Reading about the GPLVM -Gaussian Process Latent Variable Models- in the Neil D. Lawrence 2003 paper I understood how the dimensionality reduction is performed. From my understanding, the algorithm is not supervised, since the actual classes of the data are not needed when reducing the dimensionality.
To reduce the complexity of the GP, the Informative Vector Machine is used. However, reading this second paper, I understand that this method needs the actual classes assigned to the data points, and it can be therefore considered as supervised. Moreover, in this paper the classification is binary, but in the paper above we have multiple classes.
How do we extend the Informative Vector Machine to multiple classes?