theta* = (mu, Sigma, pi)
z = latent cluster assignments
where mu, sigma, & pi are the means, covariances, and priors
i think we can show:
the constraints under which gmm++ asymptotically converges to theta* & z*
(essentially, any GMM i believe)
2) the constraints under which kmeans++ asymptotically converges to theta* and z*
i think
never for theta*
z* under certain circumstances. in particular, when k=2, and the difference of means is orthongal to principal direction of covariance, or covariance is spherically symmetric.
3) something about j-clustering. maybe if we could choose j correctly, we could get consistency and faster convergence?
theta* = (mu, Sigma, pi) z = latent cluster assignments
where mu, sigma, & pi are the means, covariances, and priors
i think we can show:
2) the constraints under which kmeans++ asymptotically converges to theta* and z* i think
3) something about j-clustering. maybe if we could choose j correctly, we could get consistency and faster convergence?