Lab10_Spatial-Data

# Lab10_Spatial-Data
## Spatial Data Manipulation and Visualization
### 曾子軒 Dennis Tseng
### 台大新聞所 NTU Journalism
### 2021/06/08

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# 今日重點: Use R as GIS

- 認識地理資訊格式
- 認識地理資料結構 in R
- 操作地理資料
- 視覺化地理資料
- Extra: Geometry Operations

---
# 今日目標

.pull-left[Taiwan 2020 Presidential Choropleth by [端傳媒](https://theinitium.com/article/20200112-taiwan-election-data-ntu/)]

.pull-right[US 2016 Presidential Vote Share Map by [Views of the World](http://www.viewsoftheworld.net/wp-content/uploads/2016/11/USelection2016Cartogram.png)]

---

# 地理資訊格式

.pull-left[[Geographic Information Systems and Science](https://andrewmaclachlan.github.io/CASA0005repo/index.html)]

---

# 地理資訊格式
- Vector vs. Raster, 向量 vs. 網格
- The vector data model represents the world using points, lines and polygons.(點、線、多邊形)
- The raster data model divides the surface up into cells of constant size.(切成固定大小的格子)
- 來看一下[範例](https://dennistseng.shinyapps.io/taipeiapp/)

---

# Data: Taipei City Demography

- 台北市民政局：[台北市各里人口數](https://data.taipei/#/dataset/detail?id=a6394e3f-3514-4542-87bd-de4310a40db3)和[台北市里界圖](https://data.taipei/#/dataset/detail?id=6b17b31d-4e16-495e-95b1-9fd1f47c80d8)，前者的資料格式為 `csv` ，後者為 `shapefile`
- 內政部：[台北市人口統計_村里](https://segis.moi.gov.tw/STAT/Web/Platform/QueryInterface/STAT_QueryProductView.aspx?pid=E8C9BC9FA3B8955DB5ED36ECB95CC2B2&spid=2379CCC54C5DD0F4FEC8CE65233993C4)與和[台北市人口統計_最小統計區](https://segis.moi.gov.tw/STAT/Web/Platform/QueryInterface/STAT_QueryProductView.aspx?pid=D71B7495F95BC7C4E9AA7D13F5148AD1&spid=7ED8D58E129BC680)，資料格式則是 `csv` 和 `shapefile` 都有

---

# 請大家去看/下載一下資料，[內政部](https://segis.moi.gov.tw/STAT/Web/Platform/QueryInterface/STAT_QueryInterface.aspx?Type=1)可以抓你喜歡的縣市，不用侷限在台北

---

# File Format Introduction

- `xlsx`/`ods`： 可以用 Excel/Google sheet 開啟的檔案格式，長相就是平常可以看到的試算表表格。政府單位常常以 `ods` 發布資料，台北市民政局的人口統計即是提供 `ods `
- `csv`： comma separated value, 用逗點分隔欄位，是非常常見的檔案格式。無論政府或私人單位都會以 `csv` 發布資料
- `tif`：儲存地理圖像的點陣圖格式，通常資料當中包含經緯度。衛星影像的原始格式即是 `tif`。
- `shapefile`：儲存地理圖資的檔案格式，由 `shp`, `shx`, `dbf`, `prj` 所組成，分別紀錄了地理參照資料、索引、屬性、投影。通常提供地理圖資時，會提供包含 `shp`, `shx`, `dbf`, `prj`, 等格式的壓縮檔案。
- `geojson`：基於 JSON 儲存地理資訊的檔案格式，內容包含空間範圍和屬性。

---

# File Format Introduction: Shapefile

- 最常見的地理資訊格式，由 ERSI 發明，當中包含數個檔案
    - `.shp`: 儲存幾何特徵
    - `.shx`: 儲存 `.shp` 當中特徵的 index
    - `.dbf`: 儲存屬性資訊，像是幾何特徵的名字或變數
    - `.prj`: 儲存座標系統資訊 (coordinate system information) 
- 這個格式常見到有人創了 [twitter account](https://twitter.com/shapefiIe)

---

# File Format Introduction: GeoJSON

- 使用跟 JSON 類似的原始格式，但設計上有特別考慮在表現出地理特徵以外，也保留 non-spatial 的屬性
- 地理特徵包含 points, line strings, polygons, and multi-part collections of these types.
- [Processing of GeoJSON data in R](https://cran.r-project.org/web/packages/geojsonR/vignettes/the_geojsonR_package.html)

---

# Data Structure: Simple Feature

- sf, simple feature
    - 可以想像成幾何圖形加上 data frame 的組合
    - data frame 的內容就是區域的屬性(attribute)，像是人口
    - 幾何圖形有很多種 e.g. point, line string, polygon
    - 不是簡介的介紹: [Simple Features for R](http://r-spatial.github.io/sf/articles/sf1.html); photo [source](https://geocompr.robinlovelace.net/spatial-class.html#intro-sf)

---

# Data Structure: Simple Feature

- 讀取原始資料
    - 區分一下: file format & data sturcture
    - import shapefile/GeoJSON 到 R 裏面變成 sf
    - `st_read()`, `dsn`(data source name) and `layer`(layer name)
    - 雖然 `shp` 設計得很好，但還是盡量完整把其他檔案也讀進來

```r
library(tidyverse)
library(sf)
library(cartogram)
library(maps)
```

---

# Data Importing

```r
sf_tpe <-
  st_read(dsn = "data/Lab10/109年12月行政區人口統計_村里_臺北市_SHP/", layer = "109年12月行政區人口統計_村里", quiet = T) %>%
  mutate(across(where(is.character), ~iconv(., from = "BIG5", to = "UTF8"))) %>%
  rename_with(~str_to_lower(.), everything()) %>% 
  mutate(across(where(is.double), ~if_else(is.na(.),as.double(0),.))) %>%
  st_set_crs(3826) %>% st_transform(4326) %>% filter(str_detect(county, "臺北市")) %>%
  mutate(village = if_else(str_detect(village,"糖"),"糖廍里",village))
```

---

# Data Importing

```r
sf_tpe
```

```
## Simple feature collection with 456 features and 12 fields
## geometry type:  MULTIPOLYGON
## dimension:      XY
## bbox:           xmin: 121.4571 ymin: 24.9605 xmax: 121.6659 ymax: 25.21018
## geographic CRS: WGS 84
## First 10 features:
##    county   town village county_id  town_id         v_id village_id h_cnt p_cnt
## 1  臺北市 文山區  樟新里     63000 63000080 63000080-031        031  2199  5697
## 2  臺北市 文山區  老泉里     63000 63000080 63000080-037        037   362   923
## 3  臺北市 文山區  樟腳里     63000 63000080 63000080-032        032  2108  5674
## 4  臺北市 文山區  樟文里     63000 63000080 63000080-041        041  2374  6311
## 5  臺北市 文山區  樟樹里     63000 63000080 63000080-043        043  1825  4898
## 6  臺北市 文山區  順興里     63000 63000080 63000080-029        029  2902  7642
## 7  臺北市 文山區  指南里     63000 63000080 63000080-036        036  1766  4108
## 8  臺北市 文山區  樟林里     63000 63000080 63000080-030        030  3247  8424
## 9  臺北市 文山區  忠順里     63000 63000080 63000080-038        038  1781  4213
## 10 臺北市 文山區  試院里     63000 63000080 63000080-023        023  2808  6901
##    m_cnt f_cnt info_time                       geometry
## 1   2682  3015   109Y12M MULTIPOLYGON (((121.5595 24...
## 2    485   438   109Y12M MULTIPOLYGON (((121.5715 24...
## 3   2735  2939   109Y12M MULTIPOLYGON (((121.5691 24...
## 4   3048  3263   109Y12M MULTIPOLYGON (((121.5599 24...
## 5   2324  2574   109Y12M MULTIPOLYGON (((121.5625 24...
## 6   3674  3968   109Y12M MULTIPOLYGON (((121.5678 24...
## 7   2099  2009   109Y12M MULTIPOLYGON (((121.5799 24...
## 8   4103  4321   109Y12M MULTIPOLYGON (((121.5585 24...
## 9   1986  2227   109Y12M MULTIPOLYGON (((121.5683 24...
## 10  3276  3625   109Y12M MULTIPOLYGON (((121.5507 24...
```

---

# Simple Feature 的組成

- 資料結構 - Simple feature collection
- 幾何組成 - geometry type
- 維度 - dimension
- 地理區域 - bbox
- 大地座標系統 - geographic CRS

---

# 馬上來畫一張圖

```r
sf_tpe %>% ggplot() + geom_sf()
```

![](Lab10_Tutorial_Spatical-Data_files/figure-html/unnamed-chunk-5-1.png)

---

# 上個顏色

```r
sf_tpe %>% ggplot(aes(fill = p_cnt)) + geom_sf(color = NA) +
  scale_fill_gradient(low = "white", high = "purple")
```

![](Lab10_Tutorial_Spatical-Data_files/figure-html/unnamed-chunk-6-1.png)

```r
# 260 萬
```

---

# 上個顏色

```r
sf_tpe %>% mutate(p_density = p_cnt/(as.double(st_area(.))/1000000)) %>%
  ggplot(aes(fill = p_density)) + geom_sf(color = NA) + scale_fill_gradient(low = "white", high = "purple")
```

![](Lab10_Tutorial_Spatical-Data_files/figure-html/unnamed-chunk-7-1.png)

```r
# 272 平方公里
```

---

# 重要概念: 投影

- 投影系統 = 告訴你怎麼在地圖上呈現資料的數學公式
- 大地座標系統(geographic coordiate reference systems) 
    - 視資料為球體，舉例: a minute type of resolution，代表把地球切成 360 度，每度有 60 分，每分有 60 秒
    - 經緯: Arc-seconds of latitude (緯線) 幾乎保持固定，但 arc-seconds of longitude (經線) 越往極點會越小
- 投影座標系統(projected coordinate reference systems)
    - 視資料為二維平面，所以長寬、角度、面積都是固定的

---

# 重要概念: 投影

---

# 重要概念: 投影

- 考慮到上述兩種投影系統的差別，分析或視覺化的時候，因為尺度(scale)通常都是以國家、地區為單位，需要從立體投影到平面
- 大部分國家/地區有自己的投影座標系統，也就是把中心(0,0)從地球中心移到國家/地區的中心
- 區分: 以角度為單位(angular)，譬如 degrees, latitude and longitude，或者資料是全球尺度，則使用 GCRS，以線性為單位；譬如英尺、公尺，或者資料是地方尺度，則使用 PCRS

---

# 重要概念: 投影

- 從立體到平面
- 地球是立體的橢圓形，用參考橢球體(Ellipsoid)代表它
- 會有一個跟參考橢球體相符的大地基準面，用來作為 CRS 的依據

---

# 重要概念: 投影

- 每個區域都有適合的參考橢球體和大地基準面
- 基準點(Datum)分為區域性的的(local)和全球的(global)，用來讓人從地球表面對應到笛卡兒座標系（就常見的 XY 啦XD）
- global 最常用: WGS84，以地球質心為中心
- local 最常用 TWD97，舊版是用 TWD67
- 如果你是地理狂可以看[
大地座標系統漫談](https://www.sunriver.com.tw/grid_tm2.htm)跟[座標系統介紹](http://140.121.160.124/GEO/%E5%BA%A7%E6%A8%99%E7%B3%BB%E7%B5%B1.pdf)

---

# 重要概念: 投影

- proj4string
    - 可以用來快速看 CRS 屬於哪種
    - a compact way of identifying a coordinate reference system
    - 組成包含 projection, datum, units, ellps, etc.，用 + 號分隔

```r
st_crs(sf_tpe)$proj4string
```

```
## [1] "+proj=longlat +datum=WGS84 +no_defs"
```

---

# 重要概念: 投影

- EPSG
    - 投影法有對應的代號稱為 EPSG(歐洲石油探勘組織)，他們制定了空間參考識別系統(SRID)
    - 可以記兩個重要的: WGS84 = 4326, TWD97 = 3826

```r
st_crs(sf_tpe)
```

```
## Coordinate Reference System:
##   User input: EPSG:4326 
##   wkt:
## GEOGCRS["WGS 84",
##     DATUM["World Geodetic System 1984",
##         ELLIPSOID["WGS 84",6378137,298.257223563,
##             LENGTHUNIT["metre",1]]],
##     PRIMEM["Greenwich",0,
##         ANGLEUNIT["degree",0.0174532925199433]],
##     CS[ellipsoidal,2],
##         AXIS["geodetic latitude (Lat)",north,
##             ORDER[1],
##             ANGLEUNIT["degree",0.0174532925199433]],
##         AXIS["geodetic longitude (Lon)",east,
##             ORDER[2],
##             ANGLEUNIT["degree",0.0174532925199433]],
##     USAGE[
##         SCOPE["unknown"],
##         AREA["World"],
##         BBOX[-90,-180,90,180]],
##     ID["EPSG",4326]]
```

---

# 重要概念: 投影

- 用得到投影的情境
    - 研究區域，想轉換座標(changing projections)
    - 原始資料就缺投影方法
- 解方
    - 修改 EPSG code 或是改掉 `proj4string` 的內容
    - 加上 EPSG code 或是加上 `proj4string` 的內容
- function
    - `st_crs()` 取用
    - `st_transform()` 變換
    - `st_set_crs()` 設定

---

# 變換投影看看

```r
# sf_tpe %>% st_crs_set(4326)
sf_tpe %>% st_transform(3826) %>% st_crs()
```

```
## Coordinate Reference System:
##   User input: EPSG:3826 
##   wkt:
## PROJCRS["TWD97 / TM2 zone 121",
##     BASEGEOGCRS["TWD97",
##         DATUM["Taiwan Datum 1997",
##             ELLIPSOID["GRS 1980",6378137,298.257222101,
##                 LENGTHUNIT["metre",1]]],
##         PRIMEM["Greenwich",0,
##             ANGLEUNIT["degree",0.0174532925199433]],
##         ID["EPSG",3824]],
##     CONVERSION["Taiwan 2-degree TM zone 121",
##         METHOD["Transverse Mercator",
##             ID["EPSG",9807]],
##         PARAMETER["Latitude of natural origin",0,
##             ANGLEUNIT["degree",0.0174532925199433],
##             ID["EPSG",8801]],
##         PARAMETER["Longitude of natural origin",121,
##             ANGLEUNIT["degree",0.0174532925199433],
##             ID["EPSG",8802]],
##         PARAMETER["Scale factor at natural origin",0.9999,
##             SCALEUNIT["unity",1],
##             ID["EPSG",8805]],
##         PARAMETER["False easting",250000,
##             LENGTHUNIT["metre",1],
##             ID["EPSG",8806]],
##         PARAMETER["False northing",0,
##             LENGTHUNIT["metre",1],
##             ID["EPSG",8807]]],
##     CS[Cartesian,2],
##         AXIS["easting (X)",east,
##             ORDER[1],
##             LENGTHUNIT["metre",1]],
##         AXIS["northing (Y)",north,
##             ORDER[2],
##             LENGTHUNIT["metre",1]],
##     USAGE[
##         SCOPE["unknown"],
##         AREA["Taiwan - 120°E to 122°E"],
##         BBOX[20.41,119.99,26.72,122.06]],
##     ID["EPSG",3826]]
```

---

# 投影講完惹！！再來下載一下整個台灣的[地理圖資](https://data.gov.tw/dataset/7442)

---

# 操作 sf

- 可以用 `st_()` 開頭
    - 引入圖資 `st_read()`, `st_as_sf()`
    - 座標系統 `st_crs()`, `st_set_crs()`, `st_transform()`
    - 處理圖資 `st_crop()`, `st_bbox()`, `st_simplify()`
- 或者也可以用 `dplyr` 的動詞，`rename()`、`filter()`、`mutate()`、`select()`、`group_by()` 配 `summarize()`

---

# 操作 sf

```r
sf_taiwan <-
  st_read(dsn = "data/Lab10/直轄市縣市界線/", layer = "COUNTY_MOI_1090820", quiet = T) %>%
  rename_with(~str_to_lower(.), everything()) %>% st_transform(3826)

sf_taiwan
```

```
## Simple feature collection with 22 features and 4 fields
## geometry type:  MULTIPOLYGON
## dimension:      XY
## bbox:           xmin: -478698 ymin: 1154437 xmax: 606875.6 ymax: 2919551
## projected CRS:  TWD97 / TM2 zone 121
## First 10 features:
##    countyid countycode countyname         countyeng
## 1         Z      09007     連江縣 Lienchiang County
## 2         G      10002     宜蘭縣      Yilan County
## 3         N      10007     彰化縣   Changhua County
## 4         M      10008     南投縣     Nantou County
## 5         P      10009     雲林縣     Yunlin County
## 6         C      10017     基隆市      Keelung City
## 7         A      63000     臺北市       Taipei City
## 8         F      65000     新北市   New Taipei City
## 9         B      66000     臺中市     Taichung City
## 10        D      67000     臺南市       Tainan City
##                          geometry
## 1  MULTIPOLYGON (((146282.4 28...
## 2  MULTIPOLYGON (((346997.1 27...
## 3  MULTIPOLYGON (((194797.1 26...
## 4  MULTIPOLYGON (((277507.6 26...
## 5  MULTIPOLYGON (((156164 2602...
## 6  MULTIPOLYGON (((321581.3 27...
## 7  MULTIPOLYGON (((307543.1 27...
## 8  MULTIPOLYGON (((304125.1 27...
## 9  MULTIPOLYGON (((283293.5 27...
## 10 MULTIPOLYGON (((192793.9 25...
```

---

# 操作 sf

```r
sf_taiwan_simplify <- sf_taiwan %>% st_transform(3826) %>% 
  st_simplify(dTolerance = 100) %>% st_transform(4326)
sf_taiwan_simplify %>% object.size()
```

```
## 216704 bytes
```

```r
sf_taiwan %>% object.size()
```

```
## 5471680 bytes
```
---

# 操作 sf

```r
sf_taiwan_simplify %>% st_bbox()
```

```
##      xmin      ymin      xmax      ymax 
## 114.35968  10.37135 124.56115  26.38394
```

---

# 畫圖 - 4326

```r
sf_taiwan_simplify %>% ggplot() + geom_sf()
```

![](Lab10_Tutorial_Spatical-Data_files/figure-html/unnamed-chunk-16-1.png)

---

# 畫圖 - 3826

```r
sf_taiwan_simplify %>% st_transform(3826) %>% ggplot() + geom_sf()
```

![](Lab10_Tutorial_Spatical-Data_files/figure-html/unnamed-chunk-17-1.png)

---

# 畫圖 - 切台灣本島

- `filter()`

```r
sf_taiwan_simplify %>% 
  filter(! str_detect(countyname, "連江|金門|澎湖")) %>%
  ggplot() + geom_sf()
```

![](Lab10_Tutorial_Spatical-Data_files/figure-html/unnamed-chunk-18-1.png)

---

# 畫圖 - 切台灣本島

- `st_crop()`

```r
sf_taiwan_simplify %>% 
  st_crop(xmin = 120, xmax = 122, ymin = 22, ymax = 25.5) %>%
  ggplot() + geom_sf()
```

![](Lab10_Tutorial_Spatical-Data_files/figure-html/unnamed-chunk-19-1.png)

---

# 再次回到面量圖！來畫 2020 總統大選得票，幫我去中選會[下載資料](https://db.cec.gov.tw/histMain.jsp?voteSel=20200101A1)

---

# Map: Choropleth

<ul>
<li>Definition
    <ul>
    <li>A choropleth map displays divided geographical areas or regions that are coloured in relation to a numeric variable.</li>
    <li><a href="https://www.r-graph-gallery.com/choropleth-map.html">Choropleth Map by the R Graph Gallery</a></li>
    </ul>
<li>Process
    <ul>
    <li>Get Taiwan 2020 Election Results Data</li>
    <li>Decide the variable plotted, such as KMT vote per</li>
    <li>Join Election with Taiwan sf object</li>
    <li>Draw the map colored by the variable</li>
    </ul>
</ul>

---

# R time: Choropleth

---

# Map: Dot Distribution Map/Bubble Map

<ul>
<li>Definition
    <ul>
    <li>Choropleths aggregate individual data points into a single geographic region. In contrast, a dot distribution/density map uses a dot symbol to show the presence of a feature or a phenomenon.</li>
    <li><a href="https://www.r-graph-gallery.com/bubble-map.html">Bubble map by the R Graph Gallery</a></li>
    </ul>
<li>Process
    <ul>
    <li>Get Taiwan Cities Population Data</li>
    <li>Decide the variable plotted, such as city population</li>
    <li>Plot the base map and add city dots</li>
    </ul>
</ul>

---

# R time: Dot Distribution Map

---

# Map: Cartogram

<ul>
<li>Definition
    <ul>
    <li>A cartogram is a map in which the geometry of regions is distorted in order to convey the information of an alternate variable.</li>
    <li><a href="https://www.r-graph-gallery.com/cartogram.html">Cartogram by the R Graph Gallery</a></li>
    </ul>
<li>Process
    <ul>
    <li>Get Taiwan 2020 Election Results Data and population data</li>
    <li>Decide the variable for distortion, such as population</li>
    <li>Also decide the variable cared about, such as KMT vote per</li>
    <li>Distort the sf object based on the variable</li>
    <li>Plot the distorted map and colored by chosen variable</li>
    </ul>
</ul>

---

# R time: Cartogram

---

# Map: Parliament Plots

<ul>
<li>Definition
    <ul>
    <li>A visual representations of the composition of legislatures that display seats colour-coded by party.</li>
    <li><a href="https://github.com/RobWHickman/ggparliament">ggparliament by RobWHickman</a></li>
    <li><a href="https://erocoar.github.io/ggpol/">ggpol by Frederik Tiedemann</a></li>
    </ul>
<li>Process
    <ul>
    <li>Get Taiwan 2020 Parliament Raw Data</li>
    <li>Create x, y, and theta columns</li>
    <li>Plot Parliament Composition</li>
    </ul>
</ul>

---

# R time: Parliament Plots

---
# Map: Hexmap

<ul>
<li>Definition
    <ul>
    <li>A a geospatial object where all regions of the map are represented as hexagons.</li>
    <li><a href="https://pitchinteractiveinc.github.io/tilegrams/">tilegramps showcase with JS</a></li>
    <li><a href="https://github.com/olihawkins/clhex">library(clhex)</a></li>
    <li><a href="https://olihawkins.com/project/hexjson-editor/">Hexmap Editor</a></li>
    </ul>
<li>Process
    <ul>
    <li>Create empty Taiwan Constituency hexjson with library(clhex)</li>
    <li>Draw Taiwan Constituency with hexjson editor according to geographical posistion</li>
    <li>Import edited hexjson into R and plot with geom_sf()</li>
    <li>Export the .SVG for further use</li>
    </ul>
</ul>

---

# R time: Hexmap

---

# Map: Summary

<ul>
<li>Plots
    <ul>
    <li>背景地圖/Background Map</li>
    <li>統計地圖/Choropleth</li>
    <li>點示地圖/Dot Distribution Map; Bubble Map</li>
    <li>示意地圖/Cartogram</li>
    <li>國會席次圖/Parliament Plots</li>
    <li>六邊型網格圖/Hexmap/Tilegram</li>
    </ul>

---

# Some Map

.pull-left[Taiwan 2020 Presidential Choropleth by [端傳媒](https://theinitium.com/article/20200112-taiwan-election-data-ntu/)]

.pull-right[US 2016 Presidential Vote Share Map by [Views of the World](http://www.viewsoftheworld.net/wp-content/uploads/2016/11/USelection2016Cartogram.png)]
---
# Some Map

.pull-left[US 2012 Presidential Vote Lead Map by [The New York Times](https://www.nytimes.com/interactive/2016/11/01/upshot/many-ways-to-map-election-results.html)]

.pull-right[Taiwan 2020 Parliament Hexmap by [端傳媒](https://theinitium.com/article/20200112-taiwan-election-data-ntu-1/)]

---
# Some Map

<img src="photo/reddit_map_hex_swing.png" width="50%" height="50%" /><img src="photo/關鍵_plot_parliament.png" width="50%" height="50%" />
.pull-left[UK 2019 Parliament Swing Map by [TeHuia](https://www.reddit.com/r/MapPorn/comments/eah5j1/uk_2019_election_swing_map/)]

---

# 今日重點: Use R as GIS

- 認識地理資訊格式
- 認識地理資料結構 in R
- 操作地理資料
- 視覺化地理資料
- Extra: Geometry Operations

---

# 之後有機會: 空間分析

- [Geometry Operations](https://geocompr.robinlovelace.net/geometric-operations.html#buffers)
    - [可達性空間](https://medium.com/ivc-invisiblecities/passive-space-remake-4faea442d78a)
    - [重疊區域切分](https://medium.com/geopainter/%E7%94%A8%E6%8D%B7%E9%81%8B%E8%B3%87%E6%96%99%E8%A7%80%E5%AF%9F%E4%B9%98%E5%AE%A2%E7%9A%84%E7%A7%BB%E5%8B%95%E8%BB%8C%E8%B7%A1-%E4%B8%8B-22d70ea76ddb)
    - [空間層級變換](https://medium.com/ivc-invisiblecities/%E5%8F%B0%E5%8C%97%E4%BA%BA%E5%8F%A3%E5%88%86%E5%B8%83%E5%9C%B0%E5%9C%96%E7%A9%BA%E9%96%93%E8%B3%87%E6%96%99%E7%9A%84%E5%B0%BA%E5%BA%A6%E8%AE%8A%E6%8F%9B-7278e319c5fe)
- Spatial Analysis
    - 熱點分析
    - 空間自相關
    - 熱區分析

---

# Thanks