hotspots using a fixed coverage, we achieve a standardised scale on which to compare different methods, assuming a constant level of available police resources. Alternative methods include defining a threshold intensity value and labelling all regions with intensity above the threshold as hotspots (Roerdink and Meijster 2000), using a scanning algorithm (Patil et al 2010), or selecting regions based on a statistical test for significance (Brimicombe 2012). These approaches emphasise the varying level of demand for police presence over space and time.…”

Ranking and hotspot detection methods on infant health for districts in Java, Indonesia

“…Since each cell is introduced in a unique node in the ULS tree, the ULS tree has at most N nodes. Hence |Ω ULS | ≤ N, the equality holding if and only if m = N. [13] Several geometric properties should be satisfied by a collection of cells from tessellation of study area before it could be considered as a candidate for a hotspot cluster 1) the union of the cells should comprise a geographically connected subset of the region R. Such collections of cells will be referred to as zones and the set of all zones is denoted by Ω. A zone Z∈Ω is a collection of cells that are connected.…”

“…If not all cells in Z have the same rates then let e = min{ g a | a ∈ Z} and connected components of Z -{a ∈ Z: g a = e} are members of Z. [13] Since our search for a hotspot is based on cellular response rates, we assign a unique level to each node of the ULS tree in terms of its response rate and then scan the tree by level starting with nodes level 1 down. Members of C 1 are level 1 nodes.…”

Hamiltonian Cycle with the Least Weight

“…It will apply, adapt, and validate methods and tools for national applications, such as public health, ecohealth, ecosystem condition, watershed management, invasive species, carbon sources and sinks, networked infrastructure security, and object recognition and tracking, among others, leading to a sophisticated next-generation analytical and computational decision support system, beyond the present day health-area-based circular spatial scan. The innovation employs the notion of the upper level set (ULS), and is accordingly called the ULS scan statistic system (Patil and Taillie 2004a;Patil et al 2006a). The proposed effort will also apply, adapt, and validate a prioritization innovation that provides capability for prioritization and ranking of detected hotspots based on multiple criteria indicators without integration of indicators into an index.…”