A conceptualization of spatial relationships defines the spatial relationships between features by grouping features into neighborhoods and quantifying the influence (weight) of each neighbor in a neighborhood. In Neighborhood Explorer, you can set the conceptualization of spatial relationships with the Conceptualization of Spatial Relationships parameter. Each conceptualization of spatial relationships requires a method to identify neighbors, the Neighborhood Type parameter, and a method to quantify the weight of neighbors, the Method parameter.

The options under the Neighborhood Options heading configure how neighbors are identified. Each feature will have a set of neighbors that form its neighborhood. The target feature, referred to as a focal feature, will not be included in its own neighborhood. The size of different neighborhoods may vary. Some neighborhoods may include no neighbors while others include many. The relationships between features are not necessarily symmetrical. For example, feature A may be a neighbor of feature B; however, feature B may not be a neighbor of feature A.

Once the neighbors of a feature are identified, they are assigned a weight. The options under the Weighting Options heading determine how neighbor weight is calculated. The weights of neighbors in a neighborhood may be equal or a function of distance. Weights can be any positive value; negative weights are not accepted.

## Conceptualizations of spatial relationships

Neighborhood Explorer includes several standard conceptualizations of spatial relationships with preconfigured methods to identify and assign weights to neighbors. If you select a preconfigured option, Neighborhood Explorer will set the Neighborhood Type and Method parameter values to the appropriate method.

### Fixed distance

For the Fixed Distance option , all features within a specified distance of a focal feature are neighbors of that focal feature. If you select this option, you must specify the Distance Band parameter. This option also provides the following additional parameters you can set to control how neighbors are identified: Distance Method and Minimum Number of Neighbors. You can ensure that each feature has at least one neighbor by setting the minimum number of neighbors parameter value to 1. The Method parameter value is Binary, which assigns each neighbor a weight of 1.

##### Note:

The Minimum Number of Neighbors option uses the K nearest neighbors conceptualization to identify the nearest features.

### Inverse distance

For the Inverse Distance option , all features within a specified distance of a focal feature are neighbors of the focal feature. The Method parameter value is Inverse Distance, which assigns neighbor weight using the inverse distance function. Use the Exponent parameter to set how drastically weight decays with distance.

### K nearest neighbors

For the K nearest neighbors option , the K nearest features to a focal feature are included in its neighborhood. Specify K with the Number of Neighbors parameter. Select this option if you want to ensure that all the neighborhoods are the same size. The Method parameter value is Binary, which assigns each neighbor a weight of 1.

### Contiguity edges only

For the Contiguity edges only option , polygon features that share an edge are neighbors. This option is only available if the feature layer contains polygons. The Method parameter value is Binary, which assigns each neighbor a weight of 1.

### Contiguity edges corners

For the Contiguity edges corners option , polygon features that share an edge or a corner are neighbors. This option is only available if the feature layer contains polygons. The Method parameter value is Binary, which assigns each neighbor a weight of 1.

### Trimmed Delaunay triangulation

For the Trimmed Delaunay triangulation option , point features, or the centroids of polygons, are triangulated using Delaunay Triangulation. Points that are connected by the triangulation are considered neighbors. The result of the Delaunay Triangulation is trimmed to the boundary of the convex hull of the set of points. Any neighbor connections that intersect the convex hull are removed. The Method parameter value is Binary, which assigns every neighbor a weight of 1.

## Manual

If none of the preconfigured options capture the spatial relationships between the features in your dataset, select the Manual option and manually set the Neighborhood Type and Method parameters. The Neighborhood Type parameter options include: Distance Band, Contiguity Edges Only, Contiguity Edges Corners, K Nearest Neighbors, and Trimmed Delauney Triangulation. The Method parameter options include: Binary, Inverse Distance, Gaussian, Bisquare, Triangular, and Quartic. Gaussian, Bisquare, Triangular, and Quartic are kernel functions. Each kernel function uses a bandwidth in its calculation. Fixed distance uses a fixed bandwidth whereas K nearest neighbors uses an adaptive bandwidth.

## Get spatial weights from file

If you have an existing spatial weights matrix, you can select the Get Spatial Weights from File option and import a spatial weights matrix (.swm) file by specifying the Spatial Weight Matrix File parameter.

Learn more about loading a spatial weights matrix (.swm) file