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<a class="navbar-brand" href="week47-bs.html">Week 47: Unsupervised learning (PCA and Clustering) and Summary of Course</a>
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
<ul class="dropdown-menu">
<!-- navigation toc: --> <li><a href="._week47-bs001.html#overview-of-week-47" style="font-size: 80%;"><b>Overview of week 47</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs002.html#basic-ideas-of-the-principal-component-analysis-pca" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs003.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs004.html#more-on-the-covariance" style="font-size: 80%;"><b>More on the covariance</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs005.html#reminding-ourselves-about-linear-regression" style="font-size: 80%;"><b>Reminding ourselves about Linear Regression</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs006.html#simple-example" style="font-size: 80%;"><b>Simple Example</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs007.html#the-correlation-matrix" style="font-size: 80%;"><b>The Correlation Matrix</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs008.html#numpy-functionality" style="font-size: 80%;"><b>Numpy Functionality</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs009.html#correlation-matrix-again" style="font-size: 80%;"><b>Correlation Matrix again</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs010.html#using-pandas" style="font-size: 80%;"><b>Using Pandas</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs011.html#and-then-the-franke-function" style="font-size: 80%;"><b>And then the Franke Function</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs012.html#links-with-the-design-matrix" style="font-size: 80%;"><b>Links with the Design Matrix</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs013.html#computing-the-expectation-values" style="font-size: 80%;"><b>Computing the Expectation Values</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs014.html#towards-the-pca-theorem" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs015.html#more-on-the-pca-theorem" style="font-size: 80%;"><b>More on the PCA Theorem</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs016.html#a-kind-of-bird-s-view-on-pca" style="font-size: 80%;"><b>A kind of Bird's view on PCA</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs017.html#writing-our-own-pca-code" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs018.html#implementing-it" style="font-size: 80%;"><b>Implementing it</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs019.html#first-step" style="font-size: 80%;"><b>First Step</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs020.html#scaling" style="font-size: 80%;"><b>Scaling</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs021.html#centered-data" style="font-size: 80%;"><b>Centered Data</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs022.html#exploring" style="font-size: 80%;"><b>Exploring</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs023.html#diagonalize-the-sample-covariance-matrix-to-obtain-the-principal-components" style="font-size: 80%;"><b>Diagonalize the sample covariance matrix to obtain the principal components</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs024.html#collecting-all-steps" style="font-size: 80%;"><b>Collecting all Steps</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs025.html#classical-pca-theorem" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs026.html#the-pca-theorem" style="font-size: 80%;"><b>The PCA Theorem</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs027.html#geometric-interpretation-and-link-with-singular-value-decomposition" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs028.html#pca-and-scikit-learn" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs029.html#back-to-the-cancer-data" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs030.html#incremental-pca" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs030.html#randomized-pca" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs030.html#kernel-pca" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs031.html#other-techniques" style="font-size: 80%;"><b>Other techniques</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs032.html#clustering-and-unsupervised-learning" style="font-size: 80%;"><b>Clustering and Unsupervised Learning</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs033.html#basic-idea-of-the-k-means-clustering-algorithm" style="font-size: 80%;"><b>Basic Idea of the \( k \)-means Clustering Algorithm</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs034.html#the-k-means-algorithm" style="font-size: 80%;"><b>The \( k \)-means Algorithm</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs035.html#basic-math-of-the-k-means-algorithm" style="font-size: 80%;"><b>Basic Math of the \( k \)-means Algorithm</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs036.html#within-cluster-point-scatter" style="font-size: 80%;"><b>Within Cluster Point Scatter</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs037.html#more-details" style="font-size: 80%;"><b>More Details</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs038.html#total-cluster-variance" style="font-size: 80%;"><b>Total Cluster Variance</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs039.html#the-k-means-clustering-algorithm" style="font-size: 80%;"><b>The \( k \)-means Clustering Algorithm</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs040.html#summarizing" style="font-size: 80%;"><b>Summarizing</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs041.html#writing-our-own-code-the-data-set" style="font-size: 80%;"><b>Writing our own Code, the Data Set</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs042.html#implementing-the-k-means-algorithm" style="font-size: 80%;"><b>Implementing the \( k \)-means Algorithm</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs043.html#plotting" style="font-size: 80%;"><b>Plotting</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs044.html#continuing" style="font-size: 80%;"><b>Continuing</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs045.html#wrapping-it-up" style="font-size: 80%;"><b>Wrapping it up</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs046.html#summary-of-course" style="font-size: 80%;"><b>Summary of course</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs047.html#what-me-worry-no-final-exam-in-this-course" style="font-size: 80%;"><b>What? Me worry? No final exam in this course!</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs048.html#what-is-the-link-between-artificial-intelligence-and-machine-learning-and-some-general-remarks" style="font-size: 80%;"><b>What is the link between Artificial Intelligence and Machine Learning and some general Remarks</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs049.html#going-back-to-the-beginning-of-the-semester" style="font-size: 80%;"><b>Going back to the beginning of the semester</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs050.html#not-so-sharp-distinctions" style="font-size: 80%;"><b>Not so sharp distinctions</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs051.html#topics-we-have-covered-this-year" style="font-size: 80%;"><b>Topics we have covered this year</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs052.html#statistical-analysis-and-optimization-of-data" style="font-size: 80%;"><b>Statistical analysis and optimization of data</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs053.html#machine-learning" style="font-size: 80%;"><b>Machine learning</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs054.html#learning-outcomes-and-overarching-aims-of-this-course" style="font-size: 80%;"><b>Learning outcomes and overarching aims of this course</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs055.html#perspective-on-machine-learning" style="font-size: 80%;"><b>Perspective on Machine Learning</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs056.html#machine-learning-research" style="font-size: 80%;"><b>Machine Learning Research</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs057.html#starting-your-machine-learning-project" style="font-size: 80%;"><b>Starting your Machine Learning Project</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs058.html#choose-a-model-and-algorithm" style="font-size: 80%;"><b>Choose a Model and Algorithm</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs059.html#preparing-your-data" style="font-size: 80%;"><b>Preparing Your Data</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs060.html#which-activation-and-weights-to-choose-in-neural-networks" style="font-size: 80%;"><b>Which Activation and Weights to Choose in Neural Networks</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs061.html#optimization-methods-and-hyperparameters" style="font-size: 80%;"><b>Optimization Methods and Hyperparameters</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs062.html#resampling" style="font-size: 80%;"><b>Resampling</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs063.html#other-courses-on-data-science-and-machine-learning-at-uio" style="font-size: 80%;"><b>Other courses on Data science and Machine Learning at UiO</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs064.html#additional-courses-of-interest" style="font-size: 80%;"><b>Additional courses of interest</b></a></li>
<!-- navigation toc: --> <li><a href="#what-s-the-future-like" style="font-size: 80%;"><b>What's the future like?</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs066.html#types-of-machine-learning-a-repetition" style="font-size: 80%;"><b>Types of Machine Learning, a repetition</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs067.html#why-boltzmann-machines" style="font-size: 80%;"><b>Why Boltzmann machines?</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs068.html#boltzmann-machines" style="font-size: 80%;"><b>Boltzmann Machines</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs069.html#some-similarities-and-differences-from-dnns" style="font-size: 80%;"><b>Some similarities and differences from DNNs</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs070.html#boltzmann-machines-bm" style="font-size: 80%;"><b>Boltzmann machines (BM)</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs071.html#a-standard-bm-setup" style="font-size: 80%;"><b>A standard BM setup</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs072.html#the-structure-of-the-rbm-network" style="font-size: 80%;"><b>The structure of the RBM network</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs073.html#the-network" style="font-size: 80%;"><b>The network</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs074.html#goals" style="font-size: 80%;"><b>Goals</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs075.html#joint-distribution" style="font-size: 80%;"><b>Joint distribution</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs076.html#network-elements-the-energy-function" style="font-size: 80%;"><b>Network Elements, the energy function</b></a></li>
<!-- navigation toc: --> <li><a href="._week47-bs077.html#defining-different-types-of-rbms" style="font-size: 80%;"><b>Defining different types of RBMs</b></a></li>
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<h2 id="what-s-the-future-like" class="anchor">What's the future like? </h2>
<p>Based on multi-layer nonlinear neural networks, deep learning can
learn directly from raw data, automatically extract and abstract
features from layer to layer, and then achieve the goal of regression,
classification, or ranking. Deep learning has made breakthroughs in
computer vision, speech processing and natural language, and reached
or even surpassed human level. The success of deep learning is mainly
due to the three factors: big data, big model, and big computing.
</p>
<p>In the past few decades, many different architectures of deep neural
networks have been proposed, such as
</p>
<ol>
<li> Convolutional neural networks, which are mostly used in image and video data processing, and have also been applied to sequential data such as text processing;</li>
<li> Recurrent neural networks, which can process sequential data of variable length and have been widely used in natural language understanding and speech processing;</li>
<li> Encoder-decoder framework, which is mostly used for image or sequence generation, such as machine translation, text summarization, and image captioning.</li>
</ol>
<p>
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