A dimension reduction technique applied to regression on high dimension, low sample size neurophysiological data sets

A common problem in neurophysiological signal processing is the extraction of meaningful information from high dimension, low sample size data (HDLSS). We present RoLDSIS (regression on low-dimension spanned input space), a regression technique based on dimensionality reduction that constrains the solution to the subspace spanned by the available observations. This avoids regularization parameters in the regression procedure, as needed in shrinkage regression methods.

We applied RoLDSIS to the EEG data collected in a phonemic identification experiment. In the experiment, morphed syllables in the continuum /da/-/ta/ were presented as acoustic stimuli to the participants and the event-related potentials (ERP) were recorded and then represented as a set of features in the time-frequency domain via the discrete wavelet transform. Each set of stimuli was chosen from a preliminary identification task executed by the participant. Physical and psychophysical attributes were associated to each stimulus. RoLDSIS was then used to infer the neurophysiological axes, in the feature space, associated with each attribute. We show that these axes can be reliably estimated and that their separation is correlated with the individual strength of phonemic categorization. The results provided by RoLDSIS are interpretable in the time-frequency domain and may be used to infer the neurophysiological correlates of phonemic categorization. A comparison with commonly used regularized regression techniques was carried out by cross-validation.

The prediction errors obtained by RoLDSIS are comparable to those obtained with Ridge Regression and smaller than those obtained with LASSO and SPLS. However, RoLDSIS achieves this without the need for cross-validation, a procedure that requires the extraction of a large amount of observations from the data and, consequently, a decreased signal-to-noise ratio when averaging trials. We show that, even though RoLDSIS is a simple technique, it is suitable for the processing and interpretation of neurophysiological signals.