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I am solving a clustering problem on a trivial dataset with the k-means algorithm. I am running a couple of tests and, from time to time, one centroid doesn't attract any points, i.e. I've got an empty cluster (see the purple "x" in the picture).

What should I do? Shall I delete it or just stop updating its value? Why?

I am aware that built-in functions (e.g., kmeans() in R) have automatic ways of dealing with this situation, but I am trying to write the standard algorithm from scratch. As soon as I fix it I'll be able to compare my results to built-in functions. At this moment I'm looking for some theoretical reasons why I should prefer one solution or another.

In the picture each colour represents a cluster according to the current iteration and each "X" is its centroid (old ones have been kept and marked with the number of the iteration in which they were computed).

[Some related links about empty cluster case, added later by @ttnphns: http://stackoverflow.com/q/41634047/868905; https://stats.stackexchange.com/q/152333/3277; https://stats.stackexchange.com/q/125655/3277; https://stats.stackexchange.com/q/13744/3277; http://stackoverflow.com/q/24919346/868905; http://stackoverflow.com/q/18009664/868905; http://stackoverflow.com/q/29243800/868905; http://stackoverflow.com/q/11075272/868905; ]

I am solving a clustering problem on a trivial dataset with the k-means algorithm. I am running a couple of tests and, from time to time, one centroid doesn't attract any points, i.e. I've got an empty cluster (see the purple "x" in the picture).

What should I do? Shall I delete it or just stop updating its value? Why?

I am aware that built-in functions (e.g., kmeans() in R) have automatic ways of dealing with this situation, but I am trying to write the standard algorithm from scratch. As soon as I fix it I'll be able to compare my results to built-in functions. At this moment I'm looking for some theoretical reasons why I should prefer one solution or another.

In the picture each colour represents a cluster according to the current iteration and each "X" is its centroid (old ones have been kept and marked with the number of the iteration in which they were computed).

[Some related links about empty cluster case, added later by @ttnphns: https://stackoverflow.com/q/41634047/868905; https://stats.stackexchange.com/q/152333/3277; https://stats.stackexchange.com/q/125655/3277; https://stats.stackexchange.com/q/13744/3277; https://stackoverflow.com/q/24919346/868905; https://stackoverflow.com/q/18009664/868905; https://stackoverflow.com/q/29243800/868905; https://stackoverflow.com/q/11075272/868905; ]

I am solving a clustering problem on a trivial dataset with the k-means algorithm. I am running a couple of tests and, from time to time, one centroid doesn't attract any points, i.e. I've got an empty cluster (see the purple "x" in the picture).

What should I do? Shall I delete it or just stop updating its value? Why?

I am aware that built-in functions (e.g., kmeans() in R) have automatic ways of dealing with this situation, but I am trying to write the standard algorithm from scratch. As soon as I fix it I'll be able to compare my results to built-in functions. At this moment I'm looking for some theoretical reasons why I should prefer one solution or another.

In the picture each colour represents a cluster according to the current iteration and each "X" is its centroid (old ones have been kept and marked with the number of the iteration in which they were computed).

[Some related links about empty cluster case, added later by @ttnphns: http://stackoverflow.com/q/41634047/868905; http://stats.stackexchange.com/q/152333/3277; http://stats.stackexchange.com/q/125655/3277; http://stats.stackexchange.com/q/13744/3277; http://stackoverflow.com/q/24919346/868905; http://stackoverflow.com/q/18009664/868905; http://stackoverflow.com/q/29243800/868905; http://stackoverflow.com/q/11075272/868905; ]

I am solving a clustering problem on a trivial dataset with the k-means algorithm. I am running a couple of tests and, from time to time, one centroid doesn't attract any points, i.e. I've got an empty cluster (see the purple "x" in the picture).

What should I do? Shall I delete it or just stop updating its value? Why?

I am aware that built-in functions (e.g., kmeans() in R) have automatic ways of dealing with this situation, but I am trying to write the standard algorithm from scratch. As soon as I fix it I'll be able to compare my results to built-in functions. At this moment I'm looking for some theoretical reasons why I should prefer one solution or another.

In the picture each colour represents a cluster according to the current iteration and each "X" is its centroid (old ones have been kept and marked with the number of the iteration in which they were computed).

[Some related links about empty cluster case, added later by @ttnphns: http://stackoverflow.com/q/41634047/868905; https://stats.stackexchange.com/q/152333/3277; https://stats.stackexchange.com/q/125655/3277; https://stats.stackexchange.com/q/13744/3277; http://stackoverflow.com/q/24919346/868905; http://stackoverflow.com/q/18009664/868905; http://stackoverflow.com/q/29243800/868905; http://stackoverflow.com/q/11075272/868905; ]

I am solving a clustering problem on a trivial dataset with the k-means algorithm. I am running a couple of tests and, from time to time, one centroid doesn't attract any points, i.e. I've got an empty cluster (see the purple "x" in the picture).

What should I do? Shall I delete it or just stop updating its value? Why?

I am aware that built-in functions (e.g., kmeans() in R) have automatic ways of dealing with this situation, but I am trying to write the standard algorithm from scratch. As soon as I fix it I'll be able to compare my results to built-in functions. At this moment I'm looking for some theoretical reasons why I should prefer one solution or another.

In the picture each colour represents a cluster according to the current iteration and each "X" is its centroid (old ones have been kept and marked with the number of the iteration in which they were computed).

[Some related links about empty cluster case, added by @ttnphns: http://stackoverflow.com/q/41634047/868905; http://stats.stackexchange.com/q/152333/3277; http://stats.stackexchange.com/q/125655/3277; http://stats.stackexchange.com/q/13744/3277 ]

I am solving a clustering problem on a trivial dataset with the k-means algorithm. I am running a couple of tests and, from time to time, one centroid doesn't attract any points, i.e. I've got an empty cluster (see the purple "x" in the picture).

What should I do? Shall I delete it or just stop updating its value? Why?

I am aware that built-in functions (e.g., kmeans() in R) have automatic ways of dealing with this situation, but I am trying to write the standard algorithm from scratch. As soon as I fix it I'll be able to compare my results to built-in functions. At this moment I'm looking for some theoretical reasons why I should prefer one solution or another.

In the picture each colour represents a cluster according to the current iteration and each "X" is its centroid (old ones have been kept and marked with the number of the iteration in which they were computed).

[Some related links about empty cluster case, added later by @ttnphns: http://stackoverflow.com/q/41634047/868905; http://stats.stackexchange.com/q/152333/3277; http://stats.stackexchange.com/q/125655/3277; http://stats.stackexchange.com/q/13744/3277; http://stackoverflow.com/q/24919346/868905; http://stackoverflow.com/q/18009664/868905; http://stackoverflow.com/q/29243800/868905; http://stackoverflow.com/q/11075272/868905; ]