Longitudinal k-means sample data Having finished the Coursera's Machine Learning course, I would like to put the theories into practice.  Thanks in advance on guiding a newbie!
In particular, I am looking forward to some guidance how to:


*

*Some sample longitudinal data that would illustrate k-means grouping

*how to include time dimension into the analysis?  Say if I collected 10 days worth of data, capturing long/lat every 5 minutes, I would expect at hour x every day there is a pattern.
 A: There are a number of very good references on this matter. Three I can immediately think of are:


*

*Functional clustering and identifying substructures of longitudinal data by Chiou and Li (2007)

*Clustering for Sparsely Sampled Functional Data by James and Sugar (2003) and 

*Distance-based clustering of sparsely observed stochastic processes by Peng and Mueller (2008)


For your particular problem, I would argue (in very short) that instead of doing the $k$-means on the data matrix themselves you calculate the principal components of your data (clearly you do this after smoothing and interpolating your data on a common grid). You would then perform the $k$-means clustering on the principal components' scores. This two-step approach will almost certainly allow you to visualize your data clustering more effectively.
Other approaches (mostly on non-parametric clustering) also exist but I think they are an overkill at this point. Jacques and Preda (2013) have recently provided an excellent survey on the matter: Functional data clustering: a survey (I tried to link to author-provided reprints where possible).
A: *

*Google's My Track android app allows output of long/lat.
However, I wrote my own client to capture the data every 5 minutes.

*Time dimension - depending on how you want to do it...  I "normalize" the data upfront to do every hour, so the grouping makes more sense.  For example
2
37.88    -122.22    11
37.88    -122.22    11
37.88    -122.22    11
37.88    -122.22    11
37.33    -122.50    12
37.33    -122.51    12
37.33    -122.52    12

The k-means algorithm, if implemented properly, can handle a matrix.  Using the coursera's machine learning exercise #8, I modified it to handle/visualize 3 dimensional data.  Not too bad.
I don't think more than 3 dimensions can be visualized, though a vectorized implementation will still work.
Cheers,
Simon
