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Unformatted text preview: 1 KMeans Clustering Given N observations {x 1 , , x N } where x R d How do we partition the N observations into k sets S = {S_1, , S_k} where k < N? In general: Difficult problem whether working with identifying 2 d R. Siegwart, I. Nourbakhsh MEM380: Fundamental Robotics I Fal 2009 1 clusters in R d OR identifying k clusters in 2D Often used in many applications An Example MEM380: Fundamental Robotics I Fal 2009 2 A Simple Algorithm Given N observations Let m i denote the centroid of the set S i for i=1, , k Two steps: 1. Assignment step 2. Update step MEM380: Fundamental Robotics I Fal 2009 3 Some Pseudocode % Iterate kmeans means = initialGuesses; while true % Compute cluster membership membership = assign_clusters(means, data); old_means = means; % Update means based on new membership information for i = 1:k means(i,:) = mean(all x_j \in S_i); end % Decide if you are done MEM380: Fundamental Robotics I Fal 2009 4 2 An Example Matlab Demo MEM380: Fundamental Robotics I Fal 2009 5 Our Initial Example MEM380: Fundamental Robotics I Fal 2009 6 Applying kmeans clustering MEM380: Fundamental Robotics I Fal 2009 7 Localization Where am I? 3 Localization via Triangulation (x, y) ? MEM380: Fundamental Robotics I Fal 2009 9 Uncertainty is Everywhere Environment Sensors Level of uncertainty depends on the application How do we handle uncertainty?...
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This note was uploaded on 03/29/2010 for the course MEM MEM380 taught by Professor Zhou during the Spring '09 term at Drexel.
 Spring '09
 ZHOU

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