How do I obtain the weight and variance of a k-means cluster?
It is valid to use the k-means to initialize the EM for Mixture of Gaussian modeling. As you said, the mean of each component will be the average of all samples belong to the same cluster (it depends on the used clustering algorithm, some times the centroid is not the average of the cluster but is one of the samples). for the weight you can use the following: the weight of cluster x = the number of samples belong to cluster x divided by the total number of samples. thus, the cluster with the highest number of samples is the cluster with the highest weight. for the variance: just find the variance of all samples belong to the same cluster.