Using variable length data inputs with EM algorithm clustering

Question

We have a set of sequences with taxi positions. We want to cluster the data by considering the sequential patterns in the data lines. For example: T1, T2, T3, T4 be the travels and a,b,c,d,e be set of places. The data we have is like,

• T1 b c b a d
• T2 a
• T3 a b a b a b c e d
• T4 b c d c b d c a

But the problem is the length of the data are not variable. How can we cluster these type of data using EM. Since it does not accept variable length data is there way we can customize it.

Answer 1

EM is a general principle. You can use it with very different models.

Probably the most popular model for EM is Gaussian Mixture Modeling, GMM.

Naturally, if you use covariances, GMM requires a fixed dimensionality.

But if you use other models, there is no reason it cannot work with variable length vectors. For example, there are EM variants that process text data, and text usually does have different length.