class: inverse, left, nonum, clear background-image: url("figs/title-cover.jpg") background-size: cover <!-- https://www.si.edu/object/cornish-landscape:saam_2020.20.236?page=3&edan_q=landscape&oa=1&edan_fq%5B0%5D=media_usage:CC0&destination=/search/collection-images&searchResults=1&id=saam_2020.20.236 --> <link rel="stylesheet" type="text/css" href="https://fonts.googleapis.com/css?family=Montserrat" /> <!-- Describing multi-layer spatial patterns using an integrated co-occurrence matrix (INCOMA) --> <br> .titlestyle2[Describing] <br> .titlestyle2[multi-layer spatial patterns] <br> .titlestyle2[using] <br> .titlestyle2[an integrated co-occurrence matrix] <br> .titlestyle2[(INCOMA)] .captionstyle[Jakub Nowosad, Tomasz Stepinski] .pull-right2[.captionstyle[GISRUK 2021, 2021-04-16]] --- # Landscape types <!-- what's that --> <!-- how this is important --> .lc[ **Landscape** - a recognizable, although often heterogeneous part of the terrestrial surface showing characteristic pattern of natural themes *(Mücher et al. 2010)*. ---- <!-- Complexity of landscapes can be grasped in terms of categorical spatial zones. --> Multiple layers (themes), including topography, land cover, climate, and soil/geology, contribute to the character of a landscape. ] .rc[ <img src="figs/spaceody.png" width="80%" style="display: block; margin: auto;" /> **Landscape types (LTs)** - foundation for planning and management to develop optimal strategies for sustainable use of land resources *(Wascher 2005; Mücher et al. 2010)*. They provide first-order information about the geographical distribution of biodiversity and ecological processes *(Heikkinen et al. 2004)*. **Identifying, and mapping LTs using available data is challenging.** ] --- # Creating landscape types for large areas .lc[ There are **three main approaches** for creating landscape types for large areas: - Manual - Cell-based - Pattern-based ] --- # Creating landscape types for large areas .lc[ There are **three main approaches** for creating landscape types for large areas: - **Manual** - Cell-based - Pattern-based ] .rc[ *Omernik and Griffith (2014)* - conterminous United States. <img src="figs/omernik.png" width="65%" style="display: block; margin: auto;" /> Patterns of biotic and abiotic phenomena, both terrestrial and aquatic, including geology, landforms, soils, vegetation, climate, land use, wildlife, and hydrology. State-by-state basis (with a few exceptions). More than 600 people was involved. <!-- “Ecoregions are identified by analyzing patterns of biotic and abiotic phenomena, both terrestrial and aquatic. These phenomena include geology, landforms, soils, vegetation, climate, land use, wildlife, and hydrology” --> <!-- State-by-state basis (with a few exceptions) --> <!-- The product of the efforts of over 600 individuals representing several federal agencies, many state agencies, and a number of non-government organizations (NGOs) and academic institutions --> ] --- # Creating landscape types for large areas .lc[ There are **three main approaches** for creating landscape types for large areas: - Manual - **Cell-based** - Pattern-based ] .rc[ *Mücher et al. 2010; Sayre et al. 2014* - global; *Sayre et al. 2009* - conterminous United States. <img src="figs/sayre2009b.png" width="70%" style="display: block; margin: auto;" /> **Overlay of cell-based maps** representing contributing variables (e.g., bioclimate, landform, lithology, and land cover) ] <!-- The majority of them covered a single country or a single region within a country, while two (Mücher et al. 2010; Sayre et al. 2014) had a continental or global coverage. This review did not focus on specific technical methodologies employed, but the two papers where landscapes were mapped on a large spatial scale both used multi-thematic datasets but were cell-based instead of being pattern-based. --> --- # Creating landscape types for large areas .lc[ There are **three main approaches** for creating landscape types for large areas: - Manual - Cell-based - **Pattern-based** ] .rc[ *Cardille et al. 2012* - Canada; *Niesterowicz et al. 2016* - conterminous United States; *Nowosad and Stepinski 2018* - global <img src="figs/niesterowicz2016.png" width="1295" style="display: block; margin: auto;" /> In such approach, **a study area is tessellated into** relatively small blocks of cells carrying values of contributing variables (**local landscapes**, LLs). **Each LLs is characterized by a pattern** formed by values of contributing variables over its extent. <!-- therefore we refer to it as a local landscape (LL) – a landscape atthe scale thatis large enough to be called a landscape but small in comparison to the sizeof the studyarea. --> Identification and delineation of LTs -- grouping similar LLs into distinct clusters (zones). ] <!-- Recent works based on the LL concept can be divided intothree groups, those devoted to mapping LTs (Long, Nelson, and Wulder 2010; Cardilleand Lambois 2010; Cardilleet al.2012; Partington and Cardille 2013; Niesterowiczand Stepinski 2013; Niesterowicz, Stepinski, and Jasiewicz 2016; Niesterowicz andStepinski 2017; Nowosad and Stepinski 2018), --> --- # Current contraints ### Manual approach - Time-consuming - Inconsistent over the large areas - Not reproducible - Hard to update -- ### Cell-based approach - Identifies LTs at the scale of the size of the cell - Results in a very large number of classes - Spatial units are homogeneous in categories of contributing variables, whereas many true LTs are heterogeneous -- ### Pattern-based approach - Currently, pattern-based methods use only a single theme, e.g, land cover data --- class: inverse, left, middle # Goal ## Expand pattern-based methods to represent multi-thematic categorical patterns. <!-- improve slide style --> <!-- The purpose of this paper is to introduce the integrated co- occurrence matrix (INCOMA) – a signature for numerical representation of multi-thematic categorical patterns. --> --- class: inverse, left, bottom # Existing methods --- # Pattern-based spatial analysis Basic idea - **dividing a study area into a large number of smaller areas** (local landscapes). .lc2[ <img src="figs/ng_grid.png" width="100%" style="display: block; margin: auto;" /> ] -- .rc2[ Next - to represent each area by a statistical description of the spatial pattern - **spatial signature**. Spatial **signatures can be compared** using a large number of existing **distance or dissimilarity measures** *(Lin 1991; Cha 2007)*. This enables spatial analyses such as **searching**, **change detection**, **clustering** or **segmentation**. ] --- # Spatial signatures .pull-left[ <img src="index_files/figure-html/index-3-1.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/index-5-1.png" style="display: block; margin: auto;" /> ] -- **Co-occurrence vector (*cove*):** <table> <tbody> <tr> <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> <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> <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> <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> -- **Co-occurrence vector (*cove*):** <table> <tbody> <tr> <td style="text-align:right;"> 136 </td> <td style="text-align:right;"> 218 </td> <td style="text-align:right;"> 19389 </td> <td style="text-align:right;"> 4 </td> <td style="text-align:right;"> 32 </td> <td style="text-align:right;"> 8 </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;"> 1 </td> </tr> </tbody> </table> -- **Normalized co-occurrence vector (*cove*):** <table> <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> --- # Distance measures .pull-left[ <img src="index_files/figure-html/index-13-1.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/index-15-1.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> ] <!-- dozens --> <!-- li paper --> -- <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 ** --- # Pattern-based spatial analysis Knowing the distances between spatial signatures can be used in several contexts ([*Nowosad 2021*](https://doi.org/10.1007/s10980-020-01135-0)): -- .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;" /> ] --- class: inverse, left, bottom # Integrated co-occurrence matrix (*incoma*) --- # Spatial signatures - many themes <!-- add an intro sentence --> <!-- Two or more categorical rasters - an **integrated co-occurrence matrix (*incoma*)** representation --> <!-- https://nowosad.github.io/comat/articles/incoma.html --> Co-occurrence matrix can represent one raster (theme) only. <img src="index_files/figure-html/index-22-1.png" width="75%" style="display: block; margin: auto;" /> **How to create a spatial signature to represent multi-thematic spatial patterns of categorized data?** --- # Spatial signatures - many themes .lc[ <img src="index_files/figure-html/index-23a-1.png" style="display: block; margin: auto;" /> ] .rc[ *Vadivel et al. (2007)* proposed a two-dimensional matrix for representing color and intensity of pixel neighborhoods in an image. <!--In the field of image recognition, --> Here, we readopt the above idea for categorized data. ---- <br><br><br> **The integrated co-occurrence matrix (INCOMA) allows for the numerical representation of multi-thematic spatial patterns of categorized data.** It contains not only information about the **patterns of all variables**, but also information about the **relative positions of different spatial patterns**. ] --- # Spatial signatures - incoma .lc[ <img src="index_files/figure-html/index-23-1.png" style="display: block; margin: auto;" /> ] .rc[ <img src="figs/coma.png" width="95%" style="display: block; margin: auto;" /> ] --- # Spatial signatures - incoma .lc[ <img src="index_files/figure-html/index-27-1.png" style="display: block; margin: auto;" /> ] .rc[ <img src="figs/coma_text.png" width="95%" style="display: block; margin: auto;" /> ] --- # Spatial signature - incove <img src="index_files/figure-html/index-29-1.png" style="display: block; margin: auto;" /> -- ** *incove*: ** <table class="table" style="font-size: 12px; margin-left: auto; margin-right: auto;"> <tbody> <tr> <td style="text-align:right;"> 0.0101419 </td> <td style="text-align:right;"> 0.00633 </td> <td style="text-align:right;"> 0.3020252 </td> <td style="text-align:right;"> 0.0001176 </td> <td style="text-align:right;"> 0.0026615 </td> <td style="text-align:right;"> 0.003676 </td> <td style="text-align:right;"> 0.0000032 </td> <td style="text-align:right;"> 0.0000095 </td> <td style="text-align:right;"> 0.000002 </td> <td style="text-align:right;"> 0.0000048 </td> <td style="text-align:right;"> 0.0000024 </td> <td style="text-align:right;"> 0.0000016 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0.0000004 </td> <td style="text-align:right;"> 0.0006084 </td> <td style="text-align:right;"> 0.0002991 </td> <td style="text-align:right;"> 0.0003561 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0.001026 </td> <td style="text-align:right;"> 0.0001525 </td> <td style="text-align:right;"> 0.0028929 </td> <td style="text-align:right;"> 0.0000008 </td> <td style="text-align:right;"> 0.0000044 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0.0030172 </td> <td style="text-align:right;"> 0.0029929 </td> <td style="text-align:right;"> 0.1095329 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0.0000008 </td> <td style="text-align:right;"> 0.0000328 </td> <td style="text-align:right;"> 0.001188 </td> <td style="text-align:right;"> 0.0000131 </td> <td style="text-align:right;"> 0.0001566 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0.0000004 </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;"> 0.000017 </td> <td style="text-align:right;"> 0.0004535 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0.0000006 </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;"> 0.00004 </td> <td style="text-align:right;"> 0.0020324 </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;"> 0.0000004 </td> <td style="text-align:right;"> 0.0001752 </td> <td style="text-align:right;"> 0.0074844 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0.0000006 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0.0000137 </td> <td style="text-align:right;"> 0.0004077 </td> <td style="text-align:right;"> 0.0146355 </td> <td style="text-align:right;"> 0.0001304 </td> <td style="text-align:right;"> 0.0000041 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0.0000382 </td> <td style="text-align:right;"> 0.0000149 </td> <td style="text-align:right;"> 0.0000556 </td> <td style="text-align:right;"> 0.0054452 </td> <td style="text-align:right;"> 0.0000367 </td> <td style="text-align:right;"> 0.0000004 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0.0000085 </td> <td style="text-align:right;"> 0.0000041 </td> <td style="text-align:right;"> 0.0021124 </td> <td style="text-align:right;"> 0.0093426 </td> <td style="text-align:right;"> 0.0004276 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0.0000017 </td> <td style="text-align:right;"> 0.0005311 </td> <td style="text-align:right;"> 0.0000116 </td> <td style="text-align:right;"> 0.0084664 </td> <td style="text-align:right;"> 0.1594694 </td> <td style="text-align:right;"> 0.004895 </td> <td style="text-align:right;"> 0.000005 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0.0011252 </td> <td style="text-align:right;"> 0.0000309 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0.0003359 </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 </td> <td style="text-align:right;"> 0.0002198 </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;"> 0.0000489 </td> <td style="text-align:right;"> 0.0009586 </td> <td style="text-align:right;"> 0.0000006 </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;"> 0.000434 </td> <td style="text-align:right;"> 0.1118513 </td> <td style="text-align:right;"> 0.0000138 </td> <td style="text-align:right;"> 0.0001397 </td> <td style="text-align:right;"> 0.0000747 </td> <td style="text-align:right;"> 0.0000163 </td> <td style="text-align:right;"> 0.000405 </td> <td style="text-align:right;"> 0.0000042 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0.0018406 </td> <td style="text-align:right;"> 0.0002832 </td> <td style="text-align:right;"> 0.0000313 </td> <td style="text-align:right;"> 0.0000467 </td> <td style="text-align:right;"> 0.0002811 </td> <td style="text-align:right;"> 0.0072919 </td> <td style="text-align:right;"> 0.0000313 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0.0001552 </td> <td style="text-align:right;"> 0.0000747 </td> <td style="text-align:right;"> 0.0146664 </td> <td style="text-align:right;"> 0.0000138 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0.0000142 </td> <td style="text-align:right;"> 0.0000496 </td> <td style="text-align:right;"> 0.000513 </td> <td style="text-align:right;"> 0.005169 </td> <td style="text-align:right;"> 0.000078 </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;"> 0.0004638 </td> <td style="text-align:right;"> 0.0000058 </td> <td style="text-align:right;"> 0.0117431 </td> <td style="text-align:right;"> 0.0000108 </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;"> 0.0000025 </td> <td style="text-align:right;"> 0.000201 </td> <td style="text-align:right;"> 0.0009447 </td> <td style="text-align:right;"> 0.1743671 </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;"> 0.00003 </td> <td style="text-align:right;"> 0.0000584 </td> <td style="text-align:right;"> 0.0000108 </td> <td style="text-align:right;"> 0.0000054 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0.0002849 </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;"> 0.0000008 </td> <td style="text-align:right;"> 0.0000188 </td> <td style="text-align:right;"> 0.0000167 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0.0000013 </td> <td style="text-align:right;"> 0.0002023 </td> <td style="text-align:right;"> 0.0014098 </td> <td style="text-align:right;"> 0.0000004 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0.0000042 </td> <td style="text-align:right;"> 0.000005 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0.0000029 </td> <td style="text-align:right;"> 0.0000188 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0.0004792 </td> </tr> </tbody> </table> .center[Now, we can compare the signature of this landscape with any other landscapes.] .center[INCOMA works on two or more themes.] .center[It allows for clustering similar spatial patterns of multi-theme patterns.] <!-- toDo - more than two layers --> <!-- toDo - add a note about applications to merge the next section --> --- class: inverse, left, bottom # Landscape types in Europe --- # Data We used **three themes**/datasets: <img src="figs/all_layers.png" width="4000" style="display: block; margin: auto;" /> .column-left[ *2018 C3S land cover (ECMWF 2019)* ] .column-center[ *The Hammond's landform regions (Karagulle et al. 2017)* ] .column-right[ *USDA soil taxonomy dataset (Hengl et al. 2017)* ] The datasets were reprojected and resampled to the same grid for Europe with 300 meters resolution. Additionally, they were simplified, resulting in nine land cover categories, four landform classes, and 12 soil categories. --- # Local landscapes Next, the study area was divided into **~40,000 15 km x 15 km** (50 x 50 cells) square blocks - **local landscapes (LLs)**. <img src="figs/all_layers2.png" width="4000" style="display: block; margin: auto;" /> Spatial patterns of the three themes were used to calculate INCOMA signature for each LLs. --- # Number of landscape types .lc2[ <img src="figs/tsne50_kmeans20.png" width="3200" style="display: block; margin: auto;" /> ] .rc2[ We performed the **t-distributed stochastic neighbor embedding (t-SNE)** *(Maaten and Hinton 2008)* to get insight into the structure of the multi-dimensional space of INCOMA signatures. The result showed a continuous structure of this space, meaning that **signatures' space is stratified but without distinct gaps**. ] --- # Landscape types .lc[ Identification of LTs was achieved via **clustering LLs using the `\(K\)`-means clustering with `\(K=20\)`**. <!-- and the `\(JSD\)` as a distance between signatures. --> ] -- .rc[ <img src="figs/tm_lts50.png" width="90%" style="display: block; margin: auto;" /> ] --- class: clear2 .lc2[ <!-- The quality of delineation depends on how similar patterns are within a single LT and how dissimilar are patterns between different LTs. --> ## The quality of delineation **The intra-cluster dissimilarity** (**homogeneity**, `\(\delta\)`) of an LT - an average dissimilarity between all LLs within a zone. Smaller values are better. **The inter-cluster dissimilarity** (**interdistance**, `\(\beta\)`) between a given LT and other LTs - a distance between the given cluster and the rest of the clusters using the average linkage. <!-- The metric for a given LT is an average of values of average linkage between this LT and all other LTs. --> Larger values are better. ] .rc2[ <table class="table" style="font-size: 13px; margin-left: auto; margin-right: auto;"> <thead> <tr> <th style="text-align:right;"> LT </th> <th style="text-align:right;"> area (km2) </th> <th style="text-align:right;"> homogeneity </th> <th style="text-align:right;"> interdistance </th> </tr> </thead> <tbody> <tr> <td style="text-align:right;"> 1 </td> <td style="text-align:right;"> 336,375 </td> <td style="text-align:right;"> 0.45 </td> <td style="text-align:right;"> 0.73 </td> </tr> <tr> <td style="text-align:right;"> 2 </td> <td style="text-align:right;"> 304,875 </td> <td style="text-align:right;"> 0.33 </td> <td style="text-align:right;"> 0.77 </td> </tr> <tr> <td style="text-align:right;"> 3 </td> <td style="text-align:right;"> 384,075 </td> <td style="text-align:right;"> 0.19 </td> <td style="text-align:right;"> 0.67 </td> </tr> <tr> <td style="text-align:right;"> 4 </td> <td style="text-align:right;"> 569,475 </td> <td style="text-align:right;"> 0.29 </td> <td style="text-align:right;"> 0.70 </td> </tr> <tr> <td style="text-align:right;"> 5 </td> <td style="text-align:right;"> 577,575 </td> <td style="text-align:right;"> 0.36 </td> <td style="text-align:right;"> 0.72 </td> </tr> <tr> <td style="text-align:right;"> 6 </td> <td style="text-align:right;"> 527,400 </td> <td style="text-align:right;"> 0.19 </td> <td style="text-align:right;"> 0.71 </td> </tr> <tr> <td style="text-align:right;font-weight: bold;color: white !important;background-color: #DB4325 !important;"> 7 </td> <td style="text-align:right;font-weight: bold;color: white !important;background-color: #DB4325 !important;"> 243,900 </td> <td style="text-align:right;font-weight: bold;color: white !important;background-color: #DB4325 !important;"> 0.73 </td> <td style="text-align:right;font-weight: bold;color: white !important;background-color: #DB4325 !important;"> 0.91 </td> </tr> <tr> <td style="text-align:right;"> 8 </td> <td style="text-align:right;"> 397,800 </td> <td style="text-align:right;"> 0.37 </td> <td style="text-align:right;"> 0.68 </td> </tr> <tr> <td style="text-align:right;"> 9 </td> <td style="text-align:right;"> 133,200 </td> <td style="text-align:right;"> 0.32 </td> <td style="text-align:right;"> 0.72 </td> </tr> <tr> <td style="text-align:right;"> 10 </td> <td style="text-align:right;"> 457,425 </td> <td style="text-align:right;"> 0.21 </td> <td style="text-align:right;"> 0.74 </td> </tr> <tr> <td style="text-align:right;"> 11 </td> <td style="text-align:right;"> 291,150 </td> <td style="text-align:right;"> 0.19 </td> <td style="text-align:right;"> 0.66 </td> </tr> <tr> <td style="text-align:right;"> 12 </td> <td style="text-align:right;"> 608,850 </td> <td style="text-align:right;"> 0.25 </td> <td style="text-align:right;"> 0.74 </td> </tr> <tr> <td style="text-align:right;"> 13 </td> <td style="text-align:right;"> 240,075 </td> <td style="text-align:right;"> 0.50 </td> <td style="text-align:right;"> 0.80 </td> </tr> <tr> <td style="text-align:right;"> 14 </td> <td style="text-align:right;"> 237,150 </td> <td style="text-align:right;"> 0.37 </td> <td style="text-align:right;"> 0.73 </td> </tr> <tr> <td style="text-align:right;"> 15 </td> <td style="text-align:right;"> 609,750 </td> <td style="text-align:right;"> 0.22 </td> <td style="text-align:right;"> 0.73 </td> </tr> <tr> <td style="text-align:right;"> 16 </td> <td style="text-align:right;"> 524,025 </td> <td style="text-align:right;"> 0.29 </td> <td style="text-align:right;"> 0.75 </td> </tr> <tr> <td style="text-align:right;"> 17 </td> <td style="text-align:right;"> 433,800 </td> <td style="text-align:right;"> 0.23 </td> <td style="text-align:right;"> 0.63 </td> </tr> <tr> <td style="text-align:right;"> 18 </td> <td style="text-align:right;"> 605,925 </td> <td style="text-align:right;"> 0.26 </td> <td style="text-align:right;"> 0.71 </td> </tr> <tr> <td style="text-align:right;font-weight: bold;color: white !important;background-color: #006164 !important;"> 19 </td> <td style="text-align:right;font-weight: bold;color: white !important;background-color: #006164 !important;"> 634,500 </td> <td style="text-align:right;font-weight: bold;color: white !important;background-color: #006164 !important;"> 0.12 </td> <td style="text-align:right;font-weight: bold;color: white !important;background-color: #006164 !important;"> 0.71 </td> </tr> <tr> <td style="text-align:right;"> 20 </td> <td style="text-align:right;"> 456,300 </td> <td style="text-align:right;"> 0.27 </td> <td style="text-align:right;"> 0.78 </td> </tr> </tbody> </table> ] --- # Example landscape types .center[**Exemplar of LT 19**, 15x15 km] <img src="figs/tm_lts50_m_19single.png" width="100%" style="display: block; margin: auto;" /> --- # Pattern mosaic **Inhomogeneity can also be assessed visually with a pattern mosaic** (225 x 225 km; 15 by 15 random LLs) . <img src="figs/lt19.png" width="80%" style="display: block; margin: auto;" /> <table class="table" style="font-size: 20px; margin-left: auto; margin-right: auto;"> <thead> <tr> <th style="text-align:left;"> </th> <th style="text-align:right;"> LT </th> <th style="text-align:right;"> area (km2) </th> <th style="text-align:right;"> homogeneity </th> <th style="text-align:right;"> interdistance </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;font-weight: bold;color: white !important;background-color: #006164 !important;"> 19 </td> <td style="text-align:right;font-weight: bold;color: white !important;background-color: #006164 !important;"> 19 </td> <td style="text-align:right;font-weight: bold;color: white !important;background-color: #006164 !important;"> 634,500 </td> <td style="text-align:right;font-weight: bold;color: white !important;background-color: #006164 !important;"> 0.12 </td> <td style="text-align:right;font-weight: bold;color: white !important;background-color: #006164 !important;"> 0.71 </td> </tr> </tbody> </table> --- # Pattern mosaic **Inhomogeneity can also be assessed visually with a pattern mosaic** (225 x 225 km; 15 by 15 random LLs). <img src="figs/lt7.png" width="80%" style="display: block; margin: auto;" /> <table class="table" style="font-size: 20px; margin-left: auto; margin-right: auto;"> <thead> <tr> <th style="text-align:left;"> </th> <th style="text-align:right;"> LT </th> <th style="text-align:right;"> area (km2) </th> <th style="text-align:right;"> homogeneity </th> <th style="text-align:right;"> interdistance </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;font-weight: bold;color: white !important;background-color: #DB4325 !important;"> 7 </td> <td style="text-align:right;font-weight: bold;color: white !important;background-color: #DB4325 !important;"> 7 </td> <td style="text-align:right;font-weight: bold;color: white !important;background-color: #DB4325 !important;"> 243,900 </td> <td style="text-align:right;font-weight: bold;color: white !important;background-color: #DB4325 !important;"> 0.73 </td> <td style="text-align:right;font-weight: bold;color: white !important;background-color: #DB4325 !important;"> 0.91 </td> </tr> </tbody> </table> --- # Comparison with other techniques .pull-left[ *Cell-based approach* <img src="figs/spain2b.png" width="73%" style="display: block; margin: auto;" /> ] -- .pull-right[ *Pattern-based approach (INCOMA)* <img src="figs/spain1.png" width="75%" style="display: block; margin: auto;" /> ] <!-- 186624 coma x 9 x 4 x 12 --> Only **INCOMA can**, without additional processing, **create a delineation that includes zones characterized by**: - **simple multi-thematic patterns** (e.g., sets of local landscapes with mostly homogeneous land cover, landforms, and soils) - **complex multi-thematic patterns** (e.g., collections of local landscapes with mostly heterogeneous land cover, landforms, and soils) --- class: inverse, left, bottom # Conclusions --- # Considerations and future work <img src="figs/spaceody4.png" width="90%" style="display: block; margin: auto;" /> .pull-left[ **Creating landscape types:** - Which layers to use? - How to prepare them (reproject, reclassify)? - What should be the spatial scale of the local landscape? What is the scale of the process we want to study? - How many categories we want to have? - Which signature should we apply? - Which distance measure should we use? <!-- superpixels? --> <!-- connection to reality? --> ] -- .pull-right[ **Future work:** - Validating the obtained LTs - Adding some additional information, e.g., climate - Developing an alternative method to k-means for grouping local landscapes, which results in zones of consistent homogeneity ] --- class: left, top, clear2 .pull-left[ ## Summary - **INCOMA is a numerical signature of a multi-thematic pattern** of natural themes - It makes identification and delineation of landscape types using the pattern-based approach possible - INCOMA can produce, in an unsupervised fashion and without post-processing, a delineation that includes zones characterized by simple motifs as well as zones characterized by complex motifs - **INCOMA can also find application in other tasks** that also require calculating similarities between multi-thematic patterns, **such as content-based search** and retrieval in spatial databases ] .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/GISRUK2021](https://nowosad.github.io/GISRUK2021/) Articles: - Nowosad J, Stepinski TF (2021) *Pattern-based identification and mapping of landscape types using multi-thematic data*. IJGIS, https://doi.org/10.1080/13658816.2021.1893324 - Nowosad, J., 2021, *Motif: an open-source R tool for pattern-based spatial analysis*. Landscape Ecol, https://doi.org/10.1007/s10980-020-01135-0 Software: https://nowosad.github.io/motif/, https://nowosad.github.io/comat/ ] .font80[.footnote[*Cover image: Watanabe Shikō, https://hvrd.art/o/340552*] ]