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Suppose I have M observation vectors, offline, $y_t$, $ t =1 ... M$, and each observation is $n$ dimensional. I then cluster these observations into $k$ clusters. For computing the clustering statistic of each observation though, I use ALL of its components, i.e. all $n$ dimensions of it.

Now a new stream of data comes in. I want to be able to assign this stream to one of the $k$ clusters. The complication is that now I want to do this classification before observing all $n$ components of it. In other words, having observed $i < n$ components of the new observation, I need to assign it to a group.

Given that the dimension of new observation is smaller than the offline ones, how would one go about the classification?

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  • $\begingroup$ Will the rest of the dimensions become available later? Will you need to continually update & reclassify the observations? When you have more data later, will you want to revisit the original cluster solution & perhaps do a new (hopefully better) clustering? $\endgroup$
    – gung - Reinstate Monica
    Aug 31, 2015 at 17:06
  • $\begingroup$ @gung Yes to all, actually. The rest would become available later, and reclassification would be desirable. However, the importance of classification is when i has many( 10 or more) missing data points $\endgroup$
    – Alex
    Aug 31, 2015 at 17:12
  • $\begingroup$ Do the coordinates fill in some fixed order? And do you believe the earlier coordinates have some predictive power over the later coordinates? $\endgroup$
    – jlimahaverford
    Sep 3, 2015 at 19:50

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The most flexible approach to me seems like a mixture model. In many cases it is possible to even train/update such a model on your incomplete data. Once trained you would be able to compute:

$$ P(Z=z | X_1=x_1, \dots, X_n=x_n), $$

Where "z"s are labels. Once this is possible conditioning on limited information is possible. This type of model would give you more flexibility than for example a distance based clustering algorithm like hierarchical or kmeans.

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