Gaussian Mean Shift Clustering
I have heard a lot of about Gaussian mean shift clustering as it is very popular, easy to implement, and one of the best for object tracking in video. Recently I have been working on structure learning, and one of my recent work is to say (in fact, boast, wahahahaha…just kidding) that structure learning can be a more general case of those classic clustering algorithms like k-mean, LBG-vector quantization, mean shift and EM algorithm. So I have to find some algorithms to compare with mine. The algorithm that I want to compare with has to come up with the number of clusters automatically once the covariance matrix or kernel width is known, so I think about LBG-VQ and Gaussian mean shift (GMS). When deriving GMS, I found that it’s very similar to the mean update equation of EM algorithm except that in EM we try to estimate the , so we take derivative w.r.t. . Unlike EM, in GMS, we take derivative w.r.t. each sample point in the space. However, in Gaussian distribution we have the term whose derivative and have opposite sign, therefore when equating the derivative to zero, we will get similar update equation.
the update equation as
which very similar to mean update in EM algorithm for mixture of Gaussian.