Detection Of Multiple Clusters Research Articles

Efficient Optimization of Partition Scan Statistics via the Consecutive Partitions Property

We generalize the spatial and subset scan statistics from the single to the multiple subset case. The two main approaches to defining the log-likelihood ratio statistic in the single subset case – the population-based and expectation-based scan statistics – are considered, leading to risk partitioning and multiple cluster detection scan statistics, respectively. We show that, for distributions in a separable exponential family, the risk partitioning scan statistic can be expressed as a scaled f-divergence of the normalized count and baseline vectors, and the multiple cluster detection scan statistic as a sum of scaled Bregman divergences. In either case, however, maximization of the scan statistic by exhaustive search over all partitionings of the data requires exponential time. To make this optimization computationally feasible, we prove sufficient conditions under which the optimal partitioning is guaranteed to be consecutive. This Consecutive Partitions Property generalizes the linear-time subset scanning property from two partitions (the detected subset and the remaining data elements) to the multiple partition case. While the number of consecutive partitionings of n elements into t partitions scales as , making it computationally expensive for large t, we present a dynamic programming approach which identifies the optimal consecutive partitioning in time, thus allowing for the exact and efficient solution of large-scale risk partitioning and multiple cluster detection problems. Finally, we demonstrate the detection performance and practical utility of partition scan statistics using simulated and real-world data.

MAD-STEC: a method for multiple automatic detection of space-time emerging clusters

Crime or disease surveillance commonly rely in space-time clustering methods to identify emerging patterns. The goal is to detect spatial-temporal clusters as soon as possible after its occurrence and to control the rate of false alarms. With this in mind, a spatio-temporal multiple cluster detection method was developed as an extension of a previous proposal based on a spatial version of the Shiryaev---Roberts statistic. Besides the capability of multiple cluster detection, the method have less input parameter than the previous proposal making its use more intuitive to practitioners. To evaluate the new methodology a simulation study is performed in several scenarios and enlighten many advantages of the proposed method. Finally, we present a case study to a crime data-set in Belo Horizonte, Brazil.