"iterations failed to converge" - K-means cluster analysis using SPSS

Question

I recently ran a k-means cluster analysis using SPSS Statistics (version 24) and got the following notation under the Iteration History in my output:

As I'm a complete novice and have found it difficult to find the relevant information online, I was wondering if someone could explain to me:

1) What exactly this means in simple terms?

2) Whether it's necessary for the iterations to converge to consider the analysis sound?

3) What effect would it have on the analysis if I increased the maximum number of iterations until convergence was reached?

Answer 1

K-means iteratively searches a better solution. Unless you stop early.

Apparently someone at SPSS decided it is enough to do 10 iterations. I doubt this will "usually" be enough. And in your case, you can see the means still change noticeably.

With a good implementation (not the one in SPSS), later iterations would be so cheap, that you can just iterate until convergence. In a naive implementation, all iterations take equally long, so 20 iterations will take 2x as long as 10.

Why don't you just try using more iterations of you can afford to wait longer?

Answer 2

Here is a link on how to increase the maximum number of iterations for K-Means clustering. Increasing Maximum Iterations for SPSS Statistics K-Means clustering

1. The iteration history is showing you the change in the centroid of your clusters through each iteration of K-Means. The lower the number between each iteration, the less improvement the algorithm makes from each iteration, the better chance it will not improve. Your history is showing continued improvement so increasing the number of iterations would likely create more "distinct" clusters. I would bump to 20 and see. In this case, SPSS is telling you that it was still improving, but didn't have enough iterations to actually get to the answer.
2. In unsupervised algorithms since there is no target and thus really is no "right" answer. In the case of building clusters, adding iterations and getting to convergence might bring about more distinct clusters - but it may not actually benefit the overall problem you are trying to solve. For example, if we are building clusters of customers - K-Means may be trying to vary the cut-off for income in order to create better clusters. In that sense, it may be statistically significant that we move the average income cut-off of one cluster from $42,000 to $45,000, but likely that would not be relevant to the actual problem you are solving.
3. Adding iterations may or may not effect the answer to your problem, the only way to check is to add additional iterations and see how it changes the variable statistics of each of your clusters.