Label spreading for classification/clustering problems

I have a question regarding label propagation and label spreading semi-supervised algorithms. I am working on building a look-alike model to identify marketing personas. Using supervised learning algorithms is getting quite complicated as it takes a lot of time to run. And using unsupervised learning is quite complicated as well, as we need to specify k. I am unsure of how to automate this process for new datasets. I need a middle ground machine learning algorithm suggestion that has lower time complexity and is reliable for new datasets.

So my question is: Can I use a graph-based semi-supervised machine learning technique to classify my dataset into personas? Specifically, label propagation and/or label spreading?

Please let me know your thoughts and any other suggestions that you may have. Thanks in advance!