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<title>Chapter 18 Case Study - Wisconsin Breast Cancer | Machine Learning with R</title>
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<meta name="author" content="François de Ryckel">
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<li class="chapter" data-level="1" data-path="index.html"><a href="index.html"><i class="fa fa-check"></i><b>1</b> Prerequisites</a><ul>
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<li class="chapter" data-level="5" data-path="softmax-and-multinomial-regressions.html"><a href="softmax-and-multinomial-regressions.html"><i class="fa fa-check"></i><b>5</b> Softmax and multinomial regressions</a><ul>
<li class="chapter" data-level="5.1" data-path="softmax-and-multinomial-regressions.html"><a href="softmax-and-multinomial-regressions.html#multinomial-logistic-regression"><i class="fa fa-check"></i><b>5.1</b> Multinomial Logistic Regression</a></li>
<li class="chapter" data-level="5.2" data-path="softmax-and-multinomial-regressions.html"><a href="softmax-and-multinomial-regressions.html#references-2"><i class="fa fa-check"></i><b>5.2</b> References</a></li>
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<li class="chapter" data-level="7" data-path="knnchapter.html"><a href="knnchapter.html"><i class="fa fa-check"></i><b>7</b> KNN - K Nearest Neighbour</a><ul>
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<li class="chapter" data-level="8" data-path="kmeans.html"><a href="kmeans.html"><i class="fa fa-check"></i><b>8</b> Kmeans clustering</a><ul>
<li class="chapter" data-level="8.1" data-path="kmeans.html"><a href="kmeans.html#multinomial-logistic-regression-1"><i class="fa fa-check"></i><b>8.1</b> Multinomial Logistic Regression</a></li>
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<li class="chapter" data-level="9" data-path="hierclust.html"><a href="hierclust.html"><i class="fa fa-check"></i><b>9</b> Hierarichal Clustering</a><ul>
<li class="chapter" data-level="9.1" data-path="hierclust.html"><a href="hierclust.html#example-on-the-pokemon-dataset"><i class="fa fa-check"></i><b>9.1</b> Example on the Pokemon dataset</a></li>
<li class="chapter" data-level="9.2" data-path="hierclust.html"><a href="hierclust.html#example-on-regressions-1"><i class="fa fa-check"></i><b>9.2</b> Example on regressions</a></li>
<li class="chapter" data-level="9.3" data-path="hierclust.html"><a href="hierclust.html#references-5"><i class="fa fa-check"></i><b>9.3</b> References</a></li>
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<li class="chapter" data-level="10" data-path="pca.html"><a href="pca.html"><i class="fa fa-check"></i><b>10</b> Principal Component Analysis</a><ul>
<li class="chapter" data-level="10.1" data-path="pca.html"><a href="pca.html#pca-on-an-easy-example."><i class="fa fa-check"></i><b>10.1</b> PCA on an easy example.</a></li>
<li class="chapter" data-level="10.2" data-path="pca.html"><a href="pca.html#references."><i class="fa fa-check"></i><b>10.2</b> References.</a></li>
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<li class="chapter" data-level="11" data-path="trees-and-classification.html"><a href="trees-and-classification.html"><i class="fa fa-check"></i><b>11</b> Trees and Classification</a><ul>
<li class="chapter" data-level="11.1" data-path="trees-and-classification.html"><a href="trees-and-classification.html#introduction-1"><i class="fa fa-check"></i><b>11.1</b> Introduction</a></li>
<li class="chapter" data-level="11.2" data-path="trees-and-classification.html"><a href="trees-and-classification.html#first-example."><i class="fa fa-check"></i><b>11.2</b> First example.</a></li>
<li class="chapter" data-level="11.3" data-path="trees-and-classification.html"><a href="trees-and-classification.html#second-example."><i class="fa fa-check"></i><b>11.3</b> Second Example.</a></li>
<li class="chapter" data-level="11.4" data-path="trees-and-classification.html"><a href="trees-and-classification.html#how-does-a-tree-decide-where-to-split"><i class="fa fa-check"></i><b>11.4</b> How does a tree decide where to split?</a></li>
<li class="chapter" data-level="11.5" data-path="trees-and-classification.html"><a href="trees-and-classification.html#third-example."><i class="fa fa-check"></i><b>11.5</b> Third example.</a></li>
<li class="chapter" data-level="11.6" data-path="trees-and-classification.html"><a href="trees-and-classification.html#references-6"><i class="fa fa-check"></i><b>11.6</b> References</a></li>
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<li class="chapter" data-level="12" data-path="random-forest.html"><a href="random-forest.html"><i class="fa fa-check"></i><b>12</b> Random Forest</a><ul>
<li class="chapter" data-level="12.1" data-path="random-forest.html"><a href="random-forest.html#how-does-it-work"><i class="fa fa-check"></i><b>12.1</b> How does it work?</a></li>
<li class="chapter" data-level="12.2" data-path="random-forest.html"><a href="random-forest.html#references-7"><i class="fa fa-check"></i><b>12.2</b> References</a></li>
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<li class="chapter" data-level="13" data-path="svm.html"><a href="svm.html"><i class="fa fa-check"></i><b>13</b> Support Vector Machine</a><ul>
<li class="chapter" data-level="13.1" data-path="svm.html"><a href="svm.html#support-vecotr-regression"><i class="fa fa-check"></i><b>13.1</b> Support Vecotr Regression</a><ul>
<li class="chapter" data-level="13.1.1" data-path="svm.html"><a href="svm.html#create-data"><i class="fa fa-check"></i><b>13.1.1</b> Create data</a></li>
<li class="chapter" data-level="13.1.2" data-path="svm.html"><a href="svm.html#tuning-a-svm-model"><i class="fa fa-check"></i><b>13.1.2</b> Tuning a SVM model</a></li>
<li class="chapter" data-level="13.1.3" data-path="svm.html"><a href="svm.html#discussion-on-parameters"><i class="fa fa-check"></i><b>13.1.3</b> Discussion on parameters</a></li>
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<li class="chapter" data-level="13.2" data-path="svm.html"><a href="svm.html#references-8"><i class="fa fa-check"></i><b>13.2</b> References</a></li>
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<li class="chapter" data-level="14" data-path="model-evaluation.html"><a href="model-evaluation.html"><i class="fa fa-check"></i><b>14</b> Model Evaluation</a><ul>
<li class="chapter" data-level="14.1" data-path="model-evaluation.html"><a href="model-evaluation.html#biais-variance-tradeoff"><i class="fa fa-check"></i><b>14.1</b> Biais variance tradeoff</a></li>
<li class="chapter" data-level="14.2" data-path="model-evaluation.html"><a href="model-evaluation.html#bagging"><i class="fa fa-check"></i><b>14.2</b> Bagging</a></li>
<li class="chapter" data-level="14.3" data-path="model-evaluation.html"><a href="model-evaluation.html#crossvalidation"><i class="fa fa-check"></i><b>14.3</b> Cross Validation</a></li>
</ul></li>
<li class="chapter" data-level="15" data-path="case-study-text-classification-spam-and-ham-.html"><a href="case-study-text-classification-spam-and-ham-.html"><i class="fa fa-check"></i><b>15</b> Case Study - Text classification: Spam and Ham.</a></li>
<li class="chapter" data-level="16" data-path="mushroom.html"><a href="mushroom.html"><i class="fa fa-check"></i><b>16</b> Case Study - Mushrooms Classification</a><ul>
<li class="chapter" data-level="16.1" data-path="mushroom.html"><a href="mushroom.html#import-the-data"><i class="fa fa-check"></i><b>16.1</b> Import the data</a></li>
<li class="chapter" data-level="16.2" data-path="mushroom.html"><a href="mushroom.html#tidy-the-data"><i class="fa fa-check"></i><b>16.2</b> Tidy the data</a></li>
<li class="chapter" data-level="16.3" data-path="mushroom.html"><a href="mushroom.html#understand-the-data-1"><i class="fa fa-check"></i><b>16.3</b> Understand the data</a><ul>
<li class="chapter" data-level="16.3.1" data-path="mushroom.html"><a href="mushroom.html#transform-the-data"><i class="fa fa-check"></i><b>16.3.1</b> Transform the data</a></li>
<li class="chapter" data-level="16.3.2" data-path="mushroom.html"><a href="mushroom.html#visualize-the-data"><i class="fa fa-check"></i><b>16.3.2</b> Visualize the data</a></li>
<li class="chapter" data-level="16.3.3" data-path="mushroom.html"><a href="mushroom.html#modeling"><i class="fa fa-check"></i><b>16.3.3</b> Modeling</a></li>
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<li class="chapter" data-level="16.4" data-path="mushroom.html"><a href="mushroom.html#communication"><i class="fa fa-check"></i><b>16.4</b> Communication</a></li>
</ul></li>
<li class="chapter" data-level="17" data-path="case-study-the-adults-dataset-.html"><a href="case-study-the-adults-dataset-.html"><i class="fa fa-check"></i><b>17</b> Case study - The adults dataset.</a><ul>
<li class="chapter" data-level="17.1" data-path="case-study-the-adults-dataset-.html"><a href="case-study-the-adults-dataset-.html#introduction-2"><i class="fa fa-check"></i><b>17.1</b> Introduction</a></li>
<li class="chapter" data-level="17.2" data-path="case-study-the-adults-dataset-.html"><a href="case-study-the-adults-dataset-.html#import-the-data-1"><i class="fa fa-check"></i><b>17.2</b> Import the data</a></li>
<li class="chapter" data-level="17.3" data-path="case-study-the-adults-dataset-.html"><a href="case-study-the-adults-dataset-.html#tidy-the-data-1"><i class="fa fa-check"></i><b>17.3</b> Tidy the data</a></li>
</ul></li>
<li class="chapter" data-level="18" data-path="breastcancer.html"><a href="breastcancer.html"><i class="fa fa-check"></i><b>18</b> Case Study - Wisconsin Breast Cancer</a><ul>
<li class="chapter" data-level="18.1" data-path="breastcancer.html"><a href="breastcancer.html#import-the-data-2"><i class="fa fa-check"></i><b>18.1</b> Import the data</a></li>
<li class="chapter" data-level="18.2" data-path="breastcancer.html"><a href="breastcancer.html#tidy-the-data-2"><i class="fa fa-check"></i><b>18.2</b> Tidy the data</a></li>
<li class="chapter" data-level="18.3" data-path="breastcancer.html"><a href="breastcancer.html#understand-the-data-2"><i class="fa fa-check"></i><b>18.3</b> Understand the data</a><ul>
<li class="chapter" data-level="18.3.1" data-path="breastcancer.html"><a href="breastcancer.html#transform-the-data-1"><i class="fa fa-check"></i><b>18.3.1</b> Transform the data</a></li>
<li class="chapter" data-level="18.3.2" data-path="breastcancer.html"><a href="breastcancer.html#pre-process-the-data"><i class="fa fa-check"></i><b>18.3.2</b> Pre-process the data</a></li>
<li class="chapter" data-level="18.3.3" data-path="breastcancer.html"><a href="breastcancer.html#model-the-data-1"><i class="fa fa-check"></i><b>18.3.3</b> Model the data</a></li>
</ul></li>
<li class="chapter" data-level="18.4" data-path="breastcancer.html"><a href="breastcancer.html#references-9"><i class="fa fa-check"></i><b>18.4</b> References</a></li>
</ul></li>
<li class="chapter" data-level="19" data-path="final-words.html"><a href="final-words.html"><i class="fa fa-check"></i><b>19</b> Final Words</a></li>
<li class="chapter" data-level="" data-path="references-10.html"><a href="references-10.html"><i class="fa fa-check"></i>References</a></li>
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<div id="breastcancer" class="section level1">
<h1><span class="header-section-number">Chapter 18</span> Case Study - Wisconsin Breast Cancer</h1>
<p>This is another classification example. We have to classify breast tumors as malign or benign.</p>
<p>The dataset is available on the <a href="https://archive.ics.uci.edu/ml/datasets/Breast+Cancer+Wisconsin+(Diagnostic)">UCI Machine learning website</a> as well as on [Kaggle](<a href="https://www.kaggle.com/uciml/breast-cancer-wisconsin-data" class="uri">https://www.kaggle.com/uciml/breast-cancer-wisconsin-data</a>.</p>
<p>We have taken ideas from several blogs listed below in the reference section.</p>
<div id="import-the-data-2" class="section level2">
<h2><span class="header-section-number">18.1</span> Import the data</h2>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">df <-<span class="st"> </span><span class="kw">read_csv</span>(<span class="st">"dataset/BreastCancer.csv"</span>)
<span class="co"># This is defintely an most important step: </span>
<span class="co"># Check for appropriate class on each of the variable. </span>
<span class="kw">glimpse</span>(df)</code></pre></div>
<pre><code>## Observations: 569
## Variables: 32
## $ id <dbl> 842302, 842517, 84300903, 84348301, 8435…
## $ diagnosis <chr> "M", "M", "M", "M", "M", "M", "M", "M", …
## $ radius_mean <dbl> 17.990, 20.570, 19.690, 11.420, 20.290, …
## $ texture_mean <dbl> 10.38, 17.77, 21.25, 20.38, 14.34, 15.70…
## $ perimeter_mean <dbl> 122.80, 132.90, 130.00, 77.58, 135.10, 8…
## $ area_mean <dbl> 1001.0, 1326.0, 1203.0, 386.1, 1297.0, 4…
## $ smoothness_mean <dbl> 0.11840, 0.08474, 0.10960, 0.14250, 0.10…
## $ compactness_mean <dbl> 0.27760, 0.07864, 0.15990, 0.28390, 0.13…
## $ concavity_mean <dbl> 0.30010, 0.08690, 0.19740, 0.24140, 0.19…
## $ concave_points_mean <dbl> 0.14710, 0.07017, 0.12790, 0.10520, 0.10…
## $ symmetry_mean <dbl> 0.2419, 0.1812, 0.2069, 0.2597, 0.1809, …
## $ fractal_dimension_mean <dbl> 0.07871, 0.05667, 0.05999, 0.09744, 0.05…
## $ radius_se <dbl> 1.0950, 0.5435, 0.7456, 0.4956, 0.7572, …
## $ texture_se <dbl> 0.9053, 0.7339, 0.7869, 1.1560, 0.7813, …
## $ perimeter_se <dbl> 8.589, 3.398, 4.585, 3.445, 5.438, 2.217…
## $ area_se <dbl> 153.40, 74.08, 94.03, 27.23, 94.44, 27.1…
## $ smoothness_se <dbl> 0.006399, 0.005225, 0.006150, 0.009110, …
## $ compactness_se <dbl> 0.049040, 0.013080, 0.040060, 0.074580, …
## $ concavity_se <dbl> 0.05373, 0.01860, 0.03832, 0.05661, 0.05…
## $ concave_points_se <dbl> 0.015870, 0.013400, 0.020580, 0.018670, …
## $ symmetry_se <dbl> 0.03003, 0.01389, 0.02250, 0.05963, 0.01…
## $ fractal_dimension_se <dbl> 0.006193, 0.003532, 0.004571, 0.009208, …
## $ radius_worst <dbl> 25.38, 24.99, 23.57, 14.91, 22.54, 15.47…
## $ texture_worst <dbl> 17.33, 23.41, 25.53, 26.50, 16.67, 23.75…
## $ perimeter_worst <dbl> 184.60, 158.80, 152.50, 98.87, 152.20, 1…
## $ area_worst <dbl> 2019.0, 1956.0, 1709.0, 567.7, 1575.0, 7…
## $ smoothness_worst <dbl> 0.1622, 0.1238, 0.1444, 0.2098, 0.1374, …
## $ compactness_worst <dbl> 0.6656, 0.1866, 0.4245, 0.8663, 0.2050, …
## $ concavity_worst <dbl> 0.71190, 0.24160, 0.45040, 0.68690, 0.40…
## $ concave_points_worst <dbl> 0.26540, 0.18600, 0.24300, 0.25750, 0.16…
## $ symmetry_worst <dbl> 0.4601, 0.2750, 0.3613, 0.6638, 0.2364, …
## $ fractal_dimension_worst <dbl> 0.11890, 0.08902, 0.08758, 0.17300, 0.07…</code></pre>
<p>So we have 569 observations with 32 variables. Ideally for so many variables, it would be appropriate to get a few more observations.</p>
</div>
<div id="tidy-the-data-2" class="section level2">
<h2><span class="header-section-number">18.2</span> Tidy the data</h2>
<p>Basics change of variable type for the outcome variable and renaming of variables badly encoded</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">df<span class="op">$</span>diagnosis <-<span class="st"> </span><span class="kw">as.factor</span>(df<span class="op">$</span>diagnosis)
<span class="co">#df <- df %>% rename(concave_points_mean = `concave points_mean`, </span>
<span class="co"># concave_points_se = `concave points_se`, </span>
<span class="co"># concave_points_worst = `concave points_worst`)</span></code></pre></div>
<p>As you might have noticed, in this case and the precedent we had very little to do here. This is not usually the case.</p>
</div>
<div id="understand-the-data-2" class="section level2">
<h2><span class="header-section-number">18.3</span> Understand the data</h2>
<p>This is the circular phase of our dealing with data. This is where each of the transforming, visualizing and modeling stage reinforce each other to create a better understanding.</p>
<p>Check for missing values</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">map_int</span>(df, <span class="cf">function</span>(.x) <span class="kw">sum</span>(<span class="kw">is.na</span>(.x)))</code></pre></div>
<pre><code>## id diagnosis radius_mean
## 0 0 0
## texture_mean perimeter_mean area_mean
## 0 0 0
## smoothness_mean compactness_mean concavity_mean
## 0 0 0
## concave_points_mean symmetry_mean fractal_dimension_mean
## 0 0 0
## radius_se texture_se perimeter_se
## 0 0 0
## area_se smoothness_se compactness_se
## 0 0 0
## concavity_se concave_points_se symmetry_se
## 0 0 0
## fractal_dimension_se radius_worst texture_worst
## 0 0 0
## perimeter_worst area_worst smoothness_worst
## 0 0 0
## compactness_worst concavity_worst concave_points_worst
## 0 0 0
## symmetry_worst fractal_dimension_worst
## 0 0</code></pre>
<p>Good news, there are no missing values.</p>
<p>In the case that there would be many missing values, we would go on the transforming data for some appropriate imputation.</p>
<p>Let’s check how balanced is our response variable</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">round</span>(<span class="kw">prop.table</span>(<span class="kw">table</span>(df<span class="op">$</span>diagnosis)), <span class="dv">2</span>)</code></pre></div>
<pre><code>##
## B M
## 0.63 0.37</code></pre>
<p>The response variable is slightly unbalanced.</p>
<p>Let’s look for correlation in the variables. Most ML algorithms assumed that the predictor variables are independent from each others.</p>
<p>Let’s check for correlations. For an anlysis to be robust it is good to remove mutlicollinearity (aka remove highly correlated predictors)<br />
</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">df_corr <-<span class="st"> </span><span class="kw">cor</span>(df <span class="op">%>%</span><span class="st"> </span><span class="kw">select</span>(<span class="op">-</span>id, <span class="op">-</span>diagnosis))
corrplot<span class="op">::</span><span class="kw">corrplot</span>(df_corr, <span class="dt">order =</span> <span class="st">"hclust"</span>, <span class="dt">tl.cex =</span> <span class="dv">1</span>, <span class="dt">addrect =</span> <span class="dv">8</span>)</code></pre></div>
<p><img src="machinelearningwithR_files/figure-html/correlation_plot-1.png" width="864" /></p>
<p>Indeed there are quite a few variables that are correlated. On the next step, we will remove the highly correlated ones using the <code>caret</code> package.</p>
<div id="transform-the-data-1" class="section level3">
<h3><span class="header-section-number">18.3.1</span> Transform the data</h3>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">library</span>(caret)
<span class="co"># The findcorrelation() function from caret package remove highly correlated predictors</span>
<span class="co"># based on whose correlation is above 0.9. This function uses a heuristic algorithm </span>
<span class="co"># to determine which variable should be removed instead of selecting blindly</span>
df2 <-<span class="st"> </span>df <span class="op">%>%</span><span class="st"> </span><span class="kw">select</span>(<span class="op">-</span><span class="kw">findCorrelation</span>(df_corr, <span class="dt">cutoff =</span> <span class="fl">0.9</span>))
<span class="co">#Number of columns for our new data frame</span>
<span class="kw">ncol</span>(df2)</code></pre></div>
<pre><code>## [1] 22</code></pre>
<p>So our new data frame <code>df2</code> is 10 variables shorter.</p>
</div>
<div id="pre-process-the-data" class="section level3">
<h3><span class="header-section-number">18.3.2</span> Pre-process the data</h3>
<div id="using-pca" class="section level4">
<h4><span class="header-section-number">18.3.2.1</span> Using PCA</h4>
<p>Let’s first go on an unsupervised analysis with a PCA analysis.<br />
To do so, we will remove the <code>id</code> and <code>diagnosis</code> variable, then we will also scale and ceter the variables.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">preproc_pca_df <-<span class="st"> </span><span class="kw">prcomp</span>(df <span class="op">%>%</span><span class="st"> </span><span class="kw">select</span>(<span class="op">-</span>id, <span class="op">-</span>diagnosis), <span class="dt">scale =</span> <span class="ot">TRUE</span>, <span class="dt">center =</span> <span class="ot">TRUE</span>)
<span class="kw">summary</span>(preproc_pca_df)</code></pre></div>
<pre><code>## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6
## Standard deviation 3.6444 2.3857 1.67867 1.40735 1.28403 1.09880
## Proportion of Variance 0.4427 0.1897 0.09393 0.06602 0.05496 0.04025
## Cumulative Proportion 0.4427 0.6324 0.72636 0.79239 0.84734 0.88759
## PC7 PC8 PC9 PC10 PC11 PC12
## Standard deviation 0.82172 0.69037 0.6457 0.59219 0.5421 0.51104
## Proportion of Variance 0.02251 0.01589 0.0139 0.01169 0.0098 0.00871
## Cumulative Proportion 0.91010 0.92598 0.9399 0.95157 0.9614 0.97007
## PC13 PC14 PC15 PC16 PC17 PC18
## Standard deviation 0.49128 0.39624 0.30681 0.28260 0.24372 0.22939
## Proportion of Variance 0.00805 0.00523 0.00314 0.00266 0.00198 0.00175
## Cumulative Proportion 0.97812 0.98335 0.98649 0.98915 0.99113 0.99288
## PC19 PC20 PC21 PC22 PC23 PC24
## Standard deviation 0.22244 0.17652 0.1731 0.16565 0.15602 0.1344
## Proportion of Variance 0.00165 0.00104 0.0010 0.00091 0.00081 0.0006
## Cumulative Proportion 0.99453 0.99557 0.9966 0.99749 0.99830 0.9989
## PC25 PC26 PC27 PC28 PC29 PC30
## Standard deviation 0.12442 0.09043 0.08307 0.03987 0.02736 0.01153
## Proportion of Variance 0.00052 0.00027 0.00023 0.00005 0.00002 0.00000
## Cumulative Proportion 0.99942 0.99969 0.99992 0.99997 1.00000 1.00000</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Calculate the proportion of variance explained</span>
pca_df_var <-<span class="st"> </span>preproc_pca_df<span class="op">$</span>sdev<span class="op">^</span><span class="dv">2</span>
pve_df <-<span class="st"> </span>pca_df_var <span class="op">/</span><span class="st"> </span><span class="kw">sum</span>(pca_df_var)
cum_pve <-<span class="st"> </span><span class="kw">cumsum</span>(pve_df)
pve_table <-<span class="st"> </span><span class="kw">tibble</span>(<span class="dt">comp =</span> <span class="kw">seq</span>(<span class="dv">1</span><span class="op">:</span><span class="kw">ncol</span>(df <span class="op">%>%</span><span class="st"> </span><span class="kw">select</span>(<span class="op">-</span>id, <span class="op">-</span>diagnosis))), pve_df, cum_pve)
<span class="kw">ggplot</span>(pve_table, <span class="kw">aes</span>(<span class="dt">x =</span> comp, <span class="dt">y =</span> cum_pve)) <span class="op">+</span><span class="st"> </span>
<span class="st"> </span><span class="kw">geom_point</span>() <span class="op">+</span><span class="st"> </span>
<span class="st"> </span><span class="kw">geom_abline</span>(<span class="dt">intercept =</span> <span class="fl">0.95</span>, <span class="dt">color =</span> <span class="st">"red"</span>, <span class="dt">slope =</span> <span class="dv">0</span>) <span class="op">+</span><span class="st"> </span>
<span class="st"> </span><span class="kw">labs</span>(<span class="dt">x =</span> <span class="st">"Number of components"</span>, <span class="dt">y =</span> <span class="st">"Cumulative Variance"</span>)</code></pre></div>
<p><img src="machinelearningwithR_files/figure-html/cumulative_variance-1.png" width="672" /></p>
<p>With the original dataset, 95% of the variance is explained with 10 PC’s.</p>
<p>Let’s check on the most influential variables for the first 2 components</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">pca_df <-<span class="st"> </span><span class="kw">as_tibble</span>(preproc_pca_df<span class="op">$</span>x)
<span class="kw">ggplot</span>(pca_df, <span class="kw">aes</span>(<span class="dt">x =</span> PC1, <span class="dt">y =</span> PC2, <span class="dt">col =</span> df<span class="op">$</span>diagnosis)) <span class="op">+</span><span class="st"> </span><span class="kw">geom_point</span>()</code></pre></div>
<p><img src="machinelearningwithR_files/figure-html/breastcancer06-1.png" width="672" /></p>
<p>It does look like the first 2 components managed to separate the diagnosis quite well. Lots of potential here.</p>
<p>If we want to get a more detailled analysis of what variables are the most influential in the first 2 components, we can use the <code>ggfortify</code> library.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">library</span>(ggfortify)
<span class="kw">autoplot</span>(preproc_pca_df, <span class="dt">data =</span> df, <span class="dt">colour =</span> <span class="st">'diagnosis'</span>,
<span class="dt">loadings =</span> <span class="ot">FALSE</span>, <span class="dt">loadings.label =</span> <span class="ot">TRUE</span>, <span class="dt">loadings.colour =</span> <span class="st">"blue"</span>)</code></pre></div>
<p><img src="machinelearningwithR_files/figure-html/pc1vspc2-1.png" width="672" /></p>
<p>Let’s visuzalize the first 3 components.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">df_pcs <-<span class="st"> </span><span class="kw">cbind</span>(<span class="kw">as_tibble</span>(df<span class="op">$</span>diagnosis), <span class="kw">as_tibble</span>(preproc_pca_df<span class="op">$</span>x))
GGally<span class="op">::</span><span class="kw">ggpairs</span>(df_pcs, <span class="dt">columns =</span> <span class="dv">2</span><span class="op">:</span><span class="dv">4</span>, ggplot2<span class="op">::</span><span class="kw">aes</span>(<span class="dt">color =</span> value))</code></pre></div>
<p><img src="machinelearningwithR_files/figure-html/pc123_in_pairs-1.png" width="672" /></p>
<p>Let’s do the same exercise with our second df, the one where we removed the highly correlated predictors.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">preproc_pca_df2 <-<span class="st"> </span><span class="kw">prcomp</span>(df2, <span class="dt">scale =</span> <span class="ot">TRUE</span>, <span class="dt">center =</span> <span class="ot">TRUE</span>)
<span class="kw">summary</span>(preproc_pca_df2)</code></pre></div>
<pre><code>## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6
## Standard deviation 3.2051 2.1175 1.46634 1.09037 0.95215 0.90087
## Proportion of Variance 0.4669 0.2038 0.09773 0.05404 0.04121 0.03689
## Cumulative Proportion 0.4669 0.6707 0.76847 0.82251 0.86372 0.90061
## PC7 PC8 PC9 PC10 PC11 PC12
## Standard deviation 0.77121 0.56374 0.5530 0.51130 0.45605 0.36602
## Proportion of Variance 0.02703 0.01445 0.0139 0.01188 0.00945 0.00609
## Cumulative Proportion 0.92764 0.94209 0.9560 0.96787 0.97732 0.98341
## PC13 PC14 PC15 PC16 PC17 PC18 PC19
## Standard deviation 0.31602 0.28856 0.2152 0.2098 0.16346 0.1558 0.1486
## Proportion of Variance 0.00454 0.00378 0.0021 0.0020 0.00121 0.0011 0.0010
## Cumulative Proportion 0.98795 0.99174 0.9938 0.9958 0.99706 0.9982 0.9992
## PC20 PC21 PC22
## Standard deviation 0.09768 0.08667 0.03692
## Proportion of Variance 0.00043 0.00034 0.00006
## Cumulative Proportion 0.99960 0.99994 1.00000</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">pca_df2_var <-<span class="st"> </span>preproc_pca_df2<span class="op">$</span>sdev<span class="op">^</span><span class="dv">2</span>
<span class="co"># proportion of variance explained</span>
pve_df2 <-<span class="st"> </span>pca_df2_var <span class="op">/</span><span class="st"> </span><span class="kw">sum</span>(pca_df2_var)
cum_pve_df2 <-<span class="st"> </span><span class="kw">cumsum</span>(pve_df2)
pve_table_df2 <-<span class="st"> </span><span class="kw">tibble</span>(<span class="dt">comp =</span> <span class="kw">seq</span>(<span class="dv">1</span><span class="op">:</span><span class="kw">ncol</span>(df2)), pve_df2, cum_pve_df2)
<span class="kw">ggplot</span>(pve_table_df2, <span class="kw">aes</span>(<span class="dt">x =</span> comp, <span class="dt">y =</span> cum_pve_df2)) <span class="op">+</span><span class="st"> </span>
<span class="st"> </span><span class="kw">geom_point</span>() <span class="op">+</span><span class="st"> </span>
<span class="st"> </span><span class="kw">geom_abline</span>(<span class="dt">intercept =</span> <span class="fl">0.95</span>, <span class="dt">color =</span> <span class="st">"red"</span>, <span class="dt">slope =</span> <span class="dv">0</span>) <span class="op">+</span><span class="st"> </span>
<span class="st"> </span><span class="kw">labs</span>(<span class="dt">x =</span> <span class="st">"Number of components"</span>, <span class="dt">y =</span> <span class="st">"Cumulative Variance"</span>)</code></pre></div>
<p><img src="machinelearningwithR_files/figure-html/cumulative_variance2-1.png" width="672" /></p>
<p>In this case, around 8 PC’s explained 95% of the variance.</p>
</div>
<div id="using-lda" class="section level4">
<h4><span class="header-section-number">18.3.2.2</span> Using LDA</h4>
<p>The advantage of using LDA is that it takes into consideration the different class.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">preproc_lda_df <-<span class="st"> </span>MASS<span class="op">::</span><span class="kw">lda</span>(diagnosis <span class="op">~</span>., <span class="dt">data =</span> df, <span class="dt">center =</span> <span class="ot">TRUE</span>, <span class="dt">scale =</span> <span class="ot">TRUE</span>)
preproc_lda_df</code></pre></div>
<pre><code>## Call:
## lda(diagnosis ~ ., data = df, center = TRUE, scale = TRUE)
##
## Prior probabilities of groups:
## B M
## 0.6274165 0.3725835
##
## Group means:
## id radius_mean texture_mean perimeter_mean area_mean
## B 26543825 12.14652 17.91476 78.07541 462.7902
## M 36818050 17.46283 21.60491 115.36538 978.3764
## smoothness_mean compactness_mean concavity_mean concave_points_mean
## B 0.09247765 0.08008462 0.04605762 0.02571741
## M 0.10289849 0.14518778 0.16077472 0.08799000
## symmetry_mean fractal_dimension_mean radius_se texture_se perimeter_se
## B 0.174186 0.06286739 0.2840824 1.220380 2.000321
## M 0.192909 0.06268009 0.6090825 1.210915 4.323929
## area_se smoothness_se compactness_se concavity_se concave_points_se
## B 21.13515 0.007195902 0.02143825 0.02599674 0.009857653
## M 72.67241 0.006780094 0.03228117 0.04182401 0.015060472
## symmetry_se fractal_dimension_se radius_worst texture_worst
## B 0.02058381 0.003636051 13.37980 23.51507
## M 0.02047240 0.004062406 21.13481 29.31821
## perimeter_worst area_worst smoothness_worst compactness_worst
## B 87.00594 558.8994 0.1249595 0.1826725
## M 141.37033 1422.2863 0.1448452 0.3748241
## concavity_worst concave_points_worst symmetry_worst
## B 0.1662377 0.07444434 0.2702459
## M 0.4506056 0.18223731 0.3234679
## fractal_dimension_worst
## B 0.07944207
## M 0.09152995
##
## Coefficients of linear discriminants:
## LD1
## id -2.512117e-10
## radius_mean -1.080876e+00
## texture_mean 2.338408e-02
## perimeter_mean 1.172707e-01
## area_mean 1.595690e-03
## smoothness_mean 5.251575e-01
## compactness_mean -2.094197e+01
## concavity_mean 6.955923e+00
## concave_points_mean 1.047567e+01
## symmetry_mean 4.938898e-01
## fractal_dimension_mean -5.937663e-02
## radius_se 2.101503e+00
## texture_se -3.979869e-02
## perimeter_se -1.121814e-01
## area_se -4.083504e-03
## smoothness_se 7.987663e+01
## compactness_se 1.387026e-01
## concavity_se -1.768261e+01
## concave_points_se 5.350520e+01
## symmetry_se 8.143611e+00
## fractal_dimension_se -3.431356e+01
## radius_worst 9.677207e-01
## texture_worst 3.540591e-02
## perimeter_worst -1.204507e-02
## area_worst -5.012127e-03
## smoothness_worst 2.612258e+00
## compactness_worst 3.636892e-01
## concavity_worst 1.880699e+00
## concave_points_worst 2.218189e+00
## symmetry_worst 2.783102e+00
## fractal_dimension_worst 2.117830e+01</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Making a df out of the LDA for visualization purpose.</span>
predict_lda_df <-<span class="st"> </span><span class="kw">predict</span>(preproc_lda_df, df)<span class="op">$</span>x <span class="op">%>%</span><span class="st"> </span>
<span class="st"> </span><span class="kw">as_data_frame</span>() <span class="op">%>%</span><span class="st"> </span>
<span class="st"> </span><span class="kw">cbind</span>(<span class="dt">diagnosis =</span> df<span class="op">$</span>diagnosis)</code></pre></div>
<pre><code>## Warning: `as_data_frame()` is deprecated, use `as_tibble()` (but mind the new semantics).
## This warning is displayed once per session.</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">glimpse</span>(predict_lda_df)</code></pre></div>
<pre><code>## Observations: 569
## Variables: 2
## $ LD1 <dbl> 3.3257395, 2.3298023, 3.7416859, 4.0209903, 2.2754286,…
## $ diagnosis <fct> M, M, M, M, M, M, M, M, M, M, M, M, M, M, M, M, M, M, …</code></pre>
</div>
</div>
<div id="model-the-data-1" class="section level3">
<h3><span class="header-section-number">18.3.3</span> Model the data</h3>
<p>Let’s first create a testing and training set using <code>caret</code></p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">set.seed</span>(<span class="dv">1815</span>)
df3 <-<span class="st"> </span><span class="kw">cbind</span>(<span class="dt">diagnosis =</span> df<span class="op">$</span>diagnosis, df2)
df_sampling_index <-<span class="st"> </span><span class="kw">createDataPartition</span>(df3<span class="op">$</span>diagnosis, <span class="dt">times =</span> <span class="dv">1</span>, <span class="dt">p =</span> <span class="fl">0.8</span>, <span class="dt">list =</span> <span class="ot">FALSE</span>)
df_training <-<span class="st"> </span>df3[df_sampling_index, ]
df_testing <-<span class="st"> </span>df3[<span class="op">-</span>df_sampling_index, ]
df_control <-<span class="st"> </span><span class="kw">trainControl</span>(<span class="dt">method=</span><span class="st">"cv"</span>,
<span class="dt">number =</span> <span class="dv">15</span>,
<span class="dt">classProbs =</span> <span class="ot">TRUE</span>,
<span class="dt">summaryFunction =</span> twoClassSummary)</code></pre></div>
<div id="logistic-regression" class="section level4">
<h4><span class="header-section-number">18.3.3.1</span> Logistic regression</h4>
<p>Our first model is doing logistic regression on <code>df2</code>, the data frame where we took away the highly correlated variables.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">model_logreg_df <-<span class="st"> </span><span class="kw">train</span>(diagnosis <span class="op">~</span>., <span class="dt">data =</span> df_training, <span class="dt">method =</span> <span class="st">"glm"</span>,
<span class="dt">metric =</span> <span class="st">"ROC"</span>, <span class="dt">preProcess =</span> <span class="kw">c</span>(<span class="st">"scale"</span>, <span class="st">"center"</span>),
<span class="dt">trControl =</span> df_control)
prediction_logreg_df <-<span class="st"> </span><span class="kw">predict</span>(model_logreg_df, df_testing)
cm_logreg_df <-<span class="st"> </span><span class="kw">confusionMatrix</span>(prediction_logreg_df, df_testing<span class="op">$</span>diagnosis, <span class="dt">positive =</span> <span class="st">"M"</span>)
cm_logreg_df</code></pre></div>
<pre><code>## Confusion Matrix and Statistics
##
## Reference
## Prediction B M
## B 71 2
## M 0 40
##
## Accuracy : 0.9823
## 95% CI : (0.9375, 0.9978)
## No Information Rate : 0.6283
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.9617
## Mcnemar's Test P-Value : 0.4795
##
## Sensitivity : 0.9524
## Specificity : 1.0000
## Pos Pred Value : 1.0000
## Neg Pred Value : 0.9726
## Prevalence : 0.3717
## Detection Rate : 0.3540
## Detection Prevalence : 0.3540
## Balanced Accuracy : 0.9762
##
## 'Positive' Class : M
## </code></pre>
</div>
<div id="random-forest-1" class="section level4">
<h4><span class="header-section-number">18.3.3.2</span> Random Forest</h4>
<p>Our second model uses random forest. Similarly, we using the <code>df2</code> data frame, the one where we took away the highly correlated variables.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">model_rf_df <-<span class="st"> </span><span class="kw">train</span>(diagnosis <span class="op">~</span>., <span class="dt">data =</span> df_training,
<span class="dt">method =</span> <span class="st">"rf"</span>,
<span class="dt">metric =</span> <span class="st">'ROC'</span>,
<span class="dt">trControl =</span> df_control)
prediction_rf_df <-<span class="st"> </span><span class="kw">predict</span>(model_rf_df, df_testing)
cm_rf_df <-<span class="st"> </span><span class="kw">confusionMatrix</span>(prediction_rf_df, df_testing<span class="op">$</span>diagnosis, <span class="dt">positive =</span> <span class="st">"M"</span>)
cm_rf_df</code></pre></div>
<pre><code>## Confusion Matrix and Statistics
##
## Reference
## Prediction B M
## B 71 3
## M 0 39
##
## Accuracy : 0.9735
## 95% CI : (0.9244, 0.9945)
## No Information Rate : 0.6283
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.9423
## Mcnemar's Test P-Value : 0.2482
##
## Sensitivity : 0.9286
## Specificity : 1.0000
## Pos Pred Value : 1.0000
## Neg Pred Value : 0.9595
## Prevalence : 0.3717
## Detection Rate : 0.3451
## Detection Prevalence : 0.3451
## Balanced Accuracy : 0.9643
##
## 'Positive' Class : M
## </code></pre>
<p>Let’s make some diagnostic plots.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot</span>(model_rf_df)</code></pre></div>
<p><img src="machinelearningwithR_files/figure-html/randomforest_model_plot-1.png" width="672" /></p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot</span>(model_rf_df<span class="op">$</span>finalModel)</code></pre></div>
<p><img src="machinelearningwithR_files/figure-html/randomforest_model_plot-2.png" width="672" /></p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">randomForest<span class="op">::</span><span class="kw">varImpPlot</span>(model_rf_df<span class="op">$</span>finalModel, <span class="dt">sort =</span> <span class="ot">TRUE</span>,
<span class="dt">n.var =</span> <span class="dv">10</span>, <span class="dt">main =</span> <span class="st">"The 10 variables with the most predictive power"</span>)</code></pre></div>
<p><img src="machinelearningwithR_files/figure-html/randomforest_model_plot-3.png" width="672" /></p>
</div>
<div id="knn" class="section level4">
<h4><span class="header-section-number">18.3.3.3</span> KNN</h4>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">model_knn_df <-<span class="st"> </span><span class="kw">train</span>(diagnosis <span class="op">~</span>., <span class="dt">data =</span> df_training,
<span class="dt">method =</span> <span class="st">"knn"</span>,
<span class="dt">metric =</span> <span class="st">"ROC"</span>,
<span class="dt">preProcess =</span> <span class="kw">c</span>(<span class="st">"scale"</span>, <span class="st">"center"</span>),
<span class="dt">trControl =</span> df_control,
<span class="dt">tuneLength =</span><span class="dv">31</span>)
<span class="kw">plot</span>(model_knn_df)</code></pre></div>
<p><img src="machinelearningwithR_files/figure-html/breastcancer11-1.png" width="672" /></p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">prediction_knn_df <-<span class="st"> </span><span class="kw">predict</span>(model_knn_df, df_testing)
cm_knn_df <-<span class="st"> </span><span class="kw">confusionMatrix</span>(prediction_knn_df, df_testing<span class="op">$</span>diagnosis, <span class="dt">positive =</span> <span class="st">"M"</span>)
cm_knn_df</code></pre></div>
<pre><code>## Confusion Matrix and Statistics
##
## Reference
## Prediction B M
## B 70 5
## M 1 37
##
## Accuracy : 0.9469
## 95% CI : (0.888, 0.9803)
## No Information Rate : 0.6283
## P-Value [Acc > NIR] : 1.866e-15
##
## Kappa : 0.8841
## Mcnemar's Test P-Value : 0.2207
##
## Sensitivity : 0.8810
## Specificity : 0.9859
## Pos Pred Value : 0.9737
## Neg Pred Value : 0.9333
## Prevalence : 0.3717
## Detection Rate : 0.3274
## Detection Prevalence : 0.3363
## Balanced Accuracy : 0.9334
##
## 'Positive' Class : M
## </code></pre>
</div>
<div id="support-vector-machine" class="section level4">
<h4><span class="header-section-number">18.3.3.4</span> Support Vector Machine</h4>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">set.seed</span>(<span class="dv">1815</span>)
model_svm_df <-<span class="st"> </span><span class="kw">train</span>(diagnosis <span class="op">~</span>., <span class="dt">data =</span> df_training, <span class="dt">method =</span> <span class="st">"svmLinear"</span>,
<span class="dt">metric =</span> <span class="st">"ROC"</span>,
<span class="dt">preProcess =</span> <span class="kw">c</span>(<span class="st">"scale"</span>, <span class="st">"center"</span>),
<span class="dt">trace =</span> <span class="ot">FALSE</span>,
<span class="dt">trControl =</span> df_control)
prediction_svm_df <-<span class="st"> </span><span class="kw">predict</span>(model_svm_df, df_testing)
cm_svm_df <-<span class="st"> </span><span class="kw">confusionMatrix</span>(prediction_svm_df, df_testing<span class="op">$</span>diagnosis, <span class="dt">positive =</span> <span class="st">"M"</span>)
cm_svm_df</code></pre></div>
<pre><code>## Confusion Matrix and Statistics
##
## Reference
## Prediction B M
## B 71 2
## M 0 40
##
## Accuracy : 0.9823
## 95% CI : (0.9375, 0.9978)
## No Information Rate : 0.6283
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.9617
## Mcnemar's Test P-Value : 0.4795
##
## Sensitivity : 0.9524
## Specificity : 1.0000
## Pos Pred Value : 1.0000
## Neg Pred Value : 0.9726
## Prevalence : 0.3717
## Detection Rate : 0.3540
## Detection Prevalence : 0.3540
## Balanced Accuracy : 0.9762
##
## 'Positive' Class : M
## </code></pre>
<p>This is is an OK model.<br />
I am wondering though if we could achieve better results with SVM when doing it on the PCA data set.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">set.seed</span>(<span class="dv">1815</span>)
df_control_pca <-<span class="st"> </span><span class="kw">trainControl</span>(<span class="dt">method=</span><span class="st">"cv"</span>,
<span class="dt">number =</span> <span class="dv">15</span>,
<span class="dt">preProcOptions =</span> <span class="kw">list</span>(<span class="dt">thresh =</span> <span class="fl">0.9</span>), <span class="co"># threshold for pca preprocess</span>
<span class="dt">classProbs =</span> <span class="ot">TRUE</span>,
<span class="dt">summaryFunction =</span> twoClassSummary)
model_svm_pca_df <-<span class="st"> </span><span class="kw">train</span>(diagnosis<span class="op">~</span>.,
df_training, <span class="dt">method =</span> <span class="st">"svmLinear"</span>, <span class="dt">metric =</span> <span class="st">"ROC"</span>,
<span class="dt">preProcess =</span> <span class="kw">c</span>(<span class="st">'center'</span>, <span class="st">'scale'</span>, <span class="st">"pca"</span>),
<span class="dt">trControl =</span> df_control_pca)
prediction_svm_pca_df <-<span class="st"> </span><span class="kw">predict</span>(model_svm_pca_df, df_testing)
cm_svm_pca_df <-<span class="st"> </span><span class="kw">confusionMatrix</span>(prediction_svm_pca_df, df_testing<span class="op">$</span>diagnosis, <span class="dt">positive =</span> <span class="st">"M"</span>)
cm_svm_pca_df</code></pre></div>
<pre><code>## Confusion Matrix and Statistics
##
## Reference
## Prediction B M
## B 70 2
## M 1 40
##
## Accuracy : 0.9735
## 95% CI : (0.9244, 0.9945)
## No Information Rate : 0.6283
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.9429
## Mcnemar's Test P-Value : 1
##
## Sensitivity : 0.9524
## Specificity : 0.9859
## Pos Pred Value : 0.9756
## Neg Pred Value : 0.9722
## Prevalence : 0.3717
## Detection Rate : 0.3540
## Detection Prevalence : 0.3628
## Balanced Accuracy : 0.9691
##
## 'Positive' Class : M
## </code></pre>
<p>That’s already better. The treshold parameter is what we needed to play with.</p>
</div>
<div id="neural-network-with-lda" class="section level4">
<h4><span class="header-section-number">18.3.3.5</span> Neural Network with LDA</h4>
<p>To use the LDA pre-processing step, we need to also create the same training and testing set.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">lda_training <-<span class="st"> </span>predict_lda_df[df_sampling_index, ]
lda_testing <-<span class="st"> </span>predict_lda_df[<span class="op">-</span>df_sampling_index, ]
model_nnetlda_df <-<span class="st"> </span><span class="kw">train</span>(diagnosis <span class="op">~</span>., lda_training,
<span class="dt">method =</span> <span class="st">"nnet"</span>,
<span class="dt">metric =</span> <span class="st">"ROC"</span>,
<span class="dt">preProcess =</span> <span class="kw">c</span>(<span class="st">"center"</span>, <span class="st">"scale"</span>),
<span class="dt">tuneLength =</span> <span class="dv">10</span>,
<span class="dt">trace =</span> <span class="ot">FALSE</span>,
<span class="dt">trControl =</span> df_control)
prediction_nnetlda_df <-<span class="st"> </span><span class="kw">predict</span>(model_nnetlda_df, lda_testing)
cm_nnetlda_df <-<span class="st"> </span><span class="kw">confusionMatrix</span>(prediction_nnetlda_df, lda_testing<span class="op">$</span>diagnosis, <span class="dt">positive =</span> <span class="st">"M"</span>)
cm_nnetlda_df</code></pre></div>
<pre><code>## Confusion Matrix and Statistics
##
## Reference
## Prediction B M
## B 71 1
## M 0 41
##
## Accuracy : 0.9912
## 95% CI : (0.9517, 0.9998)
## No Information Rate : 0.6283
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.981
## Mcnemar's Test P-Value : 1
##
## Sensitivity : 0.9762
## Specificity : 1.0000
## Pos Pred Value : 1.0000
## Neg Pred Value : 0.9861
## Prevalence : 0.3717
## Detection Rate : 0.3628
## Detection Prevalence : 0.3628
## Balanced Accuracy : 0.9881
##
## 'Positive' Class : M
## </code></pre>
</div>
<div id="models-evaluation" class="section level4">
<h4><span class="header-section-number">18.3.3.6</span> Models evaluation</h4>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">model_list <-<span class="st"> </span><span class="kw">list</span>(<span class="dt">logisic =</span> model_logreg_df, <span class="dt">rf =</span> model_rf_df,
<span class="dt">svm =</span> model_svm_df, <span class="dt">SVM_with_PCA =</span> model_svm_pca_df,
<span class="dt">Neural_with_LDA =</span> model_nnetlda_df)
results <-<span class="st"> </span><span class="kw">resamples</span>(model_list)
<span class="kw">summary</span>(results)</code></pre></div>
<pre><code>##
## Call:
## summary.resamples(object = results)
##
## Models: logisic, rf, svm, SVM_with_PCA, Neural_with_LDA
## Number of resamples: 15
##
## ROC
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## logisic 0.8827751 0.9660088 1 0.9744418 1 1 0
## rf 0.9569378 0.9784689 1 0.9894737 1 1 0
## svm 0.9545455 0.9884370 1 0.9928761 1 1 0
## SVM_with_PCA 0.9409091 0.9952153 1 0.9932430 1 1 0
## Neural_with_LDA 0.9692982 0.9976077 1 0.9954014 1 1 0
##
## Sens
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## logisic 0.8947368 0.9473684 0.9473684 0.9615789 1 1 0
## rf 0.8947368 0.9473684 1.0000000 0.9721053 1 1 0
## svm 0.9473684 1.0000000 1.0000000 0.9929825 1 1 0
## SVM_with_PCA 0.9473684 1.0000000 1.0000000 0.9894737 1 1 0
## Neural_with_LDA 0.8947368 1.0000000 1.0000000 0.9859649 1 1 0
##
## Spec
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## logisic 0.8181818 0.9128788 1.0000000 0.9530303 1 1 0
## rf 0.6363636 0.9090909 0.9090909 0.9095960 1 1 0
## svm 0.8181818 0.9090909 0.9166667 0.9343434 1 1 0
## SVM_with_PCA 0.8181818 0.9090909 1.0000000 0.9580808 1 1 0
## Neural_with_LDA 0.8181818 0.9128788 1.0000000 0.9525253 1 1 0</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">bwplot</span>(results, <span class="dt">metric =</span> <span class="st">"ROC"</span>)</code></pre></div>
<p><img src="machinelearningwithR_files/figure-html/model_evaluation_plot-1.png" width="672" /></p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co">#dotplot(results)</span></code></pre></div>
<p>The logistic has to much variability for it to be reliable. The Random Forest and Neural Network with LDA pre-processing are giving the best results. The ROC metric measure the auc of the roc curve of each model. This metric is independent of any threshold. Let’s remember how these models result with the testing dataset. Prediction classes are obtained by default with a threshold of 0.5 which could not be the best with an unbalanced dataset like this.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">cm_list <-<span class="st"> </span><span class="kw">list</span>(<span class="dt">cm_rf =</span> cm_rf_df, <span class="dt">cm_svm =</span> cm_svm_df,
<span class="dt">cm_logisic =</span> cm_logreg_df, <span class="dt">cm_nnet_LDA =</span> cm_nnetlda_df)
results <-<span class="st"> </span><span class="kw">map_df</span>(cm_list, <span class="cf">function</span>(x) x<span class="op">$</span>byClass) <span class="op">%>%</span><span class="st"> </span><span class="kw">as_tibble</span>() <span class="op">%>%</span><span class="st"> </span>
<span class="st"> </span><span class="kw">mutate</span>(<span class="dt">stat =</span> <span class="kw">names</span>(cm_rf_df<span class="op">$</span>byClass))
results</code></pre></div>
<pre><code>## # A tibble: 11 x 5
## cm_rf cm_svm cm_logisic cm_nnet_LDA stat
## <dbl> <dbl> <dbl> <dbl> <chr>
## 1 0.929 0.952 0.952 0.976 Sensitivity
## 2 1 1 1 1 Specificity
## 3 1 1 1 1 Pos Pred Value
## 4 0.959 0.973 0.973 0.986 Neg Pred Value
## 5 1 1 1 1 Precision
## 6 0.929 0.952 0.952 0.976 Recall
## 7 0.963 0.976 0.976 0.988 F1
## 8 0.372 0.372 0.372 0.372 Prevalence
## 9 0.345 0.354 0.354 0.363 Detection Rate
## 10 0.345 0.354 0.354 0.363 Detection Prevalence
## 11 0.964 0.976 0.976 0.988 Balanced Accuracy</code></pre>
<p>The best results for sensitivity (detection of breast cases) is LDA_NNET which also has a great F1 score.</p>
</div>
</div>
</div>
<div id="references-9" class="section level2">
<h2><span class="header-section-number">18.4</span> References</h2>
<p>A useful popular kernel on this dataset on <a href="https://www.kaggle.com/lbronchal/breast-cancer-dataset-analysis">Kaggle</a> Another one, also on <a href="https://www.kaggle.com/sonicboom8/breast-cancer-data-with-logistic-randomforest">Kaggle</a> And <a href="https://www.kaggle.com/murnix/cluster-rf-boosting-svm-accuracy-97-auc-0-96/notebook">another one</a>, especially nice to compare models.</p>
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