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The K-means algorithm is a method to automatically cluster similar data examples together.

The intuition behind K-means is an iterative procedure that starts by guessing the initial centroids, and then refines this guess by repeatedly assigning examples to their closest centroids and then recomputing the centroids based on the assignments.

This algorithm was implemented as follows:

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 ```1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 ``` ```kMeansInitCentroids <- function(X, K) { rand.idx <- sample(1:nrow(X), K) centroids <- X[rand.idx,] return(centroids) }   findClosestCentroids <- function(X, centroids) { ## finding closest centroids   # set K K <- nrow(centroids)   idx <- sapply(1:nrow(X), function(i) { which.min( sapply(1:K, function(j) { sum( (X[i,]-centroids[j,])^2 ) }) ) }) return(idx) }   computeCentroids <- function(X, idx, K) { centroids <- sapply(1:K, function(i) colMeans(X[idx == i,])) centroids <- t(centroids) return(centroids) }   runkMeans <- function(X, K, max.iter = 10, plot=F, plot.progress=F) { initCentroids <- kMeansInitCentroids(X, K) K <- nrow(initCentroids) centroids <- initCentroids preCentroids <- centroids for (i in 1:max.iter) { idx <- findClosestCentroids(X, centroids) centroids <- computeCentroids(X, idx, K) if (plot.progress) { preCentroids <- rbind(preCentroids, centroids) } } xx <- data.frame(X, cluster=as.factor(idx)) if(plot) { p <- ggplot(xx, aes(V1, V2))+geom_point(aes(color=cluster)) if (plot.progress) { preCentroids <- data.frame(preCentroids, idx=rep(1:3, max.iter+1)) p <- p+geom_point(data=preCentroids, aes(x=V1, y=V2)) + geom_path(data=preCentroids, aes(x=V1, y=V2, group=idx)) } print(p) } return(xx) }```

After implemented this algorithm, I applied it to the dataset provided in ML-Class Ex 7.

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 ```1 2 3 4 ``` ```## dataset was converted from ML-class exercise 7 ex7data2.mat. X <- read.delim("d:/ex7data2.txt", header=F) K <- 3 xx <- runkMeans(X,K, plot=TRUE, plot.progress=TRUE)```

The K-means code produced a visualization that steps the progress of the algorithm at each iteration. 