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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...
... Points can also represent a fundamentally different way to approach spatial analysis
+
+# Points unlike polygons
+
+# A few examples
+
+#
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+![centered image]()
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+#
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+![centered image]()
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+#
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+![centered image]()
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+# 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
+
+
+
+![centered image]()
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+# 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)
+
+#
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+![]()
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+# 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)
+
+#
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+
+![]()
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+
+
+# 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
+
+#
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+
+![centered image]()
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+
+#
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+
+![]()
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+# 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 $j$.
+
+#
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+
+![centered image]()
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+
+# 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 ![]()
idp = 2 ![]()
+
+# Density-Based Spatial Clustering of Applications with Noise, or DBSCAN
+
+# Questions
+
+#
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[Geographic Data Science]{xmlns:dct="http://purl.org/dc/terms/" property="dct:title"} by Elisabetta Pietrostefani is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
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+# Density-Based Spatial Clustering of Applications with Noise, or DBSCAN
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+# Questions
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+#
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