Module: Linear Algebra

Learning Outcomes

Understand and apply basic concepts of Linear Algebra

You understand

• vectors in 2D, 3D, and higher dimensions
• vector arithmetic
• distances between vectors
• dot product and orthogonality
• matrix multiplication and its geometric interpretation
• the notion of distance and nearest neighbors
• the curse of dimensionality
• the effect of increasing dimensionality to the notion of nearness
• principle component analysis using SVD (aka principal components)
• linear discriminant analysis
• notion of purity and splitting criteria
• hyperplanes and linear separability
• optimization using gradient descent
• ensemble methods: random forest, gradient boosted trees

You are able to

• represent data as vectors
• use nearest neighbors for classification/regression
• use decision trees for classification/regression
• use SVD to examine the inherent dimensionality of the data
• perform dimensionality reduction using SVD or LDA
• use support vector machines for classification
• use perceptron and neural networks for classification/regression

Readings

Experiential Learning