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POINTS, LINES, PLANES • • • E G POSTULATE 9 If two planes intersect, then their intersection is a line • • J K W U THEOREMS – Statements that have been proven THEOREM 1-1 If two lines intersect, then they intersect in exactly one point
PowerPoint Presentation What you should know All the details of K-means The theory behind K-means as an optimization algorithm How K-means can get stuck The outline of Hierarchical clustering Be able to contrast between which problems would be relatively well poorly suited to K-means vs Gaussian Mixtures vs Hierarchical clustering K-means and Hierarchical Clustering
K-MEANS CLUSTERING Simply speaking k-means clustering is an algorithm to classify or to group the objects based on attributes features into K number of group K is positive integer number The grouping is done by minimizing the sum of squares of distances between data and the corresponding cluster centroid Simplify K-means: How the K-Mean Clustering algorithm works?
The Polar Coordinate System Basic Polar Graphs We graph Equations in the Polar Coordinate System that are in terms of r and q We will consider the following: r = k (r = a constant) q = k (q = a constant) Graph r = k The coordinate, r, tells us how far from the origin to put a point
K-means Clustering - University of South Carolina How can you do this efficiently? K-means Clustering Strengths Simple iterative method User provides “K” Weaknesses Often too simple bad results Difficult to guess the correct “K” K-means Clustering Basic Algorithm: Step 0: select K Step 1: randomly select initial cluster seeds Seed 1 650 Seed 2 200 Author Rose, John R Created Date
Order of Operations Is your answer 33 or 19? You can get 2 different answers depending on which operation you did first We want everyone to get the same answer so we must follow the order of operations Remember the phrase “Please Excuse My Dear Aunt Sally” or PEMDAS ORDER OF OPERATIONS 1 Parentheses - ( ) or [ ] 2 Exponents or Powers 3
PowerPoint Presentation The Order of Operations tells us how to do a math problem with more than one operation, in the correct order Please Excuse My Dear Aunt Sally This will help to you to remember the order of operations Add + Subtract - Multiply x Divide Please Excuse My Dear Aunt Sally P E M D A S Parentheses ( ) Exponents 43 Please Excuse My Dear Aunt Sally Parentheses ( ) Always do parentheses 1st Please