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Introduction.html
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Introduction.html
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<h1 class="title toc-ignore">Introduction to the evclass package</h1>
<h4 class="author"><em>Thierry Denoeux</em></h4>
<h4 class="date"><em>2017-03-19</em></h4>
<p>The package <code>evclass</code> contains methods for <em>evidential classification</em>. An evidential classifier quantifies the uncertainty about the class of a pattern by a Dempster-Shafer mass function. In evidential <em>distance-based</em> classifiers, the mass functions are computed from distances between the test pattern and either training pattern, or prototypes. The user is invited to read the papers cited in this vignette to get familiar with the main concepts underlying evidential clustering. These papers can be downloaded from the author’s web site, at <a href="https://www.hds.utc.fr/~tdenoeux" class="uri">https://www.hds.utc.fr/~tdenoeux</a>. Here, we provide a short guided tour of the main functions in the <code>evclass</code> package. The two classification methods implemented to date are:</p>
<ul>
<li>The evidential K-nearest neighbor classifier <span class="citation">(Denœux 1995, <span class="citation">Zouhal and Denœux (1998)</span>)</span>;</li>
<li>The evidential neural network classifier <span class="citation">(Denœux 2000)</span>.</li>
</ul>
<p>You first need to install this package:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">library</span>(evclass)</code></pre></div>
<p>The following sections contain a brief introduction on the way to use the main functions in the package <code>evclass</code> for evidential classification.</p>
<div id="evidential-k-nearest-neighbor-classifier" class="section level2">
<h2>Evidential K-nearest neighbor classifier</h2>
<p>The principle of the evidential K-nearest neighbor (EK-NN) classifier is explained in <span class="citation">(Denœux 1995)</span>, and the optimization of the parameters of this model is presented in <span class="citation">(Zouhal and Denœux 1998)</span>. The reader is referred to these references. Here, we focus on the practical application of this method using the functions implemented in <code>evclass</code>.</p>
<p>Consider, for instance, the <code>ionosphere</code> data. This dataset consists in 351 instances grouped in two classes and described by 34 numeric attributes. The first 175 instances are training data, the rest are test data. Let us first load the data, and split them into a training set and a test set.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">data</span>(ionosphere)
xtr<-ionosphere$x[<span class="dv">1</span>:<span class="dv">176</span>,]
ytr<-ionosphere$y[<span class="dv">1</span>:<span class="dv">176</span>]
xtst<-ionosphere$x[<span class="dv">177</span>:<span class="dv">351</span>,]
ytst<-ionosphere$y[<span class="dv">177</span>:<span class="dv">351</span>]</code></pre></div>
<p>The EK-NN classifier is implemented as three functions: <code>EkNNinit</code> for initialization, <code>EkNNfit</code> for training, and <code>EkNNval</code> for testing. Let us initialize the classifier and train it on the <code>ionosphere</code> data, with <span class="math inline">\(K=5\)</span> neighbors. (If the argument <code>param</code> is not passed to <code>EkNNfit</code>, the function <code>EkNNinit</code> is called inside <code>EkNNfit</code>; here, we make the call explicit for clarity).</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">param0<-<span class="st"> </span><span class="kw">EkNNinit</span>(xtr,ytr)
options=<span class="kw">list</span>(<span class="dt">maxiter=</span><span class="dv">300</span>,<span class="dt">eta=</span><span class="fl">0.1</span>,<span class="dt">gain_min=</span><span class="fl">1e-5</span>,<span class="dt">disp=</span><span class="ot">FALSE</span>)
fit<-<span class="kw">EkNNfit</span>(xtr,ytr,<span class="dt">param=</span>param0,<span class="dt">K=</span><span class="dv">5</span>,<span class="dt">options=</span>options)</code></pre></div>
<p>The list <code>fit</code> contains the optimized parameters, the final value of the cost function, the leave-one-out (LOO) error rate, the LOO predicted class labels and the LOO predicted mass functions. Here the LOO error rate and confusion matrix are:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">print</span>(fit$err)</code></pre></div>
<pre><code>## [1] 0.1079545</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">table</span>(fit$ypred,ytr)</code></pre></div>
<pre><code>## ytr
## 1 2
## 1 108 14
## 2 5 49</code></pre>
<p>We can then evaluate the classifier on the test data:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">val<-<span class="kw">EkNNval</span>(<span class="dt">xtrain=</span>xtr,<span class="dt">ytrain=</span>ytr,<span class="dt">xtst=</span>xtst,<span class="dt">K=</span><span class="dv">5</span>,<span class="dt">ytst=</span>ytst,<span class="dt">param=</span>fit$param)
<span class="kw">print</span>(val$err)</code></pre></div>
<pre><code>## [1] 0.1142857</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">table</span>(val$ypred,ytst)</code></pre></div>
<pre><code>## ytst
## 1 2
## 1 107 15
## 2 5 48</code></pre>
<p>To determine the best value of <span class="math inline">\(K\)</span>, we may compute the LOO error for different candidate value. Here, we will all values between 1 and 15</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">err<-<span class="kw">rep</span>(<span class="dv">0</span>,<span class="dv">15</span>)
i<-<span class="dv">0</span>
for(K in <span class="dv">1</span>:<span class="dv">15</span>){
fit<-<span class="kw">EkNNfit</span>(xtr,ytr,K,<span class="dt">options=</span><span class="kw">list</span>(<span class="dt">maxiter=</span><span class="dv">100</span>,<span class="dt">eta=</span><span class="fl">0.1</span>,<span class="dt">gain_min=</span><span class="fl">1e-5</span>,<span class="dt">disp=</span><span class="ot">FALSE</span>))
err[K]<-fit$err
}
<span class="kw">plot</span>(<span class="dv">1</span>:<span class="dv">15</span>,err,<span class="dt">type=</span><span class="st">"b"</span>,<span class="dt">xlab=</span><span class="st">'K'</span>,<span class="dt">ylab=</span><span class="st">'LOO error rate'</span>)</code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></p>
<p>The minimum LOO error rate is obtained for <span class="math inline">\(K=8\)</span>. The test error rate and confusion matrix for that value of <span class="math inline">\(K\)</span> are obtained as follows:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">fit<-<span class="kw">EkNNfit</span>(xtr,ytr,<span class="dt">K=</span><span class="dv">8</span>,<span class="dt">options=</span><span class="kw">list</span>(<span class="dt">maxiter=</span><span class="dv">100</span>,<span class="dt">eta=</span><span class="fl">0.1</span>,<span class="dt">gain_min=</span><span class="fl">1e-5</span>,<span class="dt">disp=</span><span class="ot">FALSE</span>))
val<-<span class="kw">EkNNval</span>(<span class="dt">xtrain=</span>xtr,<span class="dt">ytrain=</span>ytr,<span class="dt">xtst=</span>xtst,<span class="dt">K=</span><span class="dv">8</span>,<span class="dt">ytst=</span>ytst,<span class="dt">param=</span>fit$param)
<span class="kw">print</span>(val$err)</code></pre></div>
<pre><code>## [1] 0.09142857</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">table</span>(val$ypred,ytst)</code></pre></div>
<pre><code>## ytst
## 1 2
## 1 106 10
## 2 6 53</code></pre>
</div>
<div id="evidential-neural-network-classifier" class="section level2">
<h2>Evidential neural network classifier</h2>
<p>In the evidential neural network classifier, the output mass functions are based on distances to protypes, which allows for faster classification. The prototypes and their class-membership degrees are leanrnt by minimizing a cost function. This function is defined as the sum of an error term and, optionally, a regularization term. As for the EK-NN classifier, the evidential neural network classifier is implemented as three functions: <code>proDSinit</code> for initialization, <code>proDSfit</code> for training and <code>proDSval</code> for evaluation.</p>
<p>Let us demonstrate this method on the <code>glass</code> dataset. This data set contains 185 instances, which can be split into 89 training instances and 96 test instances.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">data</span>(glass)
xtr<-glass$x[<span class="dv">1</span>:<span class="dv">89</span>,]
ytr<-glass$y[<span class="dv">1</span>:<span class="dv">89</span>]
xtst<-glass$x[<span class="dv">90</span>:<span class="dv">185</span>,]
ytst<-glass$y[<span class="dv">90</span>:<span class="dv">185</span>]</code></pre></div>
<p>We then initialize a network with 7 prototypes:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">param0<-<span class="kw">proDSinit</span>(xtr,ytr,<span class="dt">nproto=</span><span class="dv">7</span>,<span class="dt">nprotoPerClass=</span><span class="ot">FALSE</span>,<span class="dt">crisp=</span><span class="ot">FALSE</span>)</code></pre></div>
<p>and train this network without regularization:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">options<-<span class="kw">list</span>(<span class="dt">maxiter=</span><span class="dv">500</span>,<span class="dt">eta=</span><span class="fl">0.1</span>,<span class="dt">gain_min=</span><span class="fl">1e-5</span>,<span class="dt">disp=</span><span class="dv">20</span>)
fit<-<span class="kw">proDSfit</span>(<span class="dt">x=</span>xtr,<span class="dt">y=</span>ytr,<span class="dt">param=</span>param0,<span class="dt">options=</span>options)</code></pre></div>
<pre><code>## [1] 1.0000000 0.3582862 10.0000000
## [1] 21.0000000 0.2933959 1.2426062
## [1] 41.0000000 0.2631432 0.1972797
## [1] 61.00000000 0.20079817 0.04424406
## [1] 81.00000000 0.19174016 0.01050067
## [1] 1.010000e+02 1.888532e-01 2.519525e-03
## [1] 1.210000e+02 1.885120e-01 6.370615e-04
## [1] 1.410000e+02 1.883220e-01 1.752994e-04</code></pre>
<p>Finally, we evaluate the performance of the network on the test set:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">val<-<span class="kw">proDSval</span>(xtst,fit$param,ytst)
<span class="kw">print</span>(val$err)</code></pre></div>
<pre><code>## [1] 0.3020833</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">table</span>(ytst,val$ypred)</code></pre></div>
<pre><code>##
## ytst 1 2 4
## 1 31 9 0
## 2 5 28 4
## 3 5 3 0
## 4 0 3 8</code></pre>
<p>If the training is done with regularization, the hyperparameter <code>mu</code> needs to be determined by cross-validation.</p>
</div>
<div id="decision" class="section level2">
<h2>Decision</h2>
<p>In the belief function framework, there are several definitions of expectation. Each of these definitions results in a different decision rule that can be used for classification. The reader is referred to <span class="citation">(Denœux 1997)</span> for a detailed description of theses rules and there application to classification. Here, we will illustrate the use of the function <code>decision</code> for generating decisions.</p>
<p>We consider the Iris dataset from the package <code>datasets</code>. To plot the decisions regions, we will only use two input attributes: ‘Petal.Length’ and ‘Petal.Width’. This code plots of the data and trains the evidential neural network classifiers with six prototypes:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">data</span>(<span class="st">"iris"</span>)
x<-<span class="st"> </span>iris[,<span class="dv">3</span>:<span class="dv">4</span>]
y<-<span class="kw">as.numeric</span>(iris[,<span class="dv">5</span>])
c<-<span class="kw">max</span>(y)
<span class="kw">plot</span>(x[,<span class="dv">1</span>],x[,<span class="dv">2</span>],<span class="dt">pch=</span>y,<span class="dt">xlab=</span><span class="st">"Petal Length"</span>,<span class="dt">ylab=</span><span class="st">"Petal Width"</span>)</code></pre></div>
<p><img 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" /><!-- --></p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">param0<-<span class="kw">proDSinit</span>(x,y,<span class="dv">6</span>)
fit<-<span class="kw">proDSfit</span>(x,y,param0)</code></pre></div>
<pre><code>## [1] 1.0000000 0.3100244 10.0000000
## [1] 11.0000000 0.1793266 3.5712815
## [1] 21.00000000 0.07456371 1.31427661
## [1] 31.0000000 0.0416460 0.4797702
## [1] 41.00000000 0.03069473 0.19345069
## [1] 51.00000000 0.03034766 0.07089198
## [1] 61.00000000 0.02361211 0.02867826
## [1] 71.00000000 0.02245256 0.01320300
## [1] 81.000000000 0.021613541 0.005711898
## [1] 91.000000000 0.021163977 0.002272939</code></pre>
<p>Let us assume that we have the following loss matrix:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">L=<span class="kw">cbind</span>(<span class="dv">1</span>-<span class="kw">diag</span>(c),<span class="kw">rep</span>(<span class="fl">0.3</span>,c))
<span class="kw">print</span>(L)</code></pre></div>
<pre><code>## [,1] [,2] [,3] [,4]
## [1,] 0 1 1 0.3
## [2,] 1 0 1 0.3
## [3,] 1 1 0 0.3</code></pre>
<p>This matrix has four columns, one for each possible act (decision). The first three decisions correspond to the assignment to each the three classes. The losses are 0 for a correct classification, and 1 for a misclassification. The fourth decision is rejection. For this act, the loss is 0.3, whatever the true class. The following code draws the decision regions for this loss matrix, and three decision rules: the minimization of the lower, upper and pignistic expectations (see <span class="citation">(Denœux 1997)</span> for details about these rules).</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">xx<-<span class="kw">seq</span>(-<span class="dv">1</span>,<span class="dv">9</span>,<span class="fl">0.01</span>)
yy<-<span class="kw">seq</span>(-<span class="dv">2</span>,<span class="fl">4.5</span>,<span class="fl">0.01</span>)
nx<-<span class="kw">length</span>(xx)
ny<-<span class="kw">length</span>(yy)
Dlower<-<span class="kw">matrix</span>(<span class="dv">0</span>,<span class="dt">nrow=</span>nx,<span class="dt">ncol=</span>ny)
Dupper<-Dlower
Dpig<-Dlower
for(i in <span class="dv">1</span>:nx){
X<-<span class="kw">matrix</span>(<span class="kw">c</span>(<span class="kw">rep</span>(xx[i],ny),yy),ny,<span class="dv">2</span>)
val<-<span class="kw">proDSval</span>(X,fit$param)
Dupper[i,]<-<span class="kw">decision</span>(val$m,<span class="dt">L=</span>L,<span class="dt">rule=</span><span class="st">'upper'</span>)
Dlower[i,]<-<span class="kw">decision</span>(val$m,<span class="dt">L=</span>L,<span class="dt">rule=</span><span class="st">'lower'</span>)
Dpig[i,]<-<span class="kw">decision</span>(val$m,<span class="dt">L=</span>L,<span class="dt">rule=</span><span class="st">'pignistic'</span>)
}
<span class="kw">contour</span>(xx,yy,Dlower,<span class="dt">xlab=</span><span class="st">"Petal.Length"</span>,<span class="dt">ylab=</span><span class="st">"Petal.Width"</span>,<span class="dt">drawlabels=</span><span class="ot">FALSE</span>)
for(k in <span class="dv">1</span>:c) <span class="kw">points</span>(x[y==k,<span class="dv">1</span>],x[y==k,<span class="dv">2</span>],<span class="dt">pch=</span>k)
<span class="kw">contour</span>(xx,yy,Dupper,<span class="dt">xlab=</span><span class="st">"Petal.Length"</span>,<span class="dt">ylab=</span><span class="st">"Petal.Width"</span>,<span class="dt">drawlabels=</span><span class="ot">FALSE</span>,<span class="dt">add=</span><span class="ot">TRUE</span>,<span class="dt">lty=</span><span class="dv">2</span>)
<span class="kw">contour</span>(xx,yy,Dpig,<span class="dt">xlab=</span><span class="st">"Petal.Length"</span>,<span class="dt">ylab=</span><span class="st">"Petal.Width"</span>,<span class="dt">drawlabels=</span><span class="ot">FALSE</span>,<span class="dt">add=</span><span class="ot">TRUE</span>,<span class="dt">lty=</span><span class="dv">3</span>)</code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></p>
<p>As suggested in <span class="citation">(Denœux 1997)</span>, we can also consider the case where there is an unknown class, not represented in the learning set. We can then construct a loss matrix with four rows (the last row corresponds to the unknown class) and five columns (the last column corresponds to the assignment to the unknown class). Assume that the losses are defined as follows:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">L<-<span class="kw">cbind</span>(<span class="dv">1</span>-<span class="kw">diag</span>(c),<span class="kw">rep</span>(<span class="fl">0.2</span>,c),<span class="kw">rep</span>(<span class="fl">0.22</span>,c))
L<-<span class="kw">rbind</span>(L,<span class="kw">c</span>(<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="fl">0.2</span>,<span class="dv">0</span>))
<span class="kw">print</span>(L)</code></pre></div>
<pre><code>## [,1] [,2] [,3] [,4] [,5]
## [1,] 0 1 1 0.2 0.22
## [2,] 1 0 1 0.2 0.22
## [3,] 1 1 0 0.2 0.22
## [4,] 1 1 1 0.2 0.00</code></pre>
<p>We can now plot the decision regions for the pignistic decision rule:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">for(i in <span class="dv">1</span>:nx){
X<-<span class="kw">matrix</span>(<span class="kw">c</span>(<span class="kw">rep</span>(xx[i],ny),yy),ny,<span class="dv">2</span>)
val<-<span class="kw">proDSval</span>(X,fit$param,<span class="kw">rep</span>(<span class="dv">0</span>,ny))
Dlower[i,]<-<span class="kw">decision</span>(val$m,<span class="dt">L=</span>L,<span class="dt">rule=</span><span class="st">'lower'</span>)
Dpig[i,]<-<span class="kw">decision</span>(val$m,<span class="dt">L=</span>L,<span class="dt">rule=</span><span class="st">'pignistic'</span>)
}
<span class="kw">contour</span>(xx,yy,Dpig,<span class="dt">xlab=</span><span class="st">"Petal.Length"</span>,<span class="dt">ylab=</span><span class="st">"Petal.Width"</span>,<span class="dt">drawlabels=</span><span class="ot">FALSE</span>)
for(k in <span class="dv">1</span>:c) <span class="kw">points</span>(x[y==k,<span class="dv">1</span>],x[y==k,<span class="dv">2</span>],<span class="dt">pch=</span>k)</code></pre></div>
<p><img 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" /><!-- --></p>
<p>The outer region corresponds to the assignment to the unknown class: this hypothesis becomes more plausible when the test vector is far from all the prototypes representing the training data.</p>
</div>
<div id="references" class="section level2 unnumbered">
<h2>References</h2>
<div id="refs" class="references">
<div id="ref-denoeux95a">
<p>Denœux, T. 1995. “A <span class="math inline">\(k\)</span>-Nearest Neighbor Classification Rule Based on Dempster-Shafer Theory.” <em>IEEE Trans. on Systems, Man and Cybernetics</em> 25 (05): 804–13.</p>
</div>
<div id="ref-denoeux96b">
<p>———. 1997. “Analysis of Evidence-Theoretic Decision Rules for Pattern Classification.” <em>Pattern Recognition</em> 30 (7): 1095–1107.</p>
</div>
<div id="ref-denoeux00a">
<p>———. 2000. “A Neural Network Classifier Based on Dempster-Shafer Theory.” <em>IEEE Trans. on Systems, Man and Cybernetics A</em> 30 (2): 131–50.</p>
</div>
<div id="ref-zouhal97b">
<p>Zouhal, L. M., and T. Denœux. 1998. “An Evidence-Theoretic <span class="math inline">\(k\)</span>-NN Rule with Parameter Optimization.” <em>IEEE Trans. on Systems, Man and Cybernetics C</em> 28 (2): 263–71.</p>
</div>
</div>
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