# 7.4. Lesson: 공간 통계¶

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이 강의는 Linfiniti와 S. Motala(남아프리카공화국 케이프 페닌슐라 기술대학교)가 작성했습니다.

공간 통계를 이용하면 주어진 벡터 데이터셋이 어떤 의미인지 분석하고 이해할 수 있습니다. QGIS는 이런 목적에 대해 유용하다고 알려진 몇몇 표준 통계 분석 도구를 포함하고 있습니다.

The goal for this lesson: To know how to use QGIS’ spatial statistics tools.

## 7.4.1. Follow Along: 테스트용 데이터셋 생성¶

강의에서 사용할 포인트 데이터셋을 얻기 위해, 랜덤한 포인트들을 생성해보겠습니다.

이 때 포인트를 생성하려는 구역의 범위를 정의하는 폴리곤 데이터셋이 필요합니다.

거리들이 차지한 구역을 사용하겠습니다.

• Create a new empty map.

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You might find that your SRTM DEM layer has a different CRS to that of the roads layer. If so, you can reproject either the roads or DEM layer using techniques learnt earlier in this module.

• Use the Convex hull(s) tool (available under Vector ‣ Geoprocessing Tools) to generate an area enclosing all the roads:
• Save the output under exercise_data/spatial_statistics/ as roads_hull.shp.
• Check Add result to canvas option to add the output to the TOC (Layers list).

### 7.4.1.1. 랜덤한 포인트 생성¶

• Create random points in this area using the tool at Vector ‣ Research Tools ‣ Random points:
• Save the output under exercise_data/spatial_statistics/ as random_points.shp.
• Check Add result to canvas option to add the output to the TOC (Layers list).

### 7.4.1.2. 데이터 샘플링¶

• To create a sample dataset from the raster, you’ll need to use the Point sampling tool plugin.
• Refer ahead to the module on plugins if necessary.
• Search for the phrase point sampling in the Plugin ‣ Manage and Install Plugins... and you will find the plugin.
• As soon as it has been activated with the Plugin Manager, you will find the tool under Plugins ‣ Analyses ‣ Point sampling tool:
• Select random_points as the layer containing sampling points, and the SRTM raster as the band to get values from.
• Make sure that “Add created layer to the TOC” is checked.
• Save the output under exercise_data/spatial_statistics/ as random_samples.shp.

Now you can check the sampled data from the raster file in the attributes table of the random_samples layer, they will be in a column named srtm_41_19.tif.

다음과 비슷한 샘플 레이어가 보일 것입니다.

The sample points are classified by their value such that darker points are at a lower altitude.

나머지 통계 실습 동안 이 샘플 레이어를 사용할 것입니다.

## 7.4.2. Follow Along: 기본 통계¶

이제 이 레이어에 대한 기본적인 통계를 내보겠습니다.

• Click on the Vector ‣ Analysis Tools ‣ Basic statistics menu entry.
• In the dialog that appears, specify the random_samples layer as the source.
• Make sure that the Target field is set to srtm_41_19.tif which is the field you will calculate statistics for.
• Click OK. You’ll get results like this:

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You can copy and paste the results into a spreadsheet. The data uses a (colon :) separator.

• Close the plugin dialog when done.

To understand the statistics above, refer to this definition list:

Mean

중간(평균)값은 값을 모두 더한 것을 값의 개수로 나눈 값입니다.

StdDev

표준편차입니다. 값들이 얼마나 중간값에 가까이 모여 있는지를 나타냅니다. 표준편차가 작을수록 값들이 중간값에 더 가까이 모이는 경향이 있습니다.

Sum

모든 값들을 더한 값입니다.

Min

최소값입니다.

Max

최대값입니다.

N

샘플/값의 개수입니다.

CV
The spatial covariance of the dataset.
Number of unique values
The number of values that are unique across this dataset. If there are 90 unique values in a dataset with N=100, then the 10 remaining values are the same as one or more of each other.
Range

최소/최대값의 차이입니다.

Median

모든 값을 최소에서 최대로 배열할 경우, 그 중앙에 있는 (또는 N이 짝수라면 두 중앙값의 평균) 값을 중앙값이라 합니다.

## 7.4.3. Follow Along: Compute a Distance Matrix¶

• Create a new point layer in the same projection as the other datasets (WGS 84 / UTM 34S).
• Enter edit mode and digitize three point somewhere among the other points.
• Alternatively, use the same random point generation method as before, but specify only three points.
• Save your new layer as distance_points.shp.

To generate a distance matrix using these points:

• Open the tool Vector ‣ Analysis Tools ‣ Distance matrix.
• Select the distance_points layer as the input layer, and the random_samples layer as the target layer.
• 다음과 같이 설정하십시오.

• Save the result as distance_matrix.csv.
• Click OK to generate the distance matrix.
• Open it in a spreadsheet program to see the results. Here is an example:

## 7.4.4. Follow Along: Nearest Neighbor Analysis¶

To do a nearest neighbor analysis:

• Click on the menu item Vector ‣ Analysis Tools ‣ Nearest neighbor analysis.
• In the dialog that appears, select the random_samples layer and click OK.
• The results will appear in the dialog’s text window, for example:

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You can copy and paste the results into a spreadsheet. The data uses a (colon :) separator.

## 7.4.5. Follow Along: 평균 좌표¶

데이터의 평균 좌표를 얻으려면,

• Click on the Vector ‣ Analysis Tools ‣ Mean coordinate(s) menu item.
• In the dialog that appears, specify random_samples as the input layer, but leave the optional choices unchanged.
• Specify the output layer as mean_coords.shp.
• Click OK.
• Add the layer to the Layers list when prompted.

이 레이어를 랜덤 샘플을 생성하는 데 쓰인 폴리곤의 중앙 좌표와 비교해봅시다.

• Click on the Vector ‣ Geometry Tools ‣ Polygon centroids menu item.
• In the dialog that appears, select roads_hull as the input layer.
• Save the result as center_point.
• Add it to the Layers list when prompted.

As you can see from the example below, the mean coordinates and the center of the study area (in orange) don’t necessarily coincide:

## 7.4.6. Follow Along: 이미지 히스토그램¶

The histogram of a dataset shows the distribution of its values. The simplest way to demonstrate this in QGIS is via the image histogram, available in the Layer Properties dialog of any image layer.

• In your Layers list, right-click on the SRTM DEM layer.
• Properties 를 선택합니다.

• Histogram 탭을 선택하십시오. 그래픽을 생성하려면 Compute Histogram 버튼을 클릭해야 할 수도 있습니다. 이미지 안의 값들의 빈도를 나타내는 그래프를 볼 수 있을 것입니다.

• 다음과 같이 그래프를 이미지로 내보낼 수 있습니다.

• Select the Metadata tab, you can see more detailed information inside the Properties box.

The mean value is 332.8, and the maximum value is 1699! But those values don’t show up on the histogram. Why not? It’s because there are so few of them, compared to the abundance of pixels with values below the mean. That’s also why the histogram extends so far to the right, even though there is no visible red line marking the frequency of values higher than about 250.

따라서 히스토그램은 값들의 분포를 보여줄 뿐, 그래프 상에 모든 값을 보여주지 않을 수도 있다는 점을 기억해야 합니다.

• (You may now close Layer Properties.)

## 7.4.7. Follow Along: 공간 보간법¶

Let’s say you have a collection of sample points from which you would like to extrapolate data. For example, you might have access to the random_samples dataset we created earlier, and would like to have some idea of what the terrain looks like.

To start, launch the Grid (Interpolation) tool by clicking on the Raster ‣ Analysis ‣ Grid (Interpolation) menu item.

• In the Input file field, select random_samples.
• Check the Z Field box, and select the field srtm_41_19.
• Set the Output file location to exercise_data/spatial_statistics/interpolation.tif.
• Check the Algorithm box and select Inverse distance to a power.
• Set the Power to 5.0 and the Smoothing to 2.0. Leave the other values as-is.
• Check the Load into canvas when finished box and click OK.
• When it’s done, click OK on the dialog that says Process completed, click OK on the dialog showing feedback information (if it has appeared), and click Close on the Grid (Interpolation) dialog.

다음은 원래 데이터셋(왼쪽)과 샘플 포인트로부터 구축한 데이터셋(오른쪽)을 비교한 그림입니다. 사용자가 구축한 데이터셋은 샘플 포인트들의 위치의 랜덤성에 따라 달라 보일 수도 있습니다.

As you can see, 100 sample points aren’t really enough to get a detailed impression of the terrain. It gives a very general idea, but it can be misleading as well. For example, in the image above, it is not clear that there is a high, unbroken mountain running from east to west; rather, the image seems to show a valley, with high peaks to the west. Just using visual inspection, we can see that the sample dataset is not representative of the terrain.

## 7.4.8. Try Yourself¶

• Use the processes shown above to create a new set of 1000 random points.
• 이 포인트들을 이용해서 원 DEM을 샘플링하십시오.

• Use the Grid (Interpolation) tool on this new dataset as above.
• Set the output filename to interpolation_1000.tif, with Power and Smoothing set to 5.0 and 2.0, respectively.

결과물은 (여러분의 랜덤 포인트 위치에 따라) 다음과 비슷하게 보일 것입니다.

The border shows the roads_hull layer (which represents the boundary of the random sample points) to explain the sudden lack of detail beyond its edges. This is a much better representation of the terrain, due to the much greater density of sample points.

Here is an example of what it looks like with 10 000 sample points:

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It’s not recommended that you try doing this with 10 000 sample points if you are not working on a fast computer, as the size of the sample dataset requires a lot of processing time.

Originally a separate project and then accessible as a plugin, the SEXTANTE software has been added to QGIS as a core function from version 2.0. You can find it as a new QGIS menu with its new name Processing from where you can access a rich toolbox of spatial analysis tools allows you to access various plugin tools from within a single interface.

• Activate this set of tools by enabling the Processing ‣ Toolbox menu entry. The toolbox looks like this:

You will probably see it docked in QGIS to the right of the map. Note that the tools listed here are links to the actual tools. Some of them are SEXTANTE’s own algorithms and others are links to tools that are accessed from external applications such as GRASS, SAGA or the Orfeo Toolbox. This external applications are installed with QGIS so you are already able to make use of them. In case you need to change the configuration of the Processing tools or, for example, you need to update to a new version of one of the external applications, you can access its setting from Processing ‣ Options and configurations.

## 7.4.10. Follow Along: Spatial Point Pattern Analysis¶

For a simple indication of the spatial distribution of points in the random_samples dataset, we can make use of SAGA’s Spatial Point Pattern Analysis tool via the Processing Toolbox you just opened.

• In the Processing Toolbox, search for this tool Spatial Point Pattern Analysis.
• Double-click on it to open its dialog.

### 7.4.10.1. Installing SAGA¶

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If SAGA is not installed on your system, the plugin’s dialog will inform you that the dependency is missing. If this is not the case, you can skip these steps.

### 7.4.10.2. On Windows¶

Included in your course materials you will find the SAGA installer for Windows.

• Start the program and follow its instructions to install SAGA on your Windows system. Take note of the path you are installing it under!

Once you have installed SAGA, you’ll need to configure SEXTANTE to find the path it was installed under.

• Click on the menu entry Analysis ‣ SAGA options and configuration.
• In the dialog that appears, expand the SAGA item and look for SAGA folder. Its value will be blank.
• In this space, insert the path where you installed SAGA.

### 7.4.10.3. On Ubuntu¶

• Search for SAGA GIS in the Software Center, or enter the phrase sudo apt-get install saga-gis in your terminal. (You may first need to add a SAGA repository to your sources.)
• QGIS will find SAGA automatically, although you may need to restart QGIS if it doesn’t work straight away.

### 7.4.10.4. On Mac¶

Homebrew users can install SAGA with this command:

• brew install saga-core

http://sourceforge.net/apps/trac/saga-gis/wiki/Compiling%20SAGA%20on%20Mac%20OS%20X

### 7.4.10.5. After installing¶

Now that you have installed and configured SAGA, its functions will become accessible to you.

### 7.4.10.6. Using SAGA¶

• Open the SAGA dialog.
• SAGA produces three outputs, and so will require three output paths.
• Save these three outputs under exercise_data/spatial_statistics/, using whatever file names you find appropriate.

The output will look like this (the symbology was changed for this example):

The red dot is the mean center; the large circle is the standard distance, which gives an indication of how closely the points are distributed around the mean center; and the rectangle is the bounding box, describing the smallest possible rectangle which will still enclose all the points.

## 7.4.11. Follow Along: Minimum Distance Analysis¶

Often, the output of an algorithm will not be a shapefile, but rather a table summarizing the statistical properties of a dataset. One of these is the Minimum Distance Analysis tool.

• Find this tool in the Processing Toolbox as Minimum Distance Analysis.

It does not require any other input besides specifying the vector point dataset to be analyzed.

• Choose the random_points dataset.
• Click OK. On completion, a DBF table will appear in the Layers list.
• Select it, then open its attribute table. Although the figures may vary, your results will be in this format:

## 7.4.12. In Conclusion¶

QGIS를 사용하면 데이터셋의 속성에 대해 다양한 공간 통계 분석을 할 수 있습니다.

## 7.4.13. What’s Next?¶

이제 벡터 분석에 대한 내용을 마쳤으니, 래스터에 대해 알아보는 것은 어떨까요? 이것이 다음 모듈의 주제입니다!