# Spatial relationship definition

### Modeling spatial relationships—ArcGIS Pro | ArcGIS Desktop

Define spatial relation. spatial relation synonyms, spatial relation pronunciation, spatial relation translation, English dictionary definition of spatial relation. Understanding tool parameter options, as well as essential vocabulary and concepts, is an important first step in using the tools in the Spatial Statistics toolbox. Spatial relationships can also refer to any sort of interaction between two locations, For example, a city has a spatial relationship with the surrounding farms or with other cities. What is the definition of the term "sustainability" in geography?.

This method is available using the Generate Spatial Weights Matrix tool. The K nearest neighbors option with 8 for Number of Neighbors is the default conceptualization used with Exploratory Regression to assess regression residuals. Delaunay triangulation natural neighbors The Delaunay Triangulation option constructs neighbors by creating Voronoi triangles from point features or from feature centroids such that each point or centroid is a triangle node.

Nodes connected by a triangle edge are considered neighbors. Using Delaunay triangulation ensures every feature will have at least one neighbor even when data includes islands or widely varying feature densities. Do not use the Delaunay Triangulation option when you have coincident features.

Space-Time window With this option you define feature relationships in terms of both a space fixed distance and a time fixed-time interval window. This option is available when you create a spatial weights matrix file using the Generate Spatial Weights Matrix tool. The interval value is an integer.

**Spatial Relationships (6.2)**

With this conceptualization, features are neighbors if they fall within the specified distance and also fall within the specified time interval of the target feature. As one possible example, you would select Space time window from Conceptualization of Spatial Relationships if you wanted to create a spatial weights matrix file to use with Hot Spot Analysis to identify space-time hot spots.

Additional information, including how to visualize results, is presented in Space-Time Analysis. Other opportunities are available to help you visualize, in 3D, a netCDF space-time cube. Get spatial weights from file user-defined spatial relationships You can create a file to store feature neighbor relationships using the Generate Spatial Weights Matrix tool tool. If the spatial relationships for your features are defined in a table, use the Generate Spatial Weights Matrix tool to convert that table into a spatial weights matrix.

Particular fields should be included in your table in order to use the Convert table option to obtain an SWM file. You can also provide a path to a formatted ASCII text file that defines your own custom conceptualization of spatial relationships based on spatial interaction for example. Selecting a conceptualization of spatial relationships: Best practices The more realistically you can model how features interact with each other in space, the more accurate your results will be.

Your choice for the Conceptualization of Spatial Relationships parameter should reflect inherent relationships among the features you are analyzing. Sometimes your choice will also be influenced by characteristics of your data. The inverse distance methods Inverse distance and Inverse distance squaredfor example, are most appropriate with continuous data or to model processes where the closer two features are in space, the more likely they are to interact with or influence each other.

With this spatial conceptualization, every feature is potentially a neighbor of every other feature, and with large datasets, the number of computations involved will be enormous.

You should always try to include a Distance Band or Threshold Distance value when using the inverse distance conceptualizations. This is particularly important for large datasets. If you leave the Distance Band or Threshold Distance parameter blank, a threshold distance will be computed for you, but this may not be the most appropriate distance for your analysis.

The default distance threshold will be the minimum distance that ensures every feature has at least one neighbor. The Fixed distance band method works well for point data. It is often a good option for polygon data when there is a large variation in polygon size very large polygons at the edge of the study area and very small polygons at the center of the study area for exampleand you want to ensure a consistent scale of analysis.

See the Selecting a fixed-distance band value section below for strategies to help you determine an appropriate distance band value for your analysis. The Zone of indifference conceptualization works well when fixed distance is appropriate but imposing sharp boundaries on neighborhood relationships is not an accurate representation of your data.

Keep in mind that the zone of indifference conceptual model considers every feature to be a neighbor of every other feature.

- Chapter 4 Spatial Relations
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Consequently, this option is not appropriate for large datasets since the Distance Band or Threshold Distance value supplied does not limit the number of neighbors but only specifies where the intensity of spatial relationships begins to wane. The polygon contiguity conceptualizations Contiguity edges only and Contiguity edges corners are effective when polygons are similar in size and distribution, and when spatial relationships are a function of polygon proximity the idea that if two polygons share a boundary, spatial interaction between them increases.

When you select a polygon contiguity conceptualization, you will almost always want to select row standardization for tools that have the Row Standardization parameter. The K nearest neighbors option is effective when you want to ensure you have a minimum number of neighbors for your analysis. Especially when the values associated with your features are skewed are not normally distributedit is important that each feature is evaluated in the context of at least eight neighbors this is a rule of thumb only.

When the distribution of your data varies across your study area so that some features are far away from all other features, this method works well.

Note, however, that the spatial context of your analysis changes depending on variations in the sparsity or density of your features. When fixing the scale of analysis is less important than fixing the number of neighbors, the K nearest neighbors method is appropriate. Some analysts consider the Delaunay triangulation option a way to construct natural neighbors for a set of features. This is a good option when your data includes island polygons isolated polygons that do not share any boundaries with other polygons or in cases where there is a very uneven spatial distribution of features.

It is not appropriate when you have coincident features however. Similar to the K nearest neighbors method, Delaunay triangulation ensures every feature has at least one neighbor but uses the distribution of the data itself to determine how many neighbors each feature gets. The Space time window option allows you to define feature relationships in terms of both their spatial and their temporal proximity.

You would use this option if you wanted to identify space-time hot spots or construct groups where membership was constrained by space and time proximity.

Examples of space-time analysis as well as strategies for effectively rendering the results from this type of analysis are provided in Space-Time Analysis. For some applications, spatial interaction is best modeled in terms of travel time or travel distance.

## Visuospatial Skills

If you are modeling accessibility to urban services, for example, or looking for urban crime hot spots, modeling spatial relationships in terms of a network is a good option. Use the Generate Network Spatial Weights tool to create a spatial weights matrix file. Many organizations maintain their own street network datasets that you may already have access to. These network datasets can be used directly by this tool. If none of the options for the Conceptualization of Spatial Relationships parameter work well for your analysis, you can create an ASCII text file or table with the feature-to-feature relationships you want and use these to build a spatial weights matrix file.

If one of the options above is close but not perfect for your purposes, you can use the Generate Spatial Weights Matrix tool to create a basic SWM file, and edit your spatial weights matrix file. Selecting a fixed-distance band value Think of the fixed-distance band you select as a moving window that momentarily settles on top of each feature and views that feature within the context of its neighbors.

There are several guidelines to help you identify an appropriate distance band for analysis: Select a distance based on what you know about the geographic extent of the spatial processes promoting clustering for the phenomena you are studying. Often you won't know this, but if you do, you should use your knowledge to select a distance value. Suppose, for example, you know that the average journey-to-work commute distance is 15 miles. Using 15 miles for the distance band is a good strategy for analyzing commuting data.

Use a distance band that is large enough to ensure all features will have at least one neighbor, or results will not be valid. Especially if the input data is skewed does not create a bell curve when you plot the values as a histogramyou will want to make sure that your distance band is neither too small most features have only one or two neighbors nor too large several features include all other features as neighborsbecause that would make resultant z-scores less reliable.

The z-scores are reliable even with skewed data as long as the distance band is large enough to ensure several neighbors approximately eight for each feature. Even if none of the features have all other features as neighbors, performance issues and even potential memory limitations can result if you create a distance band where features have thousands of neighbors.

Sometimes ensuring all features have at least one neighbor results in some features having many thousands of neighbors, and this is not ideal. This can happen when some of your features are spatial outliers. To resolve this problem, determine an appropriate distance band for all but the spatial outliers, and use the Generate Spatial Weights Matrix tool to create a spatial weights matrix file using that distance. When you run the Generate Spatial Weights Matrix tool, however, specify a minimum number of neighbors value for the Number of Neighbors parameter.

For example, suppose you are evaluating access to healthy food in Los Angeles County using census tract data. You know that more than 90 percent of the population live within 3 miles of shopping opportunities. If you are analyzing census tracts you will find that distances between tracts based on tract centroids in the downtown region are about 1, meters on average, but distances between tracts in outlying areas are more than 18, meters.

To ensure every feature has at least one neighbor, your distance band would need to be more than 18, meters, and this scale of analysis distance is not appropriate for the questions you are asking. The solution is to create a spatial weights matrix file for the census tract feature class using the Generate Spatial Weights Matrix tool.

Specify a Threshold Distance of meters approximately 3 miles and a minimum number of neighbors value 2 for instance for the Number of Neighbors parameter.

This will apply the 4, meter fixed-distance neighborhood to all features except those that do not have a least 2 neighbors using that distance.

For those outlier features and only for those outlier featuresthe distance will be expanded just far enough to ensure every feature has at least 2 neighbors. Use a distance band that reflects maximum spatial autocorrelation. Whenever you see spatial clustering on the landscape, you are seeing evidence of underlying spatial processes at work.

The distance band that exhibits maximum clustering, as measured by the Incremental Spatial Autocorrelation tool, is the distance where those spatial process are most active or most pronounced. Run the Incremental Spatial Autocorrelation tool and note where the resulting z-scores seems to peak. Use the distance associated with the peak value for your analysis.

Distance values should be entered using the same units as specified by the geoprocessing environment output coordinate system. Every peak represents a distance where the processes promoting spatial clustering are pronounced. Multiple peaks are common. Generally, the peaks associated with larger distances reflect broad trends a broad east-to-west trend, for example, where the west is a giant hot spot and the east is a giant cold spot.

Generally, you will be most interested in peaks associated with smaller distances, often the first peak.

### What does spatial relation mean?

An inconspicuous peak often means there are many different spatial processes operating at a variety of spatial scales. You may want to look for other criteria to determine which fixed distance to use for your analysis perhaps the most effective distance for remediation. If the z-score never peaks in other words, it keeps increasing and if you are using aggregated data for example, countiesit usually means the aggregation scheme is too coarse; the spatial processes of interest are operating at a scale that is smaller than the scale of your aggregation units.

If you can move to a smaller scale of analysis moving from counties to tracts for examplethis may help find a peak distance. If you are working with point data and the z-score never peaks, it means there are many different spatial processes operating at a variety of spatial scales and you will likely need to come up with different criteria for determining the fixed distance to use in your analysis.

You will also want to check that the Beginning Distance value when you run the Incremental Spatial Autocorrelation tool isn't too large. If you do not specify a beginning distance, the Incremental Spatial Autocorrelation tool will use the distance that ensures all features have at least one neighbor.

## Spatial relationships

If your data includes spatial outliers, that distance may be too large for your analysis, however, and may be the reason you do not see a pronounced peak in the Output Report File. The solution is to run the Incremental Spatial Autocorrelation tool on a selection set that temporarily excludes all spatial outliers. If a peak is found with the outliers excluded, use the strategy outlined above with that peak distance applied to all of your features including the spatial outliersand force each feature to have at least one or two neighbors.

If you're not sure if any of your features are spatial outliers, try the following: For polygon data, render polygon areas using a Standard Deviation rendering scheme and consider polygons with areas that are greater than three standard deviations to be spatial outliers.

You can use Calculate Field to create a field with polygon areas if you don't already have one. For point data, use the Near tool to compute each feature's nearest neighbor distance. To do this, set both the Input Features and Near Features to your point dataset.

Once you have a field with nearest neighbor distances, render those values using a Standard Deviation rendering scheme and consider distances that are greater than three standard deviations to be spatial outliers. Identify a distance where the processes promoting clustering are most pronounced.

Try not to get stuck on the idea that there is only one correct distance band. Reality is never that simple. Most likely, there are multiple or interacting spatial processes promoting observed clustering. Rather than thinking you need one distance band, think of the pattern analysis tools as effective methods for exploring spatial relationships at multiple spatial scales.

Consider that when you change the scale change the distance band valueyou could be asking a different question. Suppose you are looking at income data. With small distance bands, you can examine neighborhood income patterns, middle scale distances might reflect community or city income patterns, and the largest distance bands would highlight broad regional income patterns.

Distance method Many of the tools in the Spatial Statistics toolbox use distance in their calculations. These tools provide you with the choice of either Euclidean or Manhattan distance. It is the distance you must travel if you are restricted to north—south and east—west travel only. This method is generally more appropriate than Euclidean distance when travel is restricted to a street network and where actual street network travel costs are not available.

When your input features are not projected that is, when coordinates are given in degrees, minutes, and seconds or when the output coordinate system is set to a geographic coordinate systemor when you specify an output feature class path to a feature dataset that has a geographic coordinate system spatial reference, distances will be computed using chordal measurements and the Distance Method parameter will be disabled.

Chordal distance measurements are used because they can be computed quickly and provide very good estimates of true geodesic distances, at least for points within about 30 degrees of each other.

Chordal distances are based on a sphere rather than the true oblate ellipsoid shape of the earth. Given any two points on the earth's surface, the chordal distance between them is the length of a line, passing through the three dimensional earth, to connect those two points. Chordal distances are reported in meters. Be sure to project your data if your study area extends beyond 30 degrees. Chordal distances are not a good estimate of geodesic distances beyond 30 degrees.

Distances, speed and placement will be integrated so that the child will know what they can reach and can't reach when they stretch their arm. Signs and Symptoms As spatial awareness develops the child will learn the concepts of direction, distance and location. They will understand that when they walk to an object the object will become closer to their body. They begin to appreciate the space around themselves and the proximity of others around them.

As they grow older their movements become more controlled and constrained around others as they are more aware of their personal space. Children with poor spatial awareness tend to have visual perceptual difficulties as well. They may appear clumsy and may bump into others. They often stand too close or too far away from the people or objects that they are interacting with.

In the classroom they may have difficulty with presentation of written work and may find it hard to structure and organise such work. These children often find it hard to tell their left from right and they confuse positional language i. This makes it hard for them to follow directions that use such language. They may have difficulty with PE, team games and games that use apparatus. In the classroom the child with spatial awareness difficulties often finds mathematics hard.

This is due to the abstract concepts of the subject especially where shapes, areas, volume and space is involved. They will have problems reproducing patterns, sequences and shapes. Their strengths, however, are with the more practical and concrete subjects. These children will often find that they excel at using a multisensory way of learning.

They tend to have good auditory memory skills and have strength in speaking confidently whilst being able to listen well. They tend to have good verbal comprehension skills and their strength is usually in verbal and non verbal reasoning. Developing Spatial Awareness In order to be able to relate ourselves to objects in a given space, we need to have an accurate body schema. This is a sense of where your body is in space and where it is in relation to the whole of you.

For example we need to know the exact location of our arms in relation to our trunk. The body schema develops through our muscles and touch receptors proprioception and tactile senses combined with other senses. This gives us a map or image of the way we perceive ourselves to look and is linked with our body awareness.

Asking a child to draw a picture of a person will give a trained therapist a very good indication of the child's body schema and it will provide the therapist with information on the child's spatial awareness. The therapist can also detect spatial awareness difficulties in a child's handwriting. A child with poor spatial awareness may leave out the spaces between words, start the sentence in the middle of the page, have difficulty keeping on the line or write diagonally instead of horizontally.

### Spatial relation - Wikipedia

These are visual perception problems that are related to spatial awareness. An occupational therapist will also be able to identify a child with spatial awareness difficulties when observing their gross motor skills. The difficulties may be seen during team sports such as football where the child needs to judge distance and speed of a ball coming towards them, as well as the distance between themselves and the person they need to kick the ball to. They may also appear clumsy, move into spaces that they are not meant to be in during the game and often bump into team members.

Spatial awareness develops naturally when children have the ability to freely explore their environment. Babies learn about themselves and how they relate to their surroundings naturally. They learn to manipulate objects as they become mobile and learn about distances and sizes when they are able to move towards the objects. There are, however, situations that interfere with or prevent the natural development of spatial awareness.