### Required Reading:

Read Chapter 2.2, pages 23-37 from the course text.

Data comes in many forms, structured and unstructured, and is obtained through a variety of sources. No matter its source or form, before the data can be used for any type of analysis, it must be assessed and transformed into a framework that can then be analyzed efficiently.

### Some Special Considerations with Spatial Data [Rogerson Text, 1.6]

There shouldn't be anything new to anyone in this class in these pages. Since analysis is almost always based on data that suffer from some or all of these limitations, these issues have a big effect on how much we can learn from spatial data, no matter how clever the analysis methods we adopt become.

The separation of entities from their representation as objects is important, and the scale-dependence issue that we read about in Lesson 1 is particularly important to keep in mind. The scale dependence of all geographic analysis is an issue that we return to frequently.

### GIS Analysis, Spatial Data Manipulation, and Spatial Analysis

From Figure 2.2, it is clear that spatial analysis requires a wide variety of analytical methods (statistical and spatial).

Spatial analysis functions fall into five classes that include: measurement, topological analysis, network analysis, surface analysis and statistical analysis (Cromley and McLafferty 2012, p. 29-32) (Table 2.0).

Function Class | Function | Description |
---|---|---|

Measurement | Distance, length, perimeter, area, centroid, buffering, volume, shape, measurement scale conversion | Allows users to calculate straight-line distances between points, distances along paths, arcs, or areas. Distance as a measure of separation in space is a key variable used in many kinds of spatial analysis and is often an important factor in interactions between people and places. |

Topological analysis | Adjacency, polygon overlay, point-in-polygon, line-in-polygon, dissolve, merge, clip, erase, intersect, union, identity, spatial join, and selection | Used to describe and analyze the spatial relationships among units of observation. Includes spatial database overlay and assessment of spatial relationships across databases, including map comparison analysis. Topological analysis functions can identify features in the landscape that are adjacent or next to each other (contiguous). Topology is important in modeling connectivity in networks and interactions. |

Network and location analysis | Connectivity, shortest path analysis, routing, service areas, location-allocation modeling, accessibility modeling | Investigates flows through a network. Network is modeled as a set of nodes and the links that connect the nodes. |

Surface analysis | Slope, aspect, filtering, line-of-sight, viewsheds, contours, watersheds; surface overlays or multi-criteria decision analysis (MCDA) | Often used to analyze terrain and other data that represent a continuous surface. Filtering techniques include smoothing (remove noise from data to reveal broader trends) and edge enhancement (accentuate contrast and aids in the identification of features). Or to perform raster-based modeling where it is necessary to perform complex mathematical operations that combine and integrate data layers (e.g., fuzzy logic, overlay, and weighted overlay methods; dasymetric mapping). |

Statistical analysis | Spatial sampling, spatial weights, exploratory data analysis, nearest neighbor analysis, global and local spatial autocorrelation, spatial interpolation, geostatistics, trend surface analysis. | Spatial data analysis is closely tied to spatial statistics and is influenced by spatial statistics and exploratory data analysis methods. These methods analyze information about the relationships being modeled based on attributes as well as their spatial relationships. |

Although maps are used to present research results (when they present known results and are represented using public, low-interaction devices), many more maps are impermanent, exploratory devices, and with the increased use of interactive web-based data graphs and maps, often driven by dynamically changing data, this is even more so the case.

With this, there is an ever-increasing need for spatial analysis, particularly since much of the data collected today contains some form of geographic attribute and every map tells a story… or does it? It is easy to feel that a pattern is present in a map. Spatial analysis allows us to explore the data, develop a hypothesis, and test that visual insight in a systematic, more reliable way.

The important point at this stage is to get used to thinking of space and spatial relations in the terms presented here—distance, adjacency, interaction, and neighborhood. The interaction weight idea is particularly commonly used. You can think of interaction as an *inverse distance* measure: near things interact more than distant things. Thus, it effectively captures the basic idea of spatial autocorrelation.

### Summarizing Relationships in Matrices [Lloyd text, section 2.2]

This week's readings discuss some of the ways matrices are used in spatial analysis. You'll notice that distances and adjacencies appear in Table 2.0. At this stage, you only need to get the basic idea that distances, adjacencies (or contiguities), or interactions can all be recorded in a matrix form. This makes for very convenient mathematical manipulation of a large number of relationships among geographic objects. We will see later how this concept is useful in **point pattern analysis** (Lesson 3), **clustering and spatial** **autocorrelation** (Lesson 4), and **interpolation** (Lesson 6).