Spatial analysis. Spatial descriptive analysis. Spatial inferential analysis:

Transcription

1 Spatial analysis Spatial descriptive analysis Point pattern analysis (minimum bounding box, mean center, weighted mean center, standard distance, nearest neighbor analysis) Spatial clustering analysis (K-means, DBSCAN, hotspot analysis) Spatial associations (Moran s I, Geary s C, semivariogram, ) GEOG176B/GEOG176C / GEOG172 Spatial inferential analysis: Regression models Spatial interpolation (in terrain analysis)

2 Spatial analysis Spatial descriptive analysis Point pattern analysis Spatial clustering analysis, Spatial associations (Moran s I, Geary s C, semivariogram, ) GEOG176B/Geog176C / GEOG172 What: You have detected clusters using a spatial clustering method (e.g., traffic congestion, hot locations visited by many tourists...) Spatial inferential analysis: Regression models Spatial interpolation (in terrain analysis) Why: But what reasons to see such a pattern? (e.g., there is a baseball game? Or the location is at a famous landmark?...)

3 Regression models General idea: develop a model to fit observed data use this model to predict the future Regression models: (Multiple) linear regression Generalized linear regression Multivariate linear regression Mixed regression (linear and nonlinear) Geographically weighted regression (GWR)

4 Linear regression To establish a linear relation between the independent variable(s) and the dependent variable. Dependent variable: the output of the model (the variable you want to predict) Independent variable: the input of the model (the variables you use to explain the dependent variable) E.g., how temperature changes with elevation. The temperature is the dependent variable and the elevation is the independent variable Only one independent variable simple linear regression More than one independent variable multiple linear regression

5 Example of simple linear regression

6 Estimation of linear regression Model: Estimation of a and b (Least square estimation ): is named as residuals Other estimation approach: maximum likelihood estimation (MLE)

7 Goodness-of-fit of linear regression Many approaches: Diagnostic on residuals R-squared Adjusted R-squared Chi-square goodness of fit tests Split the data into training and testing cross validation

8 R-squared A metric to quantify how good your model fits to your data Specifically, it describes how much variance the model explained for the data Has a value ranges between [0, 1] 0 means the model does not fit the data at all 1 means the model fits the data perfectly

9 Multiple linear regression Simple linear regression can be extended to multiple linear regression With more independent variables The estimation and evaluation approaches are the same If some independent variables are not in a linear relation with the dependent variable, we can then transform by using: ln(x), log(x), sqrt(x), An example from the textbook

10 Geographically weighted regression (GWR)

11 Example Dependent variable: number of hemorrhagic fever Independent variable: temperature, NDVI08, Land110, Elevatiuon

12 Geographically weighted regression (GWR)

13 Summary on spatial analysis Analysis on attribute data Text attribute: word frequency summary, semantic analysis Numeric attribute: descriptive and inferential statistics Analysis on spatial data Descriptive analysis: max, min, range, centroid, average nearest neighbor, spatial clustering Inference analysis: multiple linear regression (estimation, evaluation and prediction) and GWR

14 GIS tools for spatial analysis ArcGIS (ArcToolbox) Matlab R GeoDa Python...

15 GIS tools for spatial analysis

16 GEOG 176A: Introduction to Geographic Information Systems Lecture 13: Terrain Analysis I (chapter 7) Rui Zhu

17 What is terrain? Terrain is about the physical features of Earth's surface A continuous field Not only have x and y dimensions, but also z dimension (i.e., elevation) Many spatial analysis have to take terrain analysis into account (e.g., viewshed analysis) A lot of 3D geo-visualizations rely on terrain data (e.g., Google Earth)

18 Representation of terrain Vector Raster Point samples (regular and irregular) Contours DEM DTM DSM TIN Others Voxel 3D point cloud

19 Representation of terrain Vector Raster Point samples (regular and irregular) Contours DEM DTM DSM TIN Others Voxel 3D point cloud

20 Vector - Point samples Regular point samples Irregular point samples

21 Interpolation based on point samples observed individual measurements estimated continuous field Example techniques Deterministic Inverse distance weighting (IDW) Nearest neighbor interpolation Triangulation interpolation Local averaging interpolation Kernel vector (RBF & Spline) Stochastic Kriging families Multiple-point geostatistics

22 Theory behind spatial interpolation Tobler's First Law of Geography "Everything is related to everything else, but near things are more related than distant things" --- Waldo Tobler (1970) Spatial dependence / spatial autocorrelation core of spatial analysis

23 IDW interpolation Inverse Distance weighting Closer points have more influences on the target value: P is the power parameter which determines the influence of the distance towards weights: p=0: every point has the same weight regardless of their distance towards the target location p=large value: points that are further away have less influence on the target location

24 IDW interpolation

25 IDW interpretation Practice question: you have three points whose elevation are 7, 9 and 11 meters, and their distances to the target locations are 1, 2 and 3 meters respectively. Using a power of 2, what would be your estimation for the elevation at the target locations?

26 IDW interpretation Practice question: you have three points whose elevation are 7, 9 and 11 meters, and their distances to the target locations are 1, 2 and 3 meters respectively. Using a power of 2, what would be your estimation for the elevation at the target locations?

27 IDW interpolation How to determine which points goes into the estimation? Fixed radius: define a search distance (e.g., 100 meters) and all points that fall into this search distance will be used Maximum points: define a number (e.g., 5), and only use this number of points which are closest to the target location will be used

28 Your tasks Read Chapter 7 Lab 4 due Sunday, September 2nd, 23:55 pm Next lecture: Terrain Analysis II