I am a software developer struggling to understand which clustering method/algorithm would be most appropriate to spatially group 2-dimensional point data (x,y) that is arranged over a time series (an example might be location data as someone moves around a 2D map).
I've read up on techniques such as K-Means, but it doesn't seem like it would respect the ordering of the data at all.
In terms as simplistic as I can explain;
* The sample size is variable.
* I will not know the number of clusters that the algorithm should produce ahead of time. The number of clusters is also not linked to the sample size in any meaningful way.
* I will be able to provide the maximum area/spread that a cluster should cover (in other words; how tightly grouped the points must be to be considered part of the same cluster).
* I will want to ignore outliers to these clusters as the point data may have erroneous values.
* The exact time stamps are not important, but the ordering of the data is critical. For example if the series of points was focussed around a central point 'A', moved away to be focussed around a central point 'B', and then returned to be focussed around a central point near 'A' again, the ordering of the data should dictate that there should be at least 3 clusters produced, rather than the 2 that I believe K-means clustering would produce.
I appreciate you reading this far and thank you for any help you can give me.
I intend to post this same query on mathforum.org, mymathforum.com, mathhelpforum.com and mathoverflow.net (and possibly any other active forums I might find). I hope this is not unacceptable duplication.