Spatial-time motifs discovery

Abstract

Discovering motifs in time series data has been widely explored. Various techniques have been developed to tackle this problem. However, when it comes to spatial-time series, a clear gap can be observed according to the literature review. This paper tackles such a gap by presenting an approach to discover and rank motifs in spatial-time series, denominated Combined Series Approach (CSA). CSA is based on partitioning the spatial-time series into blocks. Inside each block, subsequences of spatial-time series are combined in a way that hash-based motif discovery algorithm is applied. Motifs are validated according to both temporal and spatial constraints. Later, motifs are ranked according to their entropy, the number of occurrences, and the proximity of their occurrences. The approach was evaluated using both synthetic and seismic datasets. CSA outperforms traditional methods designed only for time series. CSA was also able to prioritize motifs that were meaningful both in the context of synthetic data and also according to seismic specialists.

Identification of the North Brazil Current through spatial motifs in fixed time slices

“…If the position varies with time, it is a trajectory spatial-temporal series. Otherwise, it is a permanent spatial-temporal series [Borges et al, 2020b].…”

“…These patterns are known as spatial-temporal motifs. One can formalize a spatial-temporal motif as a subsequence q that occurs at least σ times in D and occurs in at least κ different close spatial-temporal series, where σ and κ are two support values such that σ ≤ κ [Borges et al, 2020b]. The process for discovering spatial-temporal motifs is composed of five steps: (1) normalization and indexing; (2) partition of the spatial-temporal series; (3) combination of blocks and discovery of motifs; (4) aggregation and evaluation of constraints; (5) ranking of found motifs.…”

“…Likewise, Oates et al [2013] analyzes trajectory data from moving objects. In both cases, the approaches are significantly different from the CSA [Borges et al, 2020b]. The CSA assumes that the analyzed data are collected in fixed positions, unlike the others, which focus on studying trajectories.…”

“…From them, we observe the same pattern repeating itself in space and time. For example, the discovery of motifs in seismic datasets brings relationships with horizons present in the subsoil [Borges et al, 2020b]. It can also be particularly interesting to analyze spatial patterns by fixing a time slice.…”

STMotif Explorer: A Tool for Spatiotemporal Motif Analysis

“…In this context, the motifs are specified in space and time and might not be discovered when we only analyze the temporal dimension. Discovering motifs becomes challenging when we look at the spatiotemporal series [Borges et al, 2020]. This problem is challenging for many reasons:…”