mhjensen
407 lines
26 KiB
HTML
407 lines
26 KiB
HTML
<!--
|
|
Automatically generated HTML file from DocOnce source
|
|
(https://github.com/hplgit/doconce/)
|
|
-->
|
|
<html>
|
|
<head>
|
|
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
|
|
<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
|
|
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
|
|
<meta name="description" content="Data Analysis and Machine Learning: Neural networks, from the simple perceptron to deep learning">
|
|
|
|
<title>Data Analysis and Machine Learning: Neural networks, from the simple perceptron to deep learning</title>
|
|
|
|
<!-- Bootstrap style: bootstrap -->
|
|
<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
|
|
<!-- not necessary
|
|
<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
|
|
-->
|
|
|
|
<style type="text/css">
|
|
|
|
/* Add scrollbar to dropdown menus in bootstrap navigation bar */
|
|
.dropdown-menu {
|
|
height: auto;
|
|
max-height: 400px;
|
|
overflow-x: hidden;
|
|
}
|
|
|
|
/* Adds an invisible element before each target to offset for the navigation
|
|
bar */
|
|
.anchor::before {
|
|
content:"";
|
|
display:block;
|
|
height:50px; /* fixed header height for style bootstrap */
|
|
margin:-50px 0 0; /* negative fixed header height */
|
|
}
|
|
</style>
|
|
|
|
|
|
</head>
|
|
|
|
<!-- tocinfo
|
|
{'highest level': 2,
|
|
'sections': [('Neural networks', 2, None, '___sec0'),
|
|
('Artificial neurons', 2, None, '___sec1'),
|
|
('Neural network types', 2, None, '___sec2'),
|
|
('Feed-forward neural networks', 2, None, '___sec3'),
|
|
('Convolutional Neural Network', 2, None, '___sec4'),
|
|
('Recurrent neural networks', 2, None, '___sec5'),
|
|
('Other types of networks', 2, None, '___sec6'),
|
|
('Multilayer perceptrons', 2, None, '___sec7'),
|
|
('Why multilayer perceptrons?', 2, None, '___sec8'),
|
|
('Mathematical model', 2, None, '___sec9'),
|
|
('Mathematical model', 2, None, '___sec10'),
|
|
('Mathematical model', 2, None, '___sec11'),
|
|
('Mathematical model', 2, None, '___sec12'),
|
|
('Mathematical model', 2, None, '___sec13'),
|
|
('Matrix-vector notation', 3, None, '___sec14'),
|
|
('Matrix-vector notation and activation', 3, None, '___sec15'),
|
|
('Activation functions', 3, None, '___sec16'),
|
|
('Activation functions, Logistic and Hyperbolic ones',
|
|
3,
|
|
None,
|
|
'___sec17'),
|
|
('Relevance', 3, None, '___sec18'),
|
|
('The multilayer perceptron (MLP)', 2, None, '___sec19'),
|
|
('From one to many layers, the universal approximation theorem',
|
|
2,
|
|
None,
|
|
'___sec20'),
|
|
('Deriving the back propagation code for a multilayer perceptron '
|
|
'model',
|
|
2,
|
|
None,
|
|
'___sec21'),
|
|
('Definitions', 2, None, '___sec22'),
|
|
('Derivatives and the chain rule', 2, None, '___sec23'),
|
|
('Derivative of the cost function', 2, None, '___sec24'),
|
|
('Bringing it together, first back propagation equation',
|
|
2,
|
|
None,
|
|
'___sec25'),
|
|
('Derivatives in terms of $z_j^L$', 2, None, '___sec26'),
|
|
('Bringing it together', 2, None, '___sec27'),
|
|
('Final back propagating equation', 2, None, '___sec28'),
|
|
('Setting up the Back propagation algorithm',
|
|
2,
|
|
None,
|
|
'___sec29'),
|
|
('Setting up a Multi-layer perceptron model for classification',
|
|
2,
|
|
None,
|
|
'___sec30'),
|
|
('Defining the cost function', 2, None, '___sec31'),
|
|
('Example: binary classification problem', 2, None, '___sec32'),
|
|
('The Softmax function', 2, None, '___sec33'),
|
|
('Developing a code for doing neural networks with back '
|
|
'propagation',
|
|
2,
|
|
None,
|
|
'___sec34'),
|
|
('Collect and pre-process data', 2, None, '___sec35'),
|
|
('Train and test datasets', 2, None, '___sec36'),
|
|
('Define model and architecture', 2, None, '___sec37'),
|
|
('Layers', 2, None, '___sec38'),
|
|
('Weights and biases', 2, None, '___sec39'),
|
|
('Feed-forward pass', 2, None, '___sec40'),
|
|
('Matrix multiplications', 2, None, '___sec41'),
|
|
('Choose cost function and optimizer', 2, None, '___sec42'),
|
|
('Optimizing the cost function', 2, None, '___sec43'),
|
|
('Regularization', 2, None, '___sec44'),
|
|
('Matrix multiplication', 2, None, '___sec45'),
|
|
('Improving performance', 2, None, '___sec46'),
|
|
('Full object-oriented implementation', 2, None, '___sec47'),
|
|
('Evaluate model performance on test data', 2, None, '___sec48'),
|
|
('Adjust hyperparameters', 2, None, '___sec49'),
|
|
('Visualization', 2, None, '___sec50'),
|
|
('scikit-learn implementation', 2, None, '___sec51'),
|
|
('Visualization', 2, None, '___sec52'),
|
|
('Building neural networks in Tensorflow and Keras',
|
|
2,
|
|
None,
|
|
'___sec53'),
|
|
('Tensorflow', 2, None, '___sec54'),
|
|
('Collect and pre-process data', 2, None, '___sec55'),
|
|
('Using TensorFlow backend', 2, None, '___sec56'),
|
|
('Optimizing and using gradient descent', 2, None, '___sec57'),
|
|
('Using Keras', 2, None, '___sec58'),
|
|
('Which activation function should I use?', 2, None, '___sec59'),
|
|
('Is the Logistic activation function (Sigmoid) our choice?',
|
|
2,
|
|
None,
|
|
'___sec60'),
|
|
('The derivative of the Logistic funtion', 2, None, '___sec61'),
|
|
('The RELU function family', 2, None, '___sec62'),
|
|
('Which activation function should we use?', 2, None, '___sec63'),
|
|
('A top-down perspective on Neural networks',
|
|
2,
|
|
None,
|
|
'___sec64'),
|
|
('Limitations of supervised learning with deep networks',
|
|
2,
|
|
None,
|
|
'___sec65')]}
|
|
end of tocinfo -->
|
|
|
|
<body>
|
|
|
|
|
|
|
|
<script type="text/x-mathjax-config">
|
|
MathJax.Hub.Config({
|
|
TeX: {
|
|
equationNumbers: { autoNumber: "none" },
|
|
extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
|
|
}
|
|
});
|
|
</script>
|
|
<script type="text/javascript" async
|
|
src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
|
|
</script>
|
|
|
|
|
|
|
|
|
|
<!-- Bootstrap navigation bar -->
|
|
<div class="navbar navbar-default navbar-fixed-top">
|
|
<div class="navbar-header">
|
|
<button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
|
|
<span class="icon-bar"></span>
|
|
<span class="icon-bar"></span>
|
|
<span class="icon-bar"></span>
|
|
</button>
|
|
<a class="navbar-brand" href="NeuralNet-bs.html">Data Analysis and Machine Learning: Neural networks, from the simple perceptron to deep learning</a>
|
|
</div>
|
|
|
|
<div class="navbar-collapse collapse navbar-responsive-collapse">
|
|
<ul class="nav navbar-nav navbar-right">
|
|
<li class="dropdown">
|
|
<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
|
|
<ul class="dropdown-menu">
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs001.html#___sec0" style="font-size: 80%;"><b>Neural networks</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs002.html#___sec1" style="font-size: 80%;"><b>Artificial neurons</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs003.html#___sec2" style="font-size: 80%;"><b>Neural network types</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs004.html#___sec3" style="font-size: 80%;"><b>Feed-forward neural networks</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs005.html#___sec4" style="font-size: 80%;"><b>Convolutional Neural Network</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs006.html#___sec5" style="font-size: 80%;"><b>Recurrent neural networks</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs007.html#___sec6" style="font-size: 80%;"><b>Other types of networks</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs008.html#___sec7" style="font-size: 80%;"><b>Multilayer perceptrons</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs009.html#___sec8" style="font-size: 80%;"><b>Why multilayer perceptrons?</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs010.html#___sec9" style="font-size: 80%;"><b>Mathematical model</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs011.html#___sec10" style="font-size: 80%;"><b>Mathematical model</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs012.html#___sec11" style="font-size: 80%;"><b>Mathematical model</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs013.html#___sec12" style="font-size: 80%;"><b>Mathematical model</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs014.html#___sec13" style="font-size: 80%;"><b>Mathematical model</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs015.html#___sec14" style="font-size: 80%;"> Matrix-vector notation</a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs016.html#___sec15" style="font-size: 80%;"> Matrix-vector notation and activation</a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs017.html#___sec16" style="font-size: 80%;"> Activation functions</a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs018.html#___sec17" style="font-size: 80%;"> Activation functions, Logistic and Hyperbolic ones</a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs019.html#___sec18" style="font-size: 80%;"> Relevance</a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs020.html#___sec19" style="font-size: 80%;"><b>The multilayer perceptron (MLP)</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs021.html#___sec20" style="font-size: 80%;"><b>From one to many layers, the universal approximation theorem</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs022.html#___sec21" style="font-size: 80%;"><b>Deriving the back propagation code for a multilayer perceptron model</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs023.html#___sec22" style="font-size: 80%;"><b>Definitions</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs024.html#___sec23" style="font-size: 80%;"><b>Derivatives and the chain rule</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs025.html#___sec24" style="font-size: 80%;"><b>Derivative of the cost function</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs026.html#___sec25" style="font-size: 80%;"><b>Bringing it together, first back propagation equation</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs027.html#___sec26" style="font-size: 80%;"><b>Derivatives in terms of \( z_j^L \)</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs028.html#___sec27" style="font-size: 80%;"><b>Bringing it together</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs029.html#___sec28" style="font-size: 80%;"><b>Final back propagating equation</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs030.html#___sec29" style="font-size: 80%;"><b>Setting up the Back propagation algorithm</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs031.html#___sec30" style="font-size: 80%;"><b>Setting up a Multi-layer perceptron model for classification</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs032.html#___sec31" style="font-size: 80%;"><b>Defining the cost function</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs033.html#___sec32" style="font-size: 80%;"><b>Example: binary classification problem</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs034.html#___sec33" style="font-size: 80%;"><b>The Softmax function</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs035.html#___sec34" style="font-size: 80%;"><b>Developing a code for doing neural networks with back propagation</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="#___sec35" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs037.html#___sec36" style="font-size: 80%;"><b>Train and test datasets</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs038.html#___sec37" style="font-size: 80%;"><b>Define model and architecture</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs039.html#___sec38" style="font-size: 80%;"><b>Layers</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs040.html#___sec39" style="font-size: 80%;"><b>Weights and biases</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs041.html#___sec40" style="font-size: 80%;"><b>Feed-forward pass</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs042.html#___sec41" style="font-size: 80%;"><b>Matrix multiplications</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs043.html#___sec42" style="font-size: 80%;"><b>Choose cost function and optimizer</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs044.html#___sec43" style="font-size: 80%;"><b>Optimizing the cost function</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs045.html#___sec44" style="font-size: 80%;"><b>Regularization</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs046.html#___sec45" style="font-size: 80%;"><b>Matrix multiplication</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Improving performance</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Full object-oriented implementation</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Adjust hyperparameters</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Visualization</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Visualization</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs056.html#___sec55" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs057.html#___sec56" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs058.html#___sec57" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs059.html#___sec58" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs060.html#___sec59" style="font-size: 80%;"><b>Which activation function should I use?</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs061.html#___sec60" style="font-size: 80%;"><b>Is the Logistic activation function (Sigmoid) our choice?</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs062.html#___sec61" style="font-size: 80%;"><b>The derivative of the Logistic funtion</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs063.html#___sec62" style="font-size: 80%;"><b>The RELU function family</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs064.html#___sec63" style="font-size: 80%;"><b>Which activation function should we use?</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs065.html#___sec64" style="font-size: 80%;"><b>A top-down perspective on Neural networks</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._NeuralNet-bs066.html#___sec65" style="font-size: 80%;"><b>Limitations of supervised learning with deep networks</b></a></li>
|
|
|
|
</ul>
|
|
</li>
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
</div> <!-- end of navigation bar -->
|
|
|
|
<div class="container">
|
|
|
|
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
|
|
|
<a name="part0036"></a>
|
|
<!-- !split -->
|
|
|
|
<h2 id="___sec35" class="anchor">Collect and pre-process data </h2>
|
|
|
|
<p>
|
|
Here we will be using the MNIST dataset, which is readily available through the <b>scikit-learn</b>
|
|
package. You may also find it for example <a href="http://yann.lecun.com/exdb/mnist/" target="_self">here</a>.
|
|
The <em>MNIST</em> (Modified National Institute of Standards and Technology) database is a large database
|
|
of handwritten digits that is commonly used for training various image processing systems.
|
|
The MNIST dataset consists of 70 000 images of size \( 28\times 28 \) pixels, each labeled from 0 to 9.
|
|
The scikit-learn dataset we will use consists of a selection of 1797 images of size \( 8\times 8 \) collected and processed from this database.
|
|
|
|
<p>
|
|
To feed data into a feed-forward neural network we need to represent
|
|
the inputs as a design/feature matrix \( X = (n_{inputs}, n_{features}) \). Each
|
|
row represents an <em>input</em>, in this case a handwritten digit, and
|
|
each column represents a <em>feature</em>, in this case a pixel. The
|
|
correct answers, also known as <em>labels</em> or <em>targets</em> are
|
|
represented as a 1D array of integers
|
|
\( Y = (n_{inputs}) = (5, 3, 1, 8,...) \).
|
|
|
|
<p>
|
|
As an example, say we want to build a neural network using supervised learning to predict Body-Mass Index (BMI) from
|
|
measurements of height (in m)
|
|
and weight (in kg). If we have measurements of 5 people the design/feature matrix could be for example:
|
|
|
|
$$ X = \begin{bmatrix}
|
|
1.85 & 81\\
|
|
1.71 & 65\\
|
|
1.95 & 103\\
|
|
1.55 & 42\\
|
|
1.63 & 56
|
|
\end{bmatrix} ,$$
|
|
|
|
<p>
|
|
and the targets would be:
|
|
|
|
$$ Y = (23.7, 22.2, 27.1, 17.5, 21.1) $$
|
|
|
|
<p>
|
|
Since each input image is a 2D matrix, we need to flatten the image
|
|
(i.e. "unravel" the 2D matrix into a 1D array) to turn the data into a
|
|
design/feature matrix. This means we lose all spatial information in the
|
|
image, such as locality and translational invariance. More complicated
|
|
architectures such as Convolutional Neural Networks can take advantage
|
|
of such information, and are most commonly applied when analyzing
|
|
images.
|
|
|
|
<p>
|
|
|
|
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
|
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #408080; font-style: italic"># import necessary packages</span>
|
|
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
|
|
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
|
|
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn</span> <span style="color: #008000; font-weight: bold">import</span> datasets
|
|
|
|
|
|
<span style="color: #408080; font-style: italic"># ensure the same random numbers appear every time</span>
|
|
np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>seed(<span style="color: #666666">0</span>)
|
|
|
|
<span style="color: #408080; font-style: italic"># display images in notebook</span>
|
|
<span style="color: #666666">%</span>matplotlib inline
|
|
plt<span style="color: #666666">.</span>rcParams[<span style="color: #BA2121">'figure.figsize'</span>] <span style="color: #666666">=</span> (<span style="color: #666666">12</span>,<span style="color: #666666">12</span>)
|
|
|
|
|
|
<span style="color: #408080; font-style: italic"># download MNIST dataset</span>
|
|
digits <span style="color: #666666">=</span> datasets<span style="color: #666666">.</span>load_digits()
|
|
|
|
<span style="color: #408080; font-style: italic"># define inputs and labels</span>
|
|
inputs <span style="color: #666666">=</span> digits<span style="color: #666666">.</span>images
|
|
labels <span style="color: #666666">=</span> digits<span style="color: #666666">.</span>target
|
|
|
|
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"inputs = (n_inputs, pixel_width, pixel_height) = "</span> <span style="color: #666666">+</span> <span style="color: #008000">str</span>(inputs<span style="color: #666666">.</span>shape))
|
|
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"labels = (n_inputs) = "</span> <span style="color: #666666">+</span> <span style="color: #008000">str</span>(labels<span style="color: #666666">.</span>shape))
|
|
|
|
|
|
<span style="color: #408080; font-style: italic"># flatten the image</span>
|
|
<span style="color: #408080; font-style: italic"># the value -1 means dimension is inferred from the remaining dimensions: 8x8 = 64</span>
|
|
n_inputs <span style="color: #666666">=</span> <span style="color: #008000">len</span>(inputs)
|
|
inputs <span style="color: #666666">=</span> inputs<span style="color: #666666">.</span>reshape(n_inputs, <span style="color: #666666">-1</span>)
|
|
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"X = (n_inputs, n_features) = "</span> <span style="color: #666666">+</span> <span style="color: #008000">str</span>(inputs<span style="color: #666666">.</span>shape))
|
|
|
|
|
|
<span style="color: #408080; font-style: italic"># choose some random images to display</span>
|
|
indices <span style="color: #666666">=</span> np<span style="color: #666666">.</span>arange(n_inputs)
|
|
random_indices <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>choice(indices, size<span style="color: #666666">=5</span>)
|
|
|
|
<span style="color: #008000; font-weight: bold">for</span> i, image <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">enumerate</span>(digits<span style="color: #666666">.</span>images[random_indices]):
|
|
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">1</span>, <span style="color: #666666">5</span>, i<span style="color: #666666">+1</span>)
|
|
plt<span style="color: #666666">.</span>axis(<span style="color: #BA2121">'off'</span>)
|
|
plt<span style="color: #666666">.</span>imshow(image, cmap<span style="color: #666666">=</span>plt<span style="color: #666666">.</span>cm<span style="color: #666666">.</span>gray_r, interpolation<span style="color: #666666">=</span><span style="color: #BA2121">'nearest'</span>)
|
|
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">"Label: </span><span style="color: #BB6688; font-weight: bold">%d</span><span style="color: #BA2121">"</span> <span style="color: #666666">%</span> digits<span style="color: #666666">.</span>target[random_indices[i]])
|
|
plt<span style="color: #666666">.</span>show()
|
|
</pre></div>
|
|
<p>
|
|
<p>
|
|
<!-- navigation buttons at the bottom of the page -->
|
|
<ul class="pagination">
|
|
<li><a href="._NeuralNet-bs035.html">«</a></li>
|
|
<li><a href="._NeuralNet-bs000.html">1</a></li>
|
|
<li><a href="">...</a></li>
|
|
<li><a href="._NeuralNet-bs028.html">29</a></li>
|
|
<li><a href="._NeuralNet-bs029.html">30</a></li>
|
|
<li><a href="._NeuralNet-bs030.html">31</a></li>
|
|
<li><a href="._NeuralNet-bs031.html">32</a></li>
|
|
<li><a href="._NeuralNet-bs032.html">33</a></li>
|
|
<li><a href="._NeuralNet-bs033.html">34</a></li>
|
|
<li><a href="._NeuralNet-bs034.html">35</a></li>
|
|
<li><a href="._NeuralNet-bs035.html">36</a></li>
|
|
<li class="active"><a href="._NeuralNet-bs036.html">37</a></li>
|
|
<li><a href="._NeuralNet-bs037.html">38</a></li>
|
|
<li><a href="._NeuralNet-bs038.html">39</a></li>
|
|
<li><a href="._NeuralNet-bs039.html">40</a></li>
|
|
<li><a href="._NeuralNet-bs040.html">41</a></li>
|
|
<li><a href="._NeuralNet-bs041.html">42</a></li>
|
|
<li><a href="._NeuralNet-bs042.html">43</a></li>
|
|
<li><a href="._NeuralNet-bs043.html">44</a></li>
|
|
<li><a href="._NeuralNet-bs044.html">45</a></li>
|
|
<li><a href="._NeuralNet-bs045.html">46</a></li>
|
|
<li><a href="">...</a></li>
|
|
<li><a href="._NeuralNet-bs066.html">67</a></li>
|
|
<li><a href="._NeuralNet-bs037.html">»</a></li>
|
|
</ul>
|
|
<!-- ------------------- end of main content --------------- -->
|
|
|
|
</div> <!-- end container -->
|
|
<!-- include javascript, jQuery *first* -->
|
|
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
|
|
<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
|
|
|
|
<!-- Bootstrap footer
|
|
<footer>
|
|
<a href="http://..."><img width="250" align=right src="http://..."></a>
|
|
</footer>
|
|
-->
|
|
|
|
|
|
<center style="font-size:80%">
|
|
<!-- copyright only on the titlepage -->
|
|
</center>
|
|
|
|
|
|
</body>
|
|
</html>
|
|
|
|
|