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Avaliable models
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<a href="#curtis" class="md-nav__link">
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Curtis
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Parabolic
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Stoffels
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Henriksen
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Prodan I
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Prodan II
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Artificial Neural Network
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Ranking function
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<h1 id="hypsometric-relationship">Hypsometric Relationship</h1>
<div class="admonition warning">
<p class="admonition-title">Warning</p>
<p>This library is under development, none of the presented solutions are available for download.</p>
</div>
<p>Estimate the heights of the missing trees based on the heights measured in the field.</p>
<h3 id="class-parameters">Class Parameters</h3>
<div class="highlight"><pre><span></span><code>HypRel(x, y, df, model, iterator)
</code></pre></div>
<table>
<thead>
<tr>
<th>Parameters</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><strong>x</strong></td>
<td>The name of the column that contains the tree diameters.</td>
</tr>
<tr>
<td><strong>y</strong></td>
<td>The name of the column that contains the tree heights.</td>
</tr>
<tr>
<td><strong>df</strong></td>
<td>The DataFrame containing the tree data.</td>
</tr>
<tr>
<td><strong>model</strong></td>
<td>(Optional) A list of models used for estimating tree heights. If none, will use all models avaliable.</td>
</tr>
<tr>
<td><strong>iterator</strong></td>
<td>(Optional) A column name string. Defines wich column will be used as a iterator. Could be a farm name, plot name, code or any unique identification tag.</td>
</tr>
</tbody>
</table>
<h3 id="class-functions">Class Functions</h3>
<div class="highlight"><pre><span></span><code>HypRel.run()
HypRel.metrics()
HypRel.plots(dir,show=bool)
HypRel.get_coef()
</code></pre></div>
<table>
<thead>
<tr>
<th>Parameters</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><strong>.run()</strong></td>
<td>Fit the models</td>
</tr>
<tr>
<td><strong>.metrics()</strong></td>
<td>Return a table of metrics of each evaluated model</td>
</tr>
<tr>
<td><strong>.plots()</strong></td>
<td>Return the height and residuals plots</td>
</tr>
<tr>
<td><strong>.get_coef()</strong></td>
<td>Return the coefficients for each model</td>
</tr>
</tbody>
</table>
<h3 id="example-usage">Example Usage</h3>
<div class="highlight"><table class="highlighttable"><tr><th colspan="2" class="filename"><span class="filename">hyp_rel_example.py</span></th></tr><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">1</span>
<span class="normal">2</span>
<span class="normal">3</span>
<span class="normal">4</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="c1">#import HypRel class</span>
<span class="kn">from</span> <span class="nn">fptools.hyp_rel</span> <span class="kn">import</span> <span class="n">HypRel</span>
<span class="c1">#import pandas for data manipulation</span>
<span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
</code></pre></div></td></tr></table></div>
<div class="mermaid">flowchart LR
subgraph run
runText1[Run all the available models]
end
subgraph metrics
runText2[Evaluate each fitted model]
end
subgraph plots
runText3[Generate plots]
end
subgraph coefficients
runText4[Return coefficients]
end
%% Links para os subgráficos:
HypRel-Module --> run
HypRel-Module --> metrics
HypRel-Module --> plots
HypRel-Module --> coefficients
</div>
<p>Create a variable for the HypRel Class</p>
<div class="highlight"><table class="highlighttable"><tr><th colspan="2" class="filename"><span class="filename">hyp_rel_example.py</span></th></tr><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal"> 3</span>
<span class="normal"> 4</span>
<span class="normal"> 5</span>
<span class="normal"> 6</span>
<span class="normal"> 7</span>
<span class="normal"> 8</span>
<span class="normal"> 9</span>
<span class="normal">10</span>
<span class="normal">11</span>
<span class="normal">12</span>
<span class="normal">13</span>
<span class="normal">14</span>
<span class="normal">15</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="c1">#load csv file</span>
<span class="n">df</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">read_csv</span><span class="p">(</span><span class="sa">r</span><span class="s1">'C:\Your\path\csv_inventory_file.csv'</span><span class="p">)</span>
<span class="c1">#create the variable "reg" containing the HypRel class</span>
<span class="hll"><span class="n">reg</span> <span class="o">=</span> <span class="n">HypRel</span><span class="p">(</span><span class="s1">'CAP'</span><span class="p">,</span><span class="s2">"HT"</span><span class="p">,</span><span class="n">df</span><span class="p">)</span>
</span><span class="c1">#Run the models and save in the "results" variable</span>
<span class="n">results</span> <span class="o">=</span> <span class="n">reg</span><span class="o">.</span><span class="n">run</span><span class="p">()</span>
<span class="c1">#Run a evaluation for the fitted models and save on "metrics" variable</span>
<span class="n">metrics</span> <span class="o">=</span> <span class="n">reg</span><span class="o">.</span><span class="n">metrics</span><span class="p">()</span>
<span class="c1">#Return the plots for the fitted models. </span>
<span class="c1">#If show=True, will print on screen all the heigth and residuals plots. #If a directory is passed, will save all the plots in the directory.</span>
<span class="n">reg</span><span class="o">.</span><span class="n">plots</span><span class="p">(</span><span class="s1">'C:\Your\path</span><span class="se">\t</span><span class="s1">o_save'</span><span class="p">,</span><span class="n">show</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="c1">#Get the coefficients for each model fitted</span>
<span class="n">df_coefficients</span> <span class="o">=</span> <span class="n">reg</span><span class="o">.</span><span class="n">get_coef</span><span class="p">()</span>
</code></pre></div></td></tr></table></div>
<h3 id="avaliable-models">Avaliable models</h3>
<div class="highlight"><pre><span></span><code>models = ['curtis', 'parabolic', 'stoffels', 'henriksen','prodan_i', 'prodan_ii', 'ann']
</code></pre></div>
<p><em>Where</em>:
$$
{Ht=tree \,height}
\,\,\,|\,\,\,
{x= diameter}
$$</p>
<h4 id="curtis">Curtis</h4>
<div class="arithmatex">\[
\operatorname{Ht} =e^{(\beta_0+β1*\frac{1}{x})}
\]</div>
<h4 id="parabolic">Parabolic</h4>
<div class="arithmatex">\[
\operatorname{Ht} = \beta_0 + \beta_1 * x + \beta_2 * x^2
\]</div>
<h4 id="stoffels">Stoffels</h4>
<div class="arithmatex">\[
\operatorname{Ht} = e^{(\beta_0+\beta_1*\ln(x))}
\]</div>
<h4 id="henriksen">Henriksen</h4>
<div class="arithmatex">\[
\operatorname{Ht} = \beta_0 + \beta_1 * \ln(x)
\]</div>
<h4 id="prodan-i">Prodan I</h4>
<div class="arithmatex">\[
\operatorname{Ht} = (\frac{x^2}{\beta_0+\beta_1*x+\beta_2* x^2})
\]</div>
<h4 id="prodan-ii">Prodan II</h4>
<div class="arithmatex">\[
\operatorname{Ht} =(\frac{x^2}{\beta_0+\beta_1*x+\beta_2* x^2})+1.3
\]</div>
<h4 id="artificial-neural-network">Artificial Neural Network</h4>
<p>When selecting the 'ann' model, 4 different structures of artificial neural networks will be tested. Only the result from 1 model will be returned. The model returned will be selected by the ranking function.
<div class="mermaid">---
title: ANN parameters
---
classDiagram
class MLPRegressor {
Epochs: 3000
Activation: logistic
Solver Mode: lbfgs
Batch size: dynamic
Larning rate init: 0.1
Learning rate mode: adaptive
}
class Model-0 {
Hidden layer sizes: (4,5)
}
class Model_1 {
Hidden layer sizes: (4,2)
}
class Model_2 {
Hidden layer sizes: (3,2)
}
class Model_3 {
Hidden layer sizes: (4,4)
}
MLPRegressor <|-- Model-0
MLPRegressor <|-- Model_1
MLPRegressor <|-- Model_2
MLPRegressor <|-- Model_3</div></p>
<h4 id="ranking-function">Ranking function</h4>
<p>For the 'ann' model, the module <a href="https://scikit-learn.org/stable/modules/generated/sklearn.neural_network.MLPRegressor.html">sklearn.neural_network.MLPRegressor</a> is used.</p>
<p>To select the best-performing models and rank them accordingly, the following metrics are obtained:</p>
<table>
<thead>
<tr>
<th style="text-align: center;">Métric name</th>
<th style="text-align: center;">Structure</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align: center;"><strong>Mean Absolute Error (MAE)</strong></td>
<td style="text-align: center;"><span class="arithmatex">\( MAE = \frac{1}{n} \sum_{i=1}^{n} \|y_i - \hat{y}_i\| \)</span></td>
</tr>
<tr>
<td style="text-align: center;"><strong>Mean Absolute Percentage Error (MAPE)</strong></td>
<td style="text-align: center;"><span class="arithmatex">\( MAPE = \frac{100}{n} \sum_{i=1}^{n} \left\|\frac{y_i - \hat{y}_i}{y_i}\right\| \)</span></td>
</tr>
<tr>
<td style="text-align: center;"><strong>Mean Squared Error (MSE)</strong></td>
<td style="text-align: center;"><span class="arithmatex">\( MSE = \frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2 \)</span></td>
</tr>
<tr>
<td style="text-align: center;"><strong>Root Mean Squared Error (RMSE)</strong></td>
<td style="text-align: center;"><span class="arithmatex">\( RMSE = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2} \)</span></td>
</tr>
<tr>
<td style="text-align: center;"><strong>R Squared (Coefficient of Determination)</strong></td>
<td style="text-align: center;"><span class="arithmatex">\( R^2 = 1 - \frac{\sum_{i=1}^{n} (y_i - \hat{y}_i)^2}{\sum_{i=1}^{n} (y_i - \bar{y})^2} \)</span></td>
</tr>
<tr>
<td style="text-align: center;"><strong>Explained Variance (EV)</strong></td>
<td style="text-align: center;"><span class="arithmatex">\( EV = 1 - \frac{Var(y - \hat{y})}{Var(y)} \)</span></td>
</tr>
<tr>
<td style="text-align: center;"><strong>Mean Error</strong></td>
<td style="text-align: center;"><span class="arithmatex">\( Mean\ Error = \frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i) \)</span></td>
</tr>
</tbody>
</table>
<p>After obtaining the metric for each tested model, the values are normalized from 0 to 10. The worst model receives a score of 0, and the best model receives a score of 10.</p>
</article>
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