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<p>Implementation of [Multilayer Perceptron] (<a href="https://en.wikipedia.org/wiki/Multilayer_perceptron">https://en.wikipedia.org/wiki/Multilayer_perceptron</a>).
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<a href="#details">More...</a></p>
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<div class="textblock"><code>#include <algorithm></code><br />
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/d93/classmachine__learning_1_1neural__network_1_1layers_1_1_dense_layer.html">machine_learning::neural_network::layers::DenseLayer</a></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html">machine_learning::neural_network::NeuralNetwork</a></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d77/namespacemachine__learning.html">machine_learning</a></td></tr>
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<tr class="memdesc:d8/d77/namespacemachine__learning"><td class="mdescLeft"> </td><td class="mdescRight"><a href="https://en.wikipedia.org/wiki/A*_search_algorithm" target="_blank">A* search algorithm</a> <br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d2e/namespaceneural__network.html">neural_network</a></td></tr>
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<tr class="memdesc:d0/d2e/namespaceneural__network"><td class="mdescLeft"> </td><td class="mdescRight">Neural Network or Multilayer Perceptron. <br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/d39/namespaceactivations.html">activations</a></td></tr>
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<tr class="memdesc:d5/d39/namespaceactivations"><td class="mdescLeft"> </td><td class="mdescRight">Various activation functions used in Neural network. <br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d3/d17/namespaceutil__functions.html">util_functions</a></td></tr>
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<tr class="memdesc:d3/d17/namespaceutil__functions"><td class="mdescLeft"> </td><td class="mdescRight">Various utility functions used in Neural network. <br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/d2c/namespacelayers.html">layers</a></td></tr>
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<tr class="memdesc:d5/d2c/namespacelayers"><td class="mdescLeft"> </td><td class="mdescRight">This namespace contains layers used in MLP. <br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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</table><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:a23aa9d32bcbcd65cfc85f0a41e2afadc" id="r_a23aa9d32bcbcd65cfc85f0a41e2afadc"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="#a23aa9d32bcbcd65cfc85f0a41e2afadc">machine_learning::neural_network::activations::sigmoid</a> (const double &x)</td></tr>
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<tr class="separator:a23aa9d32bcbcd65cfc85f0a41e2afadc"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a76eb66212d577f948a457b6e29d87c46" id="r_a76eb66212d577f948a457b6e29d87c46"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="#a76eb66212d577f948a457b6e29d87c46">machine_learning::neural_network::activations::dsigmoid</a> (const double &x)</td></tr>
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<tr class="separator:a76eb66212d577f948a457b6e29d87c46"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:af8f264600754602b6a9ea19cc690e50e" id="r_af8f264600754602b6a9ea19cc690e50e"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="#af8f264600754602b6a9ea19cc690e50e">machine_learning::neural_network::activations::relu</a> (const double &x)</td></tr>
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<tr class="separator:af8f264600754602b6a9ea19cc690e50e"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:aa69e95a34054d7989bf446f96b2ffaf9" id="r_aa69e95a34054d7989bf446f96b2ffaf9"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="#aa69e95a34054d7989bf446f96b2ffaf9">machine_learning::neural_network::activations::drelu</a> (const double &x)</td></tr>
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<tr class="separator:aa69e95a34054d7989bf446f96b2ffaf9"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a371aa7dd5d5add0143d1756bb0a1b32f" id="r_a371aa7dd5d5add0143d1756bb0a1b32f"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="#a371aa7dd5d5add0143d1756bb0a1b32f">machine_learning::neural_network::activations::tanh</a> (const double &x)</td></tr>
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<tr class="separator:a371aa7dd5d5add0143d1756bb0a1b32f"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a2a5e874b9774aa5362dbcf288828b95c" id="r_a2a5e874b9774aa5362dbcf288828b95c"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="#a2a5e874b9774aa5362dbcf288828b95c">machine_learning::neural_network::activations::dtanh</a> (const double &x)</td></tr>
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<tr class="separator:a2a5e874b9774aa5362dbcf288828b95c"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a45d3e30406712ada3d9713ece3c1b153" id="r_a45d3e30406712ada3d9713ece3c1b153"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="#a45d3e30406712ada3d9713ece3c1b153">machine_learning::neural_network::util_functions::square</a> (const double &x)</td></tr>
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<tr class="separator:a45d3e30406712ada3d9713ece3c1b153"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a32c00da08f2cf641dd336270f6e3c407" id="r_a32c00da08f2cf641dd336270f6e3c407"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="#a32c00da08f2cf641dd336270f6e3c407">machine_learning::neural_network::util_functions::identity_function</a> (const double &x)</td></tr>
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<tr class="separator:a32c00da08f2cf641dd336270f6e3c407"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d" id="r_aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void </td><td class="memItemRight" valign="bottom"><a class="el" href="#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
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<tr class="separator:aa8dca7b867074164d5f45b0f3851269d"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4" id="r_ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft"> </td><td class="mdescRight">Main function. <br /></td></tr>
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<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2"> </td></tr>
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</table>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<div class="textblock"><p>Implementation of [Multilayer Perceptron] (<a href="https://en.wikipedia.org/wiki/Multilayer_perceptron">https://en.wikipedia.org/wiki/Multilayer_perceptron</a>). </p>
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<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/imdeep2905" target="_blank">Deep Raval</a></dd></dl>
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<p>A multilayer perceptron (MLP) is a class of feedforward artificial neural network (ANN). The term MLP is used ambiguously, sometimes loosely to any feedforward ANN, sometimes strictly to refer to networks composed of multiple layers of perceptrons (with threshold activation). Multilayer perceptrons are sometimes colloquially referred to as "vanilla" neural networks, especially when they have a single hidden layer.</p>
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<p>An MLP consists of at least three layers of nodes: an input layer, a hidden layer and an output layer. Except for the input nodes, each node is a neuron that uses a nonlinear activation function. MLP utilizes a supervised learning technique called backpropagation for training. Its multiple layers and non-linear activation distinguish MLP from a linear perceptron. It can distinguish data that is not linearly separable.</p>
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<p>See <a href="https://en.wikipedia.org/wiki/Backpropagation" target="_blank">Backpropagation</a> for training algorithm.</p>
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<dl class="section note"><dt>Note</dt><dd>This implementation uses mini-batch gradient descent as optimizer and MSE as loss function. Bias is also not included. </dd></dl>
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<p class="definition">Definition in file <a class="el" href="../../d2/d58/neural__network_8cpp_source.html">neural_network.cpp</a>.</p>
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</div><h2 class="groupheader">Function Documentation</h2>
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<a id="aa69e95a34054d7989bf446f96b2ffaf9" name="aa69e95a34054d7989bf446f96b2ffaf9"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#aa69e95a34054d7989bf446f96b2ffaf9">◆ </a></span>drelu()</h2>
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<td class="memname">double machine_learning::neural_network::activations::drelu </td>
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<td>(</td>
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<td class="paramtype">const double &</td> <td class="paramname"><span class="paramname"><em>x</em></span></td><td>)</td>
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<td></td>
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</div><div class="memdoc">
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<p>Derivative of relu function </p><dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">X</td><td>Value </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>derivative of relu(x) </dd></dl>
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<p class="definition">Definition at line <a class="el" href="../../d2/d58/neural__network_8cpp_source.html#l00081">81</a> of file <a class="el" href="../../d2/d58/neural__network_8cpp_source.html">neural_network.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 81</span>{ <span class="keywordflow">return</span> x >= 0.0 ? 1.0 : 0.0; }</div>
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</div><!-- fragment -->
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<a id="a76eb66212d577f948a457b6e29d87c46" name="a76eb66212d577f948a457b6e29d87c46"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a76eb66212d577f948a457b6e29d87c46">◆ </a></span>dsigmoid()</h2>
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<td class="memname">double machine_learning::neural_network::activations::dsigmoid </td>
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<td>(</td>
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<p>Derivative of sigmoid function </p><dl class="params"><dt>Parameters</dt><dd>
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<dl class="section return"><dt>Returns</dt><dd>Returns derivative of sigmoid(x) </dd></dl>
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<p class="definition">Definition at line <a class="el" href="../../d2/d58/neural__network_8cpp_source.html#l00067">67</a> of file <a class="el" href="../../d2/d58/neural__network_8cpp_source.html">neural_network.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 67</span>{ <span class="keywordflow">return</span> x * (1 - x); }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a2a5e874b9774aa5362dbcf288828b95c">◆ </a></span>dtanh()</h2>
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<p>Derivative of Sigmoid function </p><dl class="params"><dt>Parameters</dt><dd>
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<dl class="section return"><dt>Returns</dt><dd>Returns derivative of tanh(x) </dd></dl>
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<p class="definition">Definition at line <a class="el" href="../../d2/d58/neural__network_8cpp_source.html#l00095">95</a> of file <a class="el" href="../../d2/d58/neural__network_8cpp_source.html">neural_network.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 95</span>{ <span class="keywordflow">return</span> 1 - x * x; }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a32c00da08f2cf641dd336270f6e3c407">◆ </a></span>identity_function()</h2>
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<p>Identity function </p><dl class="params"><dt>Parameters</dt><dd>
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<dl class="section return"><dt>Returns</dt><dd>Returns x </dd></dl>
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<p class="definition">Definition at line <a class="el" href="../../d2/d58/neural__network_8cpp_source.html#l00112">112</a> of file <a class="el" href="../../d2/d58/neural__network_8cpp_source.html">neural_network.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 112</span>{ <span class="keywordflow">return</span> x; }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">◆ </a></span>main()</h2>
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<td class="memname">int main </td>
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<p>Main function. </p>
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<p class="definition">Definition at line <a class="el" href="../../d2/d58/neural__network_8cpp_source.html#l00833">833</a> of file <a class="el" href="../../d2/d58/neural__network_8cpp_source.html">neural_network.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 833</span> {</div>
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<div class="line"><span class="lineno"> 834</span> <span class="comment">// Testing</span></div>
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<div class="line"><span class="lineno"> 835</span> <a class="code hl_function" href="#aa8dca7b867074164d5f45b0f3851269d">test</a>();</div>
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<div class="line"><span class="lineno"> 836</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><span class="lineno"> 837</span>}</div>
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<div class="ttc" id="aneural__network_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdef"><b>Definition</b> <a href="../../d2/d58/neural__network_8cpp_source.html#l00805">neural_network.cpp:805</a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#af8f264600754602b6a9ea19cc690e50e">◆ </a></span>relu()</h2>
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<td class="memname">double machine_learning::neural_network::activations::relu </td>
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<p>Relu function </p><dl class="params"><dt>Parameters</dt><dd>
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<dl class="section return"><dt>Returns</dt><dd>relu(x) </dd></dl>
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<p class="definition">Definition at line <a class="el" href="../../d2/d58/neural__network_8cpp_source.html#l00074">74</a> of file <a class="el" href="../../d2/d58/neural__network_8cpp_source.html">neural_network.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 74</span>{ <span class="keywordflow">return</span> std::max(0.0, x); }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a23aa9d32bcbcd65cfc85f0a41e2afadc">◆ </a></span>sigmoid()</h2>
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<p>Sigmoid function </p><dl class="params"><dt>Parameters</dt><dd>
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<dl class="section return"><dt>Returns</dt><dd>Returns sigmoid(x) </dd></dl>
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<p class="definition">Definition at line <a class="el" href="../../d2/d58/neural__network_8cpp_source.html#l00060">60</a> of file <a class="el" href="../../d2/d58/neural__network_8cpp_source.html">neural_network.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 60</span>{ <span class="keywordflow">return</span> 1.0 / (1.0 + std::exp(-x)); }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a45d3e30406712ada3d9713ece3c1b153">◆ </a></span>square()</h2>
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<p>Square function </p><dl class="params"><dt>Parameters</dt><dd>
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<dl class="section return"><dt>Returns</dt><dd>Returns x * x </dd></dl>
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<p class="definition">Definition at line <a class="el" href="../../d2/d58/neural__network_8cpp_source.html#l00106">106</a> of file <a class="el" href="../../d2/d58/neural__network_8cpp_source.html">neural_network.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 106</span>{ <span class="keywordflow">return</span> x * x; }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a371aa7dd5d5add0143d1756bb0a1b32f">◆ </a></span>tanh()</h2>
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<p>Tanh function </p><dl class="params"><dt>Parameters</dt><dd>
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<p class="definition">Definition at line <a class="el" href="../../d2/d58/neural__network_8cpp_source.html#l00088">88</a> of file <a class="el" href="../../d2/d58/neural__network_8cpp_source.html">neural_network.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 88</span>{ <span class="keywordflow">return</span> 2 / (1 + std::exp(-2 * x)) - 1; }</div>
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<p>Function to test neural network </p><dl class="section return"><dt>Returns</dt><dd>none </dd></dl>
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<p class="definition">Definition at line <a class="el" href="../../d2/d58/neural__network_8cpp_source.html#l00805">805</a> of file <a class="el" href="../../d2/d58/neural__network_8cpp_source.html">neural_network.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 805</span> {</div>
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<div class="line"><span class="lineno"> 809</span> {4, <span class="stringliteral">"none"</span>}, <span class="comment">// First layer with 3 neurons and "none" as activation</span></div>
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<div class="line"><span class="lineno"> 812</span> {3, <span class="stringliteral">"sigmoid"</span>} <span class="comment">// Third layer with 3 neurons and "sigmoid" as</span></div>
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<div class="line"><span class="lineno"> 814</span> });</div>
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<div class="line"><span class="lineno"> 817</span> <span class="comment">// Training Model</span></div>
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<div class="line"><span class="lineno"> 819</span> <span class="comment">// Testing predictions of model</span></div>
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<div class="line"><span class="lineno"> 820</span> assert(<a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a50480fccfb39de20ca47f1bf51ecb6ec">machine_learning::argmax</a>(</div>
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<div class="line"><span class="lineno"> 822</span> assert(<a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a50480fccfb39de20ca47f1bf51ecb6ec">machine_learning::argmax</a>(</div>
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<div class="line"><span class="lineno"> 824</span> assert(<a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a50480fccfb39de20ca47f1bf51ecb6ec">machine_learning::argmax</a>(</div>
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<div class="ttc" id="aclassmachine__learning_1_1neural__network_1_1_neural_network_html"><div class="ttname"><a href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html">machine_learning::neural_network::NeuralNetwork</a></div><div class="ttdef"><b>Definition</b> <a href="../../d2/d58/neural__network_8cpp_source.html#l00247">neural_network.cpp:247</a></div></div>
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<div class="ttc" id="aclassmachine__learning_1_1neural__network_1_1_neural_network_html_a3b9eac1824d365dce715fb17c33cb96f"><div class="ttname"><a href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#a3b9eac1824d365dce715fb17c33cb96f">machine_learning::neural_network::NeuralNetwork::single_predict</a></div><div class="ttdeci">std::vector< std::valarray< double > > single_predict(const std::vector< std::valarray< double > > &X)</div><div class="ttdef"><b>Definition</b> <a href="../../d2/d58/neural__network_8cpp_source.html#l00451">neural_network.cpp:451</a></div></div>
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<div class="ttc" id="aclassmachine__learning_1_1neural__network_1_1_neural_network_html_a5172a6791b9bd24f4232bab8d6b81fff"><div class="ttname"><a href="../../d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html#a5172a6791b9bd24f4232bab8d6b81fff">machine_learning::neural_network::NeuralNetwork::fit_from_csv</a></div><div class="ttdeci">void fit_from_csv(const std::string &file_name, const bool &last_label, const int &epochs, const double &learning_rate, const bool &normalize, const int &slip_lines=1, const size_t &batch_size=32, const bool &shuffle=true)</div><div class="ttdef"><b>Definition</b> <a href="../../d2/d58/neural__network_8cpp_source.html#l00587">neural_network.cpp:587</a></div></div>
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