Co-location Pattern

Abstract

Synonyms Spatial association pattern; Collocation pattern Definition A (spatial) co-location pattern P can be modeled by an undirected connected graph where each node corresponds to a non-spatial feature and each edge corresponds to a neighborhood relationship between the corresponding features. For example, consider a pattern with three nodes labeled "timetabling", "weather", and "ticketing", and two edges connecting "timetabling" with "weather" and "timetabling" with "ticketing". An instance of a pattern P is a set of objects that satisfy the unary (feature) and binary (neighborhood) constraints specified by the pat-tern's graph. An instance of an example pattern is a set {o 1 , o 2 , o 3 } of three spatial locations where label(o 1) = "time-tabling", label(o 2) = "weather", label(o 3) = "ticketing" (unary constraints) and dist(o 1 , o 2) ≤ ε, dist(o 1 , o 3) ≤ ε (spatial binary constraints). In general, there may be an arbitrary spatial (or spatio-temporal) constraint specified at each edge of a pattern graph (for example, topological, distance, direction, and time-difference constraints). Main Text Co-location patterns are used to derive co-location rules that associate the existence of non-spatial features in the same spatial neighborhood. An example of such a rule is "if a water reservoir is contaminated, then people who live in nearby houses have high probability of having a stomach disease". The interestingness of a co-location pattern is quantized by two measures; the prevalence and the confidence. Co-location patterns can be mined from large spatial databases with the use of algorithms that combine (multi-way) spatial join algorithms with spatial association rule mining techniques. Synonyms Co-location rule finding; Co-location mining; Co-location rule mining; Co-location rule discovery; Co-occurrence; Spatial association; Spatial association analysis Definition Spatial co-location rule discovery or spatial co-location pattern discovery is the process that identifies spatial co-location patterns from large spatial datasets with a large number of Boolean spatial features. Historical Background The co-location pattern and rule discovery are part of the spatial data mining process. The differences between spatial data mining and classical data mining are mainly related to data input, statistical foundation, output patterns, and computational process. The research accomplishments in this field are primarily focused on the output pattern category , specifically the predictive models, spatial outliers, spatial co-location rules, and clusters [1]. The spatial pattern recognition research presented here, which is focused on co-location, is also most commonly referred to as the spatial co-location pattern discovery and co-location rule discovery. To understand the concepts of spatial co-location pattern discovery and rule discovery, we will have to first examine a few basic concepts in spatial data mining. The first word to be defined is Boolean spatial features. Boolean spatial features are geographic object types. They either are absent or present regarding different locations within the domain of a two dimensional or higher (three) dimensional metric space such as the surface of the earth [1]. Some examples of Boolean spatial features are categorizations such as plant species, animal species, and types of roads, cancers, crimes and business. The next concept relates to co-location patterns and rules. Spatial co-location patterns represent the subsets of Boolean spatial features whose instances are often located in close geographic proximity [1]. It resembles frequent patterns in many aspects. Good examples are symbiotic species. The Nile crocodile and Egyptian plover in ecology prediction (Fig. 1) is one good illustration of a point spatial co-location pattern representation. Frontage roads