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# Machine Learning CS 7641

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This 0 page Class Notes was uploaded by Alayna Veum on Monday November 2, 2015. The Class Notes belongs to CS 7641 at Georgia Institute of Technology - Main Campus taught by Staff in Fall. Since its upload, it has received 14 views. For similar materials see /class/234130/cs-7641-georgia-institute-of-technology-main-campus in ComputerScienence at Georgia Institute of Technology - Main Campus.

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Date Created: 11/02/15

Principle Components Analysis A Short Primer by Chris Simpkins simpkins cc Highlevel Ideas A PCA projection represents a data set in terms of the orthonormal eigenvectors of the data sets covariance matrix A covariance matrix captures the correlation between variables in a data set PCA nds the orthonormal eigenvectors of the covariance matrix as the basis for the transformed feature space Eigenvectors can be thought of as the natural basis77 for a given multidimensional data set Higher eigenvalues in the covariance matrix indicate lower correlation between the features in the data set PCA projections seek uncorrelated variables Every data set has principle components but PCA works best if data are Gaussiandistributed For high dimensional data the Central Limit theorem allows us to assume Gaussian distributions Covariance Matrices The variance of a single variable x is given by 2 Eam e X TL 039 The variance of two variables x and y is given by COUltny ELK i Y Covariance tells you how two variable vary together 0 If the covariance between two variables is positive then as one variable increases the other will increase 0 If the covariance between two variables is negative then as one variable increases the other will decrease o If the covariance between two variables is zero then the two variables are completely independent of each other For a set of variables lt X1 Xn gt such as the features of a data set we can construct a matrix which represents the covariance between each pair of variables Xi and Xj where i and j are indexes of the feature vector vaTX1 covX1 X2 covX1Xn covX2X1 vaTX2 covX2Xn 001 covXnX1 covXnX2 vaTXn Notice that SVM SUWM Ver Machmeg MAg U 0739 AU imww Lin UN Le arm na Mahala CS oh I 6nwx M m of A cms rim 14601 MANY quot6 0012quot HY oT was quot857 Chum 54 7 MXIML MamI K ALL CHXSIIly amp CowccHyp 6 Tww guyoz T UEcwlIS I75 In many oumemsx39ous w Wave suparr reiars Verceph dh Abvr lmw FOKM Mayhem awayEu X Z A I m Ah 2 was A R mgxnxm 3 ri4 a 39 SD 53 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