Week 47: Unsupervised learning (PCA and Clustering) and Summary of Course
Contents
Overview of week 47
Basic ideas of the Principal Component Analysis (PCA)
Introducing the Covariance and Correlation functions
More on the covariance
Reminding ourselves about Linear Regression
Simple Example
The Correlation Matrix
Numpy Functionality
Correlation Matrix again
Using Pandas
And then the Franke Function
Links with the Design Matrix
Computing the Expectation Values
Towards the PCA theorem
More on the PCA Theorem
A kind of Bird's view on PCA
Writing our own PCA code
Implementing it
First Step
Scaling
Centered Data
Exploring
Diagonalize the sample covariance matrix to obtain the principal components
Collecting all Steps
Classical PCA Theorem
The PCA Theorem
Geometric Interpretation and link with Singular Value Decomposition
PCA and scikit-learn
Back to the Cancer Data
Incremental PCA
Randomized PCA
Kernel PCA
Other techniques
Clustering and Unsupervised Learning
Basic Idea of the \( k \)-means Clustering Algorithm
The \( k \)-means Algorithm
Basic Math of the \( k \)-means Algorithm
Within Cluster Point Scatter
More Details
Total Cluster Variance
The \( k \)-means Clustering Algorithm
Summarizing
Writing our own Code, the Data Set
Implementing the \( k \)-means Algorithm
Plotting
Continuing
Wrapping it up
Summary of course
What? Me worry? No final exam in this course!
What is the link between Artificial Intelligence and Machine Learning and some general Remarks
Going back to the beginning of the semester
Not so sharp distinctions
Topics we have covered this year
Statistical analysis and optimization of data
Machine learning
Learning outcomes and overarching aims of this course
Perspective on Machine Learning
Machine Learning Research
Starting your Machine Learning Project
Choose a Model and Algorithm
Preparing Your Data
Which Activation and Weights to Choose in Neural Networks
Optimization Methods and Hyperparameters
Resampling
Other courses on Data science and Machine Learning at UiO
Additional courses of interest
What's the future like?
Types of Machine Learning, a repetition
Why Boltzmann machines?
Boltzmann Machines
Some similarities and differences from DNNs
Boltzmann machines (BM)
A standard BM setup
The structure of the RBM network
The network
Goals
Joint distribution
Network Elements, the energy function
Defining different types of RBMs
More about RBMs
Autoencoders: Overarching view
Bayesian Machine Learning
Reinforcement Learning
Transfer learning
Adversarial learning
Dual learning
Distributed machine learning
Meta learning
The Challenges Facing Machine Learning
Explainable machine learning
Scientific Machine Learning
Quantum machine learning
Quantum machine learning algorithms based on linear algebra
Quantum reinforcement learning
Quantum deep learning
Social machine learning
The last words?
AI/ML and some statements you may have heard (and what do they mean?)
Best wishes to you all and thanks so much for your heroic efforts this semester
Best wishes to you all and thanks so much for your heroic efforts this semester
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