Dimensionality reduction without select components
It would be helpful to know a bit better what you're trying to achieve and why the selection of a specific number of eigenvalues bothers you.
From the generic information you gave it seems you're aiming at training a model on a compressed/dense representation of several features, in which case I would suggest to train an autoencoder (or something similar), on top of which you could then train whatever classifier you need.
Otherwise if the problem relies only on the amount of features you have you could try with some feature selection strategies