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lectures/w05_dataarch.qmd

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+---
+title: "Geographic Data Science"
+subtitle: "Point Patterns"
+author: "Elisabetta Pietrostefani & Carmen Cabrera-Arnau"
+format: 
+    revealjs:
+        navigation-mode: grid
+align-items: center;
+---
+
+# The *point* of points
+
+# Points like polygons
+
+-   Points *can* represent "fixed" entities
+-   In this case, points are qualitatively similar to polygons/lines
+-   The goal here is, taking location fixed, to model other aspects of the data
+
+# Points like polygons
+
+Examples: - Cities (in most cases) - Buildings - Polygons represented as their centroid - ...
+
+# When points are not polygons
+
+Point data are not only a different geometry than polygons or lines... <br> ... Points can also represent a fundamentally different way to approach spatial analysis
+
+# Points unlike polygons
+
+# A few examples
+
+# 
+
+<center>
+
+<img alt="centered image" data-src="./figs/l09_crime.png" width="60%" height="60%"/>
+
+<center>
+
+# 
+
+<center>
+
+<img alt="centered image" data-src="./figs/l09_trees.png" width="65%" height="65%"/>
+
+<center>
+
+# 
+
+<center>
+
+<img alt="centered image" data-src="./figs/l09_mapbox.png" width="65%" height="65%"/>
+
+<center>
+
+# Points patterns
+
+# Points patterns
+
+Distribution of **points** over a portion of **space** Assumption is a point can happen anywhere on that space, but only happens in specific locations
+
+-   **Unmarked**: locations only
+-   **Marked**: values attached to each point
+
+# Point Pattern Analysis
+
+Describe, characterize, and explain point patterns, focusing on their **generating process**
+
+-   Visual exploration
+-   Clustering properties and clusters
+-   Statistical modeling of the underlying processes
+
+# Visualization of Point Patterns
+
+# Visualization of PPs
+
+Four routes (today):
+
+-   One-to-one mapping -- "Scatter plot"
+-   Aggregate -- "Histogram"
+-   Smooth -- KDE
+-   Smooth -- Interpolation
+
+# One-to-one
+
+-   Intuitive
+-   Effective in small datasets
+-   Limited as size increases until useless
+
+# One-to-one
+
+<center>
+
+<img alt="centered image" data-src="./figs/l09_liv_pts.png" width="50%" height="50%"/>
+
+<center>
+
+# Aggregation
+
+# Points meet polygons
+
+-   Use polygon boundaries and count points per area \[Insert your skills for choropleth mapping here!!!\]
+-   But, the polygons need to *"make sense"* (their delineation needs to relate to the point generating process)
+
+# 
+
+<center>
+
+<img data-src="./figs/l09_liv_pts.png" height="400"/>   <img data-src="./figs/l09_liv_cho.png" height="400"/>
+
+<center>
+
+# Hex-binning
+
+If no polygon boundary seems like a good candidate for aggregation... ...draw a hexagonal (or squared) tesselation!!!
+
+Hexagons...
+
+-   Are regular
+-   Exhaust the space (Unlike circles)
+-   Have many sides (minimize boundary problems)
+
+# 
+
+<center>
+
+<img data-src="./figs/l09_liv_pts.png" height="300"/>   <img data-src="./figs/l09_liv_hex_empty.png" height="300"/>    <img data-src="./figs/l09_liv_hex_filled.png" height="300"/>
+
+<center>
+
+# But
+
+-   (Arbitrary) aggregation may induce MAUP 
+-   Points usually represent events that affect only part of the population and hence are best considered as rates
+
+# Kernet Density Estimation (KDE)
+
+# KDE
+
+Estimate the **(continuous)** observed distribution of a variable
+
+-   Probability of finding an observation at a given point
+-   "Continuous histogram"
+-   Solves (much of) the MAUP problem, but not the underlying population issue
+
+# Bivariate (spatial) KDE
+
+Probability of finding observations at a given point in space
+
+-   **Bivariate** version: distribution of pairs of values
+-   In **space**: values are coordinates (XY), locations
+-   Continuous "version" of a choropleth
+
+# 
+
+<center>
+
+<img alt="centered image" data-src="./figs/l09_kde2d.png" width="75%" height="75%"/>
+
+<center>
+
+# 
+
+<center>
+
+<img data-src="./figs/l09_liv_pts.png" height="350"/>   <img data-src="./figs/l09_liv_kde.png" height="350"/>
+
+<center>
+
+# Interpolation
+
+-   Estimating values spatially continuous variables for spatial locations where they **have not** been observed, based on observations.
+-   **Geostatistics**, is concerned with the modelling, prediction and simulation of spatially continuous phenomena.
+
+# Inverse Distance Weighting (IDW)
+
+-   We observe a property of a phenomenon $Z(s)$ at a **limited** number of sample locations, and are interested in the property value at **all** locations.
+-   Have to predict it for unobserved locations.
+
+# Kriging
+
+If we were predicting prices
+
+$$Price_i = \sum^N_{j=1} w_j * Price_j + \epsilon_i$$
+
+-   with $w_j = (\frac{1}{d_{ij}})^2$ for all $i$ and $j \neq i$
+-   $d$ the distance between $i$ and $j$.
+
+# 
+
+<center>
+
+<img alt="centered image" data-src="./figs/l09_idw.png" width="75%" height="75%"/>
+
+<center>
+
+# Parametres
+
+-   **Variable**: for example price
+-   **Nearest Neighbours** : the number of nearest observations that should be used
+-   **idp** : set inverse distance power to 2
+
+A super useful link [here](https://gisgeography.com/inverse-distance-weighting-idw-interpolation/)
+
+# Parametres
+
+idp = 1 <img data-src="./figs/L09_pw1.png" height="250"/> <br> idp = 2 <img data-src="./figs/L09_pw2.png" height="250"/>
+
+# Density-Based Spatial Clustering of Applications with Noise, or DBSCAN
+
+# Questions
+
+# 
+
+<a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><img src="https://i.creativecommons.org/l/by-sa/4.0/88x31.png" alt="Creative Commons License" style="border-width:0"/></a><br />[Geographic Data Science]{xmlns:dct="http://purl.org/dc/terms/" property="dct:title"} by <a xmlns:cc="http://creativecommons.org/ns#" href="http://pietrostefani.com" property="cc:attributionName" rel="cc:attributionURL">Elisabetta Pietrostefani</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike 4.0 International License</a>.