Is there a way to adaptively guess k (the number of clusters) during online k-means?

The moment you say K-means, it indicates you have knowledge of number of clusters (i.e. K) in advance and you are not going to change it later on. I believe, what you intend to ask is, is there an automatic way to adaptively changing the number of clusters as new data arrives. Normally, in online clustering you start with one sample (hence one cluster) and based on *some* criteria, you either merge or break clusters to adaptively change number of clusters; this process is not online k-means clustering but only online clustering. In online K-means clustering, you update the cluster center information for every sample and do not wait for all the samples to arrive (or else it becomes traidtional offline k-means clustering).