From a conceptual and algorithmic standpoint, I understand how K-means works. However, from a mathematical standpoint, I don't understand why minimizing the WCSS (within-cluster sums of squares) will necessarily maximize the distance between clusters.

$\begingroup$ chl: to answer briefly your questions - yes, i used it (kmeans of weka) on the same data set. firstly and secondly, with all 21 attributes - different k arguments 'of course' -> bad wcss value. afterwards weka/kmeans was applied with three selected attributes using different arguments for k (in the range 2-10). however, using rapidminer (another data mining software) …

I have read that the k-means algorithm tries to minimize the within cluster sum of squares (or variance). With some brainstorming, a question popped up. Why is it that k-means or any other clustering

2020年9月17日 · The centroids are then updated after the points are all assigned, and points are re-assigned again. The algorithm continues to iterate until the clusters do not change anymore. The algorithm tries to minimise the within-cluster sum of squares (WCSS) value which is a measure of the variance within the clusters.

2013年3月4日 · Hence when I give k=2, the output perfect matches with R's. In fact, the output is perfect for k=3 and k=4 too (I use 'nstart' to get the best output). But for k=5 and above, the values are varying. The total WCSS for R's kmeans for k=5 was …

2016年1月20日 · Furthermore, WCSS is expected to decrease with the number of clusters. Even just assigning a single point to a new cluster obvioudly decreases WCSS, but foes not yield a better clustering. So if you don't see a clear 'outlier' where the curve drops a lot and then abruptly stops dropping, then something did not work .

2018年8月2日 · Never compare WCSS across different data versions or data sets. It's trivial to see that scaling all attributes by a factor of 2 does not affect the clustering, but changes the WCSS by a factor of 4. So you can arbitrarily inflate WCSS - or …

coincidentally minimize squared Euclidean distance, because WCSS (within-cluster sum of squares) variance contribution = squared euclidean distance; coincidentally assign objects to the nearest cluster by Euclidean distance, because the sqrt function is monotone (note that the mean does not optimize Euclidean distances, but the WCSS function)

2017年10月23日 · Now that you've figured out what WCSS is visually, you'll see that the WCSS is high at the beginning and you'll notice it drop substantially and then after a while, it will still drop but there won't be any substantial change. That point where the last big drop is, that's the optimal number of clusters.

2014年1月19日 · It's basically a measure of the goodness of the classification k-means has found. SS obviously stands for Sum of Squares, so it's the usual decomposition of deviance in deviance "Between" and deviance "Within".