  Reducing dimensionality is a key preprocessing step in many data analysis
applications to address the negative effects of the curse of dimensionality and
collinearity on model performance and computational complexity, to denoise the
data or to reduce storage requirements. Moreover, in many applications it is
desirable to reduce the input dimensions by choosing a subset of variables that
best represents the entire set without any a priori information available.
Unsupervised variable selection techniques provide a solution to this second
problem. An autoencoder, if properly regularized, can solve both unsupervised
dimensionality reduction and variable selection, but the training of large
neural networks can be prohibitive in time sensitive applications. We present
an approach called Recovery of Linear Components (RLC), which serves as a
middle ground between linear and non-linear dimensionality reduction
techniques, reducing autoencoder training times while enhancing performance
over purely linear techniques. With the aid of synthetic and real world case
studies, we show that the RLC, when compared with an autoencoder of similar
complexity, shows higher accuracy, similar robustness to overfitting, and
faster training times. Additionally, at the cost of a relatively small increase
in computational complexity, RLC is shown to outperform the current
state-of-the-art for a semiconductor manufacturing wafer measurement site
optimization application.
