Pattern-based spatial analysis: an approach for discovering, describing and studying geographical patterns

class: inverse, left, nonum, clear
background-image: url("figs/cover.jpg")
background-size: cover

<br>
.titlestyle[Pattern-based spatial analysis:] <br>
.titlestyle2[an approach for] <br>
.titlestyle2[discovering,] <br>
.titlestyle2[describing,] <br>
.titlestyle2[and studying geographical patterns]

.captionstyle[Jakub Nowosad]
.pull-right2[.captionstyle[RGS-IBG GIScience Webinar Series, 2021-02-03]]

---
# Acknowledgement

.lc[
### Space Informatics Lab

http://sil.home.amu.edu.pl/

.font140[
- [Tomasz F. Stepinski](http://sil.home.amu.edu.pl/)
- [Jaroslaw Jasiewicz](http://jarekj.home.amu.edu.pl/)
- [Anna Dmowska](http://dmowska.home.amu.edu.pl/)
- [Pawel Netzel](http://pawel.netzel.pl/)
- [Jacek Niesterowicz](http://sil.home.amu.edu.pl/)
]
]

.rc[
<img src="figs/sil-logo.png" width="70%" style="display: block; margin: auto;" />

]

---
# Spatial patterns in categorical rasters

**Discovering and describing spatial patterns is an important element of many geographical studies with spatial patterns being related to ecological and sociological processes.**
.column-left[
.font90[Assessing the ecological vulnerability of forest landscape to agricultural frontier expansion]

.font60[*Bourgoin et al., 2020, https://doi.org/10.1016/j.jag.2019.101958*]
]

.column-center[
.font90[Quantifying racial diversity and segregation]

.font60[*Dmowska et at., 2020, https://doi.org/10.1016/j.apgeog.2020.102239*]

]

.column-right[
.font90[Reinterpreting classified histological images as categorical rasters and using them for disease-classification (e.g., liver cancer)]

.font60[*Kendall et al., 2020, https://doi.org/10.1038/s41598-020-74691-9*]
]

---
# Understading of spatial patterns

- A lot of effort has been put to creates methods for the quantification of spatial patterns
- Existing software for patterns' description, such as [FRAGSTATS](https://www.umass.edu/landeco/research/fragstats/fragstats.html), [GuidosToolbox](https://forest.jrc.ec.europa.eu/en/activities/lpa/gtb/), or [landscapemetrics](https://r-spatialecology.github.io/landscapemetrics/) proved to be vital is many scientific studies

---
# Pattern-based spatial analysis

- We are now able to describe different properties of spatial patterns
- We also know that spatial patterns are the cause and also a result of many environmental and social processes
- Now, the question is **how can we consistently analyze spatial patterns?**

- **Pattern-based spatial analysis** is a set of comprehensive ideas on how spatial patterns can be described and analyzed, with a focus on categorical raster data
- This enables spatial analysis such as **search**, **change detection**, **clustering**, and **segmentation**

---
# Spatial signatures

.pull-left[
<img src="index_files/figure-html/unnamed-chunk-14-1.png" style="display: block; margin: auto;" />
]

We can say that 98.6% of this area is covered by **forest** and 1.3% by **agriculture**.

Also, we can describe its diversity using **entropy** (0.116) and its spatial clumpinnes with **relative mutual information** (0.331).

---
# Spatial signatures

---
# Spatial signatures

---
# Spatial signatures

---
# Spatial signatures

<table class="table table" style="font-size: 24px; margin-left: auto; margin-right: auto; margin-left: auto; margin-right: auto;">
<tbody>
  <tr>
   <td style="text-align:left;background-color: #C1C1C1 !important;"> id </td>
   <td style="text-align:left;background-color: #C1C1C1 !important;"> 1 </td>
   <td style="text-align:left;background-color: #C1C1C1 !important;"> 2 </td>
   <td style="text-align:left;background-color: #C1C1C1 !important;"> 3 </td>
   <td style="text-align:left;background-color: #C1C1C1 !important;"> 4 </td>
   <td style="text-align:left;background-color: #C1C1C1 !important;"> 5 </td>
   <td style="text-align:left;background-color: #C1C1C1 !important;"> 6 </td>
   <td style="text-align:left;background-color: #C1C1C1 !important;"> 7 </td>
   <td style="text-align:left;background-color: #C1C1C1 !important;"> 8 </td>
   <td style="text-align:left;background-color: #C1C1C1 !important;"> 9 </td>
   <td style="text-align:left;background-color: #C1C1C1 !important;"> 10 </td>
   <td style="text-align:left;background-color: #C1C1C1 !important;"> 11 </td>
   <td style="text-align:left;background-color: #C1C1C1 !important;"> 12 </td>
   <td style="text-align:left;background-color: #C1C1C1 !important;"> 13 </td>
   <td style="text-align:left;background-color: #C1C1C1 !important;"> 14 </td>
   <td style="text-align:left;background-color: #C1C1C1 !important;"> 15 </td>
   <td style="text-align:left;background-color: #C1C1C1 !important;"> 16 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ent </td>
   <td style="text-align:left;"> 0.12 </td>
   <td style="text-align:left;"> 0.45 </td>
   <td style="text-align:left;"> 0.53 </td>
   <td style="text-align:left;"> 0.63 </td>
   <td style="text-align:left;"> 0.75 </td>
   <td style="text-align:left;"> 1.16 </td>
   <td style="text-align:left;"> 1.16 </td>
   <td style="text-align:left;"> 1.28 </td>
   <td style="text-align:left;"> 1.53 </td>
   <td style="text-align:left;"> 1.2 </td>
   <td style="text-align:left;"> 1.65 </td>
   <td style="text-align:left;"> 1.6 </td>
   <td style="text-align:left;"> 1.74 </td>
   <td style="text-align:left;"> 1.72 </td>
   <td style="text-align:left;"> 1.6 </td>
   <td style="text-align:left;"> 2.02 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> relmutinf </td>
   <td style="text-align:left;"> 0.33 </td>
   <td style="text-align:left;"> 0.39 </td>
   <td style="text-align:left;"> 0.34 </td>
   <td style="text-align:left;"> 0.52 </td>
   <td style="text-align:left;"> 0.44 </td>
   <td style="text-align:left;"> 0.51 </td>
   <td style="text-align:left;"> 0.39 </td>
   <td style="text-align:left;"> 0.33 </td>
   <td style="text-align:left;"> 0.42 </td>
   <td style="text-align:left;"> 0.36 </td>
   <td style="text-align:left;"> 0.5 </td>
   <td style="text-align:left;"> 0.58 </td>
   <td style="text-align:left;"> 0.43 </td>
   <td style="text-align:left;"> 0.34 </td>
   <td style="text-align:left;"> 0.2 </td>
   <td style="text-align:left;"> 0.38 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> forest </td>
   <td style="text-align:left;"> 0.99 </td>
   <td style="text-align:left;"> 0.93 </td>
   <td style="text-align:left;"> 0.9 </td>
   <td style="text-align:left;"> 0.84 </td>
   <td style="text-align:left;"> 0.83 </td>
   <td style="text-align:left;"> 0.76 </td>
   <td style="text-align:left;"> 0.69 </td>
   <td style="text-align:left;"> 0.68 </td>
   <td style="text-align:left;"> 0.59 </td>
   <td style="text-align:left;"> 0.57 </td>
   <td style="text-align:left;"> 0.53 </td>
   <td style="text-align:left;"> 0.5 </td>
   <td style="text-align:left;"> 0.44 </td>
   <td style="text-align:left;"> 0.4 </td>
   <td style="text-align:left;"> 0.39 </td>
   <td style="text-align:left;"> 0.36 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> agriculture </td>
   <td style="text-align:left;"> 0.01 </td>
   <td style="text-align:left;"> 0.05 </td>
   <td style="text-align:left;"> 0.08 </td>
   <td style="text-align:left;"> 0.16 </td>
   <td style="text-align:left;"> 0.16 </td>
   <td style="text-align:left;"> 0.12 </td>
   <td style="text-align:left;"> 0.25 </td>
   <td style="text-align:left;"> 0.23 </td>
   <td style="text-align:left;"> 0.24 </td>
   <td style="text-align:left;"> 0.39 </td>
   <td style="text-align:left;"> 0.3 </td>
   <td style="text-align:left;"> 0.36 </td>
   <td style="text-align:left;"> 0.36 </td>
   <td style="text-align:left;"> 0.39 </td>
   <td style="text-align:left;"> 0.36 </td>
   <td style="text-align:left;"> 0.3 </td>
  </tr>
</tbody>
</table>

---
# Spatial signatures

.pull-left[
<img src="index_files/figure-html/unnamed-chunk-23-1.png" style="display: block; margin: auto;" />
]

**Co-occurrence matrix (*coma*):**

<table>
 <thead>
  <tr>
   <th style="text-align:left;">   </th>
   <th style="text-align:right;"> agriculture </th>
   <th style="text-align:right;"> forest </th>
   <th style="text-align:right;"> grassland </th>
   <th style="text-align:right;"> water </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;font-weight: bold;"> agriculture </td>
   <td style="text-align:right;"> 272 </td>
   <td style="text-align:right;"> 218 </td>
   <td style="text-align:right;"> 4 </td>
   <td style="text-align:right;"> 0 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;"> forest </td>
   <td style="text-align:right;"> 218 </td>
   <td style="text-align:right;"> 38778 </td>
   <td style="text-align:right;"> 32 </td>
   <td style="text-align:right;"> 12 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;"> grassland </td>
   <td style="text-align:right;"> 4 </td>
   <td style="text-align:right;"> 32 </td>
   <td style="text-align:right;"> 16 </td>
   <td style="text-align:right;"> 0 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;"> water </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 12 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 2 </td>
  </tr>
</tbody>
</table>

---
# Spatial signatures

.pull-left[
<img src="index_files/figure-html/unnamed-chunk-25-1.png" style="display: block; margin: auto;" />
]

**Co-occurrence vector (*cove*):**

**Co-occurrence vector (*cove*):**

**Normalized co-occurrence vector (*cove*):**

---
# Spatial signatures

.pull-left[
<img src="index_files/figure-html/unnamed-chunk-29-1.png" style="display: block; margin: auto;" />

** *cove*: **

.pull-right[
<img src="index_files/figure-html/unnamed-chunk-31-1.png" style="display: block; margin: auto;" />

** *cove*: **

<table>
<tbody>
  <tr>
   <td style="text-align:right;"> 0.1282 </td>
   <td style="text-align:right;"> 0.0609 </td>
   <td style="text-align:right;"> 0.8105 </td>
   <td style="text-align:right;"> 0.0002 </td>
   <td style="text-align:right;"> 0.0002 </td>
   <td style="text-align:right;"> 0.0001 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 0 </td>
  </tr>
</tbody>
</table>
]

---
# Distance measures

.pull-left[
<img src="index_files/figure-html/unnamed-chunk-33-1.png" style="display: block; margin: auto;" />

<table class="table" style="font-size: 12px; margin-left: auto; margin-right: auto;">
<tbody>
  <tr>
   <td style="text-align:right;"> 0.0069 </td>
   <td style="text-align:right;"> 0.011 </td>
   <td style="text-align:right;"> 0.9792 </td>
   <td style="text-align:right;"> 0.0002 </td>
   <td style="text-align:right;"> 0.0016 </td>
   <td style="text-align:right;"> 0.0004 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 0.0006 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 0.0001 </td>
  </tr>
</tbody>
</table>
]

.pull-right[
<img src="index_files/figure-html/unnamed-chunk-35-1.png" style="display: block; margin: auto;" />

<table class="table" style="font-size: 12px; margin-left: auto; margin-right: auto;">
<tbody>
  <tr>
   <td style="text-align:right;"> 0.1282 </td>
   <td style="text-align:right;"> 0.0609 </td>
   <td style="text-align:right;"> 0.8105 </td>
   <td style="text-align:right;"> 0.0002 </td>
   <td style="text-align:right;"> 0.0002 </td>
   <td style="text-align:right;"> 0.0001 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 0 </td>
  </tr>
</tbody>
</table>
]

<br>

`$$JSD(A, B) = H(\frac{A + B}{2}) - \frac{1}{2}[H(A) + H(B)]$$`
<br>

**Jensen-Shannon distance** between the first and the fourth raster: ** 0.068 **

---
# Distance measures

.pull-left[
<img src="index_files/figure-html/unnamed-chunk-38-1.png" style="display: block; margin: auto;" /><table class="table" style="font-size: 12px; margin-left: auto; margin-right: auto;">
<tbody>
  <tr>
   <td style="text-align:right;"> 0.0069 </td>
   <td style="text-align:right;"> 0.011 </td>
   <td style="text-align:right;"> 0.9792 </td>
   <td style="text-align:right;"> 0.0002 </td>
   <td style="text-align:right;"> 0.0016 </td>
   <td style="text-align:right;"> 0.0004 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 0.0006 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 0.0001 </td>
  </tr>
</tbody>
</table>
]

.pull-right[
<img src="index_files/figure-html/unnamed-chunk-39-1.png" style="display: block; margin: auto;" /><table class="table" style="font-size: 12px; margin-left: auto; margin-right: auto;">
<tbody>
  <tr>
   <td style="text-align:right;"> 0.2033 </td>
   <td style="text-align:right;"> 0.1335 </td>
   <td style="text-align:right;"> 0.2944 </td>
   <td style="text-align:right;"> 0.1747 </td>
   <td style="text-align:right;"> 0.0562 </td>
   <td style="text-align:right;"> 0.1307 </td>
   <td style="text-align:right;"> 0.0035 </td>
   <td style="text-align:right;"> 0.0002 </td>
   <td style="text-align:right;"> 0.0004 </td>
   <td style="text-align:right;"> 0.0015 </td>
   <td style="text-align:right;"> 0.0007 </td>
   <td style="text-align:right;"> 0.0005 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 0.0005 </td>
  </tr>
</tbody>
</table>
]

<br>

`$$JSD(A, B) = H(\frac{A + B}{2}) - \frac{1}{2}[H(A) + H(B)]$$`
<br>

**Jensen-Shannon distance** between the first and the 15th raster: ** 0.444 **

---
# Spatial signatures - wecoma

.pull-left[
<img src="index_files/figure-html/unnamed-chunk-42-1.png" style="display: block; margin: auto;" />
]

**Co-occurrence matrix (*coma*):**

**Weighted co-occurrence matrix (*wecoma*):**

---
# Spatial signatures - wecove

** *wecove*: **

---
# Spatial signatures - incoma

Two or more categorical rasters - an **integrated co-occurrence matrix (*incoma*)** representation

---
# Spatial signatures - incoma

.lc[
<img src="index_files/figure-html/unnamed-chunk-49-1.png" style="display: block; margin: auto;" />
]

.rc[
<img src="figs/coma.png" width="1469" style="display: block; margin: auto;" />

]

---
# Spatial signatures - incoma

.lc[
<img src="index_files/figure-html/unnamed-chunk-53-1.png" style="display: block; margin: auto;" />
]

.rc[
<img src="figs/coma_text.png" width="1469" style="display: block; margin: auto;" />
]

---
# Spatial signature - incove

** *incove*: **

---
# Pattern-based spatial analysis

Knowing the distances between spatial signatures can be used in several contexts:

.column-left[
**one-to-many**

*finding similar spatial patterns*
<img src="figs/lsp_search4.png" width="95%" style="display: block; margin: auto;" />
]

.column-center[
**one-to-one**

*quantifying changes in spatial patterns*
<img src="figs/lsp_compare2.png" width="95%" style="display: block; margin: auto;" />
]

.column-right[
**many-to-many**

*clustering similar spatial patterns*
<img src="figs/lsp_cluster4.png" width="95%" style="display: block; margin: auto;" />
]

---
# Finding similar spatial patterns

.lc[
Spatial pattern search allows for **quantifying similarity between the query region and the search space** and finally finding regions that are the most similar to the query one
- Here, we were interested in finding areas of similar topography to the area of
Suwalski Landscape Park


- Geomorphons categorize cells in this area into one of ten landform types

]
.rc[
<img src="figs/lsp_search2.png" width="80%" style="display: block; margin: auto;" />
]

---
# Finding similar spatial patterns

.lc[
**Spatial search requires two groups of input data:**

1. The query region
2. The search space want to search
]
.rc[
<img src="figs/lsp_search1.png" width="90%" style="display: block; margin: auto;" />
]

---
# Finding similar spatial patterns

.lc[
**The searching process consists of:**
1. Dividing the search space using regular (non-overlapping) squares or using polygons 
2. Creating a signature for the query region and the search space
3. Comparing the signature of the query region with signatures for each part of the search space using a distance measure
]

.rc[
<img src="figs/lsp_search_grid.png" width="80%" style="display: block; margin: auto;" />

]

---
# Finding similar spatial patterns

.lc[
The brown color on the above map represents areas with the most similar patterns of geomorphons to the Suwalski Landscape Park

The majority of similar areas are located in northern Poland and forms a belt with homogeneous topography

]
.rc[
<img src="figs/lsp_search4.png" width="80%" style="display: block; margin: auto;" />
]

---
# Finding similar spatial patterns

.lc[
The most similar areas to the query region

<img src="figs/lsp_search2.png" width="1556" style="display: block; margin: auto;" />
]

.rc[
<img src="figs/lsp_search3.png" width="2275" style="display: block; margin: auto;" />
]

---
# Quantifying changes of spatial patterns

The above map clearly shows that there has been a large land cover change in many areas of Amazon between 1992 and 2018.
The problem now is **to find out which areas changed the most**.

---
# Quantifying changes of spatial patterns

.lc[



 
**This process consists of:**

1. Dividing the search space using regular squares or polygons
2. Calculating signatures for each smaller area in two times
3. Comparing the signatures using a distance measure for each smaller area in two times
]

.rc[
<img src="figs/lsp_compare2.png" width="80%" style="display: block; margin: auto;" />
]

---
# Quantifying changes of spatial patterns

.lc[
Here, we are looking for the areas with the largest change, which is expressed by the largest distance values

Importantly, we are not only interested in changes of categories, but also their spatial arrangements


]

.rc[
<img src="figs/lsp_compare3.png" width="2275" style="display: block; margin: auto;" />
]

---
# Clustering similar spatial patterns

**Clustering groups areas of similar spatial patterns together.**
Here, we are interested in finding clusters of regions with similar patterns
of both land covers and landforms in Africa.

---
# Clustering similar spatial patterns

.pull-left[
**This process can consists of:**

1. Dividing the search space using regular squares or polygons
2. Calculating signatures for each smaller area
3. *(Depending on the used method)* Calculating distances between every signature (a distance matrix)
4. Grouping areas with similar signatures together using a clustering method
]

.pull-right[
<img src="figs/lsp_cluster_grid.png" width="90%" style="display: block; margin: auto;" />
]

---
# Clustering similar spatial patterns

.pull-left[
A distance matrix can be used in various methods of hierarchical clustering or fuzzy clustering.

Here, we used hierarchical clustering and divided the area into eight clusters.

]

.pull-right[
<img src="figs/lsp_cluster4.png" width="90%" style="display: block; margin: auto;" />
]

---
# Clustering similar spatial patterns

Most clusters form continuous regions, so we could merge areas into larger polygons.

---
# Clustering similar spatial patterns

.lc[
**Three metrics can be used to evaluate properties of each cluster:**

- **Inhomogeneity** - a degree of mutual distance between all objects in a cluster

- **Distinction** - an average distance between the focus cluster and all the other clusters

- **Overall quality** - calculated as *1 - (inhomogeneity / distinction)*

]

.rc[
<img src="figs/lsp_cluster6.png" width="2259" style="display: block; margin: auto;" />
]
---
# Clustering similar spatial patterns

Inhomogeneity can be also assessed visually with a **pattern mosaic**.

**Pattern mosaic** is an artificial rearrangement of a subset of randomly selected areas belonging to a given cluster.

.lc[
**4th cluster**

- Inhomogeneity: 0.12
- Distinction: 0.79
- Quality: 0.85
]

.rc[
<img src="figs/lsp_cluster7.png" width="100%" style="display: block; margin: auto;" />
]

---
# Clustering similar spatial patterns

Inhomogeneity can be also assessed visually with a **pattern mosaic**.

**Pattern mosaic** is an artificial rearrangement of a subset of randomly selected areas belonging to a given cluster.

.lc[
**1th cluster**

- Inhomogeneity: 0.51
- Distinction: 0.77
- Quality: 0.34
]

.rc[
<img src="figs/lsp_cluster8.png" width="100%" style="display: block; margin: auto;" />
]

---
# Considerations and future work

.pull-left[
**Potential applications:**

- Global environmental changes
- Land management
- Sustainable development
- Environmental protection
- Forest cover change
- Urban growth monitoring
- Agriculture expansion studies

**Study considerations:**

- What is the scale of the process we want to study?
- How to preprocess the input data? 
- Which signature should we apply?
- Which distance measure should we use?

]

.pull-right[

**General considerations:**

- How to decide which scale is valid?
- What type of signatures are we still missing? 
- How to integrate categorical and continuous spatial patterns in an analysis?
- What are the advantages and disadvantages of using different distance measures?
]

---
class: left, top, clear

.pull-left[

## Summary

- Pattern-based spatial analysis helps discovering, describing, and studying geographical patterns
- Its core idea is to characterize areas using spatial signatures
- Spatial signatures can be compared using a large number of existing distance or dissimilarity measures
- This enables spatial analysis such as search, change detection, clustering, and segmentation
- Methods of pattern-based spatial analysis are implemented in open-source software, such as R package [motif](https://nowosad.github.io/motif/), GRASS GIS module [GeoPAT](http://sil.home.amu.edu.pl/index.php?id=software), and standalone [GeoPAT 2](https://github.com/Nowosad/geopat2) software 
]

.pull-right[

## Contact

Twitter: <svg role="img" viewBox="0 0 24 24" xmlns="http://www.w3.org/2000/svg" style="height:1em;fill:currentColor;position:relative;display:inline-block;top:.1em;">  <title></title>  <path d="M23.954 4.569c-.885.389-1.83.654-2.825.775 1.014-.611 1.794-1.574 2.163-2.723-.951.555-2.005.959-3.127 1.184-.896-.959-2.173-1.559-3.591-1.559-2.717 0-4.92 2.203-4.92 4.917 0 .39.045.765.127 1.124C7.691 8.094 4.066 6.13 1.64 3.161c-.427.722-.666 1.561-.666 2.475 0 1.71.87 3.213 2.188 4.096-.807-.026-1.566-.248-2.228-.616v.061c0 2.385 1.693 4.374 3.946 4.827-.413.111-.849.171-1.296.171-.314 0-.615-.03-.916-.086.631 1.953 2.445 3.377 4.604 3.417-1.68 1.319-3.809 2.105-6.102 2.105-.39 0-.779-.023-1.17-.067 2.189 1.394 4.768 2.209 7.557 2.209 9.054 0 13.999-7.496 13.999-13.986 0-.209 0-.42-.015-.63.961-.689 1.8-1.56 2.46-2.548l-.047-.02z"></path></svg> [jakub_nowosad](https://twitter.com/jakub_nowosad)

Website: https://nowosad.github.io

## Resources

- **Slides:** [nowosad.github.io/giscience-webinar-2021](https://nowosad.github.io/giscience-webinar-2021)
- **Software:** R package [motif](https://nowosad.github.io/motif/), GRASS GIS module [GeoPAT](http://sil.home.amu.edu.pl/index.php?id=software), standalone [GeoPAT 2](https://github.com/Nowosad/geopat2) software
- **Example code:** [motif-examples](https://github.com/Nowosad/motif-examples)
- **Blog posts:** https://nowosad.github.io/tags/motif, https://nowosad.github.io/tags/geopat/

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