Input-Training Neural Networks (IT-nets) are a nonlinear method for data dimensionality reduction. Starting from a large set of original variables (sensor measurements), an IT-net is trained to determine a smaller set of latent variables and a (neural-network based) model for reproducing the original variables from the latent ones. IT-nets achieve this task through input training, in which each input pattern (containing values of the latent variables) is not fixed but adjusted along with internal network parameters to reproduce its corresponding output pattern (the values of the original variables). Once trained, the network can be used to determine the latent variables (as trained inputs) for any new pattern of measured variables. Dimensionality reduction with IT-net allows process monitoring tasks such as missing sensor replacement, sensor error detection and rectification.