Constrained mixture modeling of intrinsically low-dimensional distributions

We introduce a way of modeling distributions with a low latent dimensionality our method allows for a strict control of the properties of the mapping between the latent and the feature space. Usually, as in for example generative topographic mapping, this mapping is constructed through the maximization of the log likelihood of the data set. However, if the data set is supervised, in the sense that we know the corresponding latent vector value for each feature vector; it is more sensible to use same regression method for finding the mapping in advance. The mapping is then fixed during optimization of the log likelihood of the data set. It is concluded that in terms of log likelihood the methods are comparable. The advantages however lie in the better understanding of the properties of the mapping and a clear interpretation of the latent variables