I've designed a variational autoencoder (VAE) that clusters sequential time series data. To evaluate the performance of VAE on labeled data, First, I run KMeans on the raw data and compare the generated labels with the true labels using Adjusted Mutual Info Score (AMI). Then, after the model is trained, I pass validation data to it, run KMeans on latent vectors, and compare the generated labels with the true labels of validation data using AMI. Finally, I compare the two AMI scores with each other to see if KMeans has better performance on the latent vectors than the raw data.
My question is this: How can we evaluate the performance of VAE when the data is unlabeled?
I know we can run KMeans on the raw data and generate labels for it, but in this case, since we consider the generated labels as true labels, how can we compare the performance of KMeans on the raw data with KMeans on the latent vectors?
Note: The model is totally unsupervised. Labels (if exist) are not used in the training process. They're used only for evaluation.
In unsupervised learning you evaluate the performance of a model by either using labelled data or visual analysis. In your case you do not have labelled data, so you would need to do analysis. One way to do this is by looking at the predictions. If you know how the raw data should be labelled, you can qualitatively evaluate the accuracy. Another method is, since you are using KMeans, is to visualize the clusters. If the clusters are spread apart in groups, that is usually a good sign. However, if they are closer together and overlapping, the labelling of vectors in the respective areas may be less accurate. Alternatively, there may be some sort of a metric that you can use to evaluate the clusters or come up with your own.