Overcoming Data Scarcity in Land Use Monitoring with Time-Weighted Dynamic Time Warping .wu-logo-right[]

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.title[
# Overcoming Data Scarcity in Land Use Monitoring with Time-Weighted Dynamic Time Warping .wu-logo-right[]
]
.subtitle[
## <b><br></b>
]
.author[
### Dr Victor Maus<br>.font80[Institute for Ecological Economics<br>Vienna University of Economics and Business]<br>.font80[<a href="mailto:victor.maus@wu.ac.at" class="email">victor.maus@wu.ac.at</a>]<br>.font80[<a href='https://vwmaus.github.io'>vwmaus.github.io</a>]
]
.date[
### .right[.font80[Open Earth Monitor, Global Workshop, Oct 6, 2023, Bolzano].footnote-right-title[Except where otherwise noted, content on these slides is licensed under <a href='https://creativecommons.org/licenses/by-sa/4.0'>CC BY-SA 4.0 license</a>]]
]

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background-image: url("https://upload.wikimedia.org/wikipedia/en/d/d2/Back_to_the_Future.jpg")
background-size: contain

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# Time Series Classification

<br>
.center[
<img src="https://www.victor-maus.com/assets/talks/img/source_petitjean_2012.png" width="80%" />
]

.footnote-right[Figure: [Tan et al., 2017](https://doi.org/10.1137/1.9781611974973.32)]

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# Dimensionality

.pull-left[
## 1-D Array
<table class="table" style="margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;"> b1_t1 </th>
   <th style="text-align:left;"> b1_t2 </th>
   <th style="text-align:left;"> b1_tm </th>
   <th style="text-align:left;"> b2_t1 </th>
   <th style="text-align:left;"> b2_t2 </th>
   <th style="text-align:left;"> b2_tm </th>
   <th style="text-align:left;"> bn_tm </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> . </td>
   <td style="text-align:left;"> . </td>
   <td style="text-align:left;"> . </td>
   <td style="text-align:left;"> . </td>
   <td style="text-align:left;"> . </td>
   <td style="text-align:left;"> . </td>
   <td style="text-align:left;"> . </td>
  </tr>
</tbody>
</table>
]

.pull-right[
## 2-D Array
<table class="table" style="margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;">   </th>
   <th style="text-align:left;"> band_1 </th>
   <th style="text-align:left;"> band_2 </th>
   <th style="text-align:left;"> band_3 </th>
   <th style="text-align:left;"> band_n </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> time_1 </td>
   <td style="text-align:left;"> . </td>
   <td style="text-align:left;"> . </td>
   <td style="text-align:left;"> . </td>
   <td style="text-align:left;"> . </td>
  </tr>
  <tr>
   <td style="text-align:left;"> time_2 </td>
   <td style="text-align:left;"> . </td>
   <td style="text-align:left;"> . </td>
   <td style="text-align:left;"> . </td>
   <td style="text-align:left;"> . </td>
  </tr>
  <tr>
   <td style="text-align:left;"> time_3 </td>
   <td style="text-align:left;"> . </td>
   <td style="text-align:left;"> . </td>
   <td style="text-align:left;"> . </td>
   <td style="text-align:left;"> . </td>
  </tr>
  <tr>
   <td style="text-align:left;"> [...] </td>
   <td style="text-align:left;"> . </td>
   <td style="text-align:left;"> . </td>
   <td style="text-align:left;"> . </td>
   <td style="text-align:left;"> . </td>
  </tr>
  <tr>
   <td style="text-align:left;"> time_m </td>
   <td style="text-align:left;"> . </td>
   <td style="text-align:left;"> . </td>
   <td style="text-align:left;"> . </td>
   <td style="text-align:left;"> . </td>
  </tr>
</tbody>
</table>
]

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# Dynamic Time Warping (DTW)

<br>
.center[
<img src="https://www.tandfonline.com/cms/asset/5a80ca23-5dec-4da6-99db-69972a37c2dc/tcag_a_890071_f0006_c.jpg" width="80%" />
]

.center.font-huw-red-dark.font150[
  **Allows out-of-season alignments**
]

.footnote-right[Figure: [Ranacher & Tzavella, 2014](https://doi.org/10.1080/15230406.2014.890071)]

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# Time-Weighted-DTW

.pull-left.font200[
  <br>
  `\(\omega(t_i,t_j) = \frac{1}{1 + e^{-{\alpha} (g(t_i,t_j){i,j} - {\beta})}}\)`
  <br><br>
  .font-huw-red-dark.font100[**Keep alignments within the correct season**]
]

.pull-right[
<img src="index_files/figure-html/unnamed-chunk-5-1.png" width="90%" />
]

.footnote-left[[Maus et al., 2016](http://doi.org/10.1109/JSTARS.2016.2517118)]

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# Advantages

.pull-left[
- ### Irregularly sampled time series

- ### Time series with different length

- ### No need for gap-filling

- ### .font-huw-red-dark.font100[Requires a small set of training samples]
]

.pull-right[
<img src="dtw-advnatages.png" width="120%" />
]

--
.font-huw-red-dark.font150[
  **Dynamic Time Warping (DTW) and 1-Nearest Neighbor (1NN)**
]

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# Leave-all but one out cross-validation

<br>
.center[
![](index_files/figure-html/unnamed-chunk-7-1.png)
]

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# Patterns from literature

.pull-left[
<img src="https://www.victor-maus.com/assets/img/literature-patterns.png" width="100%" />
]
.pull-right[
<img src="https://www.victor-maus.com/assets/img/literature-patterns-maps.png" width="70%" />
]

.footnote-left[[Maus et al., 2016](http://doi.org/10.1109/JSTARS.2016.2517118)]

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# Sample generation

.pull-left[
<img src="https://ars.els-cdn.com/content/image/1-s2.0-S0303243420309077-gr1_lrg.jpg" width="100%" />
]
.pull-right[
<img src="https://ars.els-cdn.com/content/image/1-s2.0-S0303243420309077-gr4_lrg.jpg" width="90%" />
]

.footnote-left[[Belgiu et al., 2021](https://doi.org/10.1016/j.jag.2020.102264)]

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# Samples

.center[
![](index_files/figure-html/unnamed-chunk-12-1.png)
]

.font-huw-red-dark.font150.center[
  **High computational cost**
]

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# Patterns

.center[
![](index_files/figure-html/unnamed-chunk-13-1.png)
]

.footnote-left[[Maus et al., 2019](http://doi.org/10.18637/jss.v088.i05)]

.font-huw-red-dark.font150.center[
  **Reduced number of comparisons**
]

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# Twenty-year maize distribution in China

.center[
<img src="https://media.springernature.com/full/springer-static/image/art%3A10.1038%2Fs41597-023-02573-6/MediaObjects/41597_2023_2573_Fig8_HTML.png?as=webp" width="60%" />
]

.footnote-left[[Peng et al., 2023](https://doi.org/10.1038/s41597-023-02573-6)]

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# CRAN

.pull-left[
## R package `dwtSat (≥ 1.0-0)`

- Fortran 90 and C++ versions

### Land use mapping useing `stars`

```r
install.packages("dtwSat")

vignette("landuse-mapping", "dtwSat")
```

### Future versions:

- `gdalcubes`
- `sits`
]

.pull-right[
<img src="./../img/qrcode_www.victor-maus.com.png" height="190"/><br>
.font100[victor.maus@wu.ac.at]<br>
.font100[<a href='https://vwmaus.github.io'>vwmaus.github.io</a>]
]