331 lines
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HTML
331 lines
18 KiB
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<!-- navigation toc: --> <li><a href="._week45-bs001.html#plan-for-week-45" style="font-size: 80%;"><b>Plan for week 45</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs002.html#material-for-the-lab-sessions-additional-ways-to-present-classification-results-and-other-practicalities" style="font-size: 80%;"><b>Material for the lab sessions, additional ways to present classification results and other practicalities</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs003.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;"><b>Searching for Optimal Regularization Parameters \( \lambda \)</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs004.html#grid-search" style="font-size: 80%;"><b>Grid Search</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs005.html#randomized-grid-search" style="font-size: 80%;"><b>Randomized Grid Search</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs006.html#wisconsin-cancer-data" style="font-size: 80%;"><b>Wisconsin Cancer Data</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs007.html#using-the-correlation-matrix" style="font-size: 80%;"><b>Using the correlation matrix</b></a></li>
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<!-- navigation toc: --> <li><a href="#discussing-the-correlation-data" style="font-size: 80%;"><b>Discussing the correlation data</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs009.html#other-ways-of-presenting-a-classification-problem" style="font-size: 80%;"><b>Other ways of presenting a classification problem</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs010.html#combinations-of-classification-results" style="font-size: 80%;"><b>Combinations of classification results</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs011.html#positive-and-negative-prediction-values" style="font-size: 80%;"><b>Positive and negative prediction values</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs012.html#other-quantities" style="font-size: 80%;"><b>Other quantities</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs013.html#f-1-score" style="font-size: 80%;"><b>\( F_1 \) score</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs014.html#roc-curve" style="font-size: 80%;"><b>ROC curve</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs015.html#cumulative-gain-curve" style="font-size: 80%;"><b>Cumulative gain curve</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs016.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;"><b>Other measures in classification studies: Cancer Data again</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs017.html#material-for-lecture-thursday-november-9" style="font-size: 80%;"><b>Material for Lecture Thursday November 9</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs018.html#recurrent-neural-networks-rnns-overarching-view" style="font-size: 80%;"><b>Recurrent neural networks (RNNs): Overarching view</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs019.html#a-simple-example" style="font-size: 80%;"><b>A simple example</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs019.html#rnns" style="font-size: 80%;"> RNNs</a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs020.html#basic-layout" style="font-size: 80%;"><b>Basic layout</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs020.html#we-need-to-specify-the-initial-activity-state-of-all-the-hidden-and-output-units" style="font-size: 80%;"> We need to specify the initial activity state of all the hidden and output units</a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs020.html#we-can-specify-inputs-in-several-ways" style="font-size: 80%;"> We can specify inputs in several ways</a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs020.html#we-can-specify-targets-in-several-ways" style="font-size: 80%;"> We can specify targets in several ways</a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs020.html#backpropagation-through-time" style="font-size: 80%;"> Backpropagation through time</a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs020.html#the-backward-pass-is-linear" style="font-size: 80%;"> The backward pass is linear</a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs021.html#the-problem-of-exploding-or-vanishing-gradients" style="font-size: 80%;"><b>The problem of exploding or vanishing gradients</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs022.html#four-effective-ways-to-learn-an-rnn" style="font-size: 80%;"><b>Four effective ways to learn an RNN</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs022.html#long-short-term-memory-lstm" style="font-size: 80%;"> Long Short Term Memory (LSTM)</a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs022.html#implementing-a-memory-cell-in-a-neural-network" style="font-size: 80%;"> Implementing a memory cell in a neural network</a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs023.html#an-extrapolation-example" style="font-size: 80%;"><b>An extrapolation example</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs024.html#formatting-the-data" style="font-size: 80%;"><b>Formatting the Data</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs025.html#predicting-new-points-with-a-trained-recurrent-neural-network" style="font-size: 80%;"><b>Predicting New Points With A Trained Recurrent Neural Network</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs026.html#other-things-to-try" style="font-size: 80%;"><b>Other Things to Try</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs027.html#other-types-of-recurrent-neural-networks" style="font-size: 80%;"><b>Other Types of Recurrent Neural Networks</b></a></li>
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</ul>
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</li>
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</div>
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<p> </p><p> </p><p> </p> <!-- add vertical space -->
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<a name="part0008"></a>
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<!-- !split -->
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<h2 id="discussing-the-correlation-data" class="anchor">Discussing the correlation data </h2>
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<p>In the above example we note two things. In the first plot we display
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the overlap of benign and malignant tumors as functions of the various
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features in the Wisconsing breast cancer data set. We see that for
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some of the features we can distinguish clearly the benign and
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malignant cases while for other features we cannot. This can point to
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us which features may be of greater interest when we wish to classify
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a benign or not benign tumour.
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</p>
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<p>In the second figure we have computed the so-called correlation
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matrix, which in our case with thirty features becomes a \( 30\times 30 \)
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matrix.
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</p>
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<p>We constructed this matrix using <b>pandas</b> via the statements</p>
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<pre style="line-height: 125%;">cancerpd <span style="color: #666666">=</span> pd<span style="color: #666666">.</span>DataFrame(cancer<span style="color: #666666">.</span>data, columns<span style="color: #666666">=</span>cancer<span style="color: #666666">.</span>feature_names)
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</pre>
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</div>
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<p>and then</p>
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<pre style="line-height: 125%;">correlation_matrix <span style="color: #666666">=</span> cancerpd<span style="color: #666666">.</span>corr()<span style="color: #666666">.</span>round(<span style="color: #666666">1</span>)
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</pre>
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</div>
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<p>Diagonalizing this matrix we can in turn say something about which
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features are of relevance and which are not. This leads us to
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the classical Principal Component Analysis (PCA) theorem with
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applications. This will be discussed later this semester (<a href="https://compphysics.github.io/MachineLearning/doc/pub/week43/html/week43-bs.html" target="_self">week 43</a>).
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