This is a non-exhaustive list, meant to be a supplement to your own study notes! You should be very familiar with everything in the homework and quizzes and everything in the lecture slides/notes class discussion/board work ------------------------- linear algebra basics know how to do matrix addition/multiplication (including when the dimensions are such that you can not do it) know what it means to be an eigenvector of a matrix (understand and know the implications of the equation A v = lambda v) -- You do NOT have to be able to compute eigenvectors/eigenvalues by hand ------------------- matlab -be familiar with all the commands you have used in homework ; ' : find .^2 ... length plot repmat for know how to use vectorized commands sin([1 2 3]) = 0.8415 0.9093 0.1411 know how to use them to eliminate loops know how to write a matlab function function [x,y,z]=cylinder(r,n) ... -------------- probability Know the 1-D Gaussian equation (and what the terms mean -- how to read off the mean and variance) Know the relationship between variance and standard deviation (std dev is the square root of the variance). Know that the integral under a valid pdf is 1 Know the equation for (and implication of and how to use) the expected value -- know that this is the mean Know the equation for (and implication of and how to use) the variance Be able to do the Gaussian integrals from using your knowledge of pdfs, expected value and variance Know the probability axioms and equation for indpendence, conditional dependence and Bayes rule (and how to use them) ----------- PCA Understand covariance matrices (how to go from matrix to an idea of what the scatter cloud of data would look like). How to compute them. Know the expectation equation Covariance = E ((X-mu)(X-mu)') understand why the sample covariance matrix for a dataset is 1/n \sum (X-Mu)(X-Mu)' where X is matrix with data as columns and Mu is matrix with mean as columns (repeated Numdatapts times -- know how to use repmat to get this matrix) understand graphically how to extract principal component directions understand the operation of rotating the axes, removing the directions of least variance and reconstructing the input using fewer principal components understand why one would use PCA understand algorithm and MATLAB code for running PCA (especially your code from the homework -- including the transpose trick when the covariance matrix is very large.) subtract the mean m = mean(hw3data, 2); centeredData = hw3data - repmat(m, 1, numSamples); compute covariance matrix C = (1 / (numSamples )) * centeredData * centeredData'; compute eigenvectors of covariance matrix (and sort by decreasing eigenvalue) [V, D] = eig(C); [V, D] = eigsort(V, D); understand algorithm and MATLAB code for transforming new points Components in PCA space are V'*(centered data) projectedData = V' * centeredData; (we have also called projected data c) Understand how to reconstruct with fewer principal components (and why one would do this) reconstructedData = V(:,1:N)*projectedData(1:10) + m