Quadratic component analysis

I present a method for analyzing multichannel recordings in response to repeated stimulus presentation. Quadratic Component Analysis (QCA) extracts responses that are stimulus-induced (triggered by the stimulus but not precisely locked in time), as opposed to stimulus-evoked (time-locked to the stimulus). Induced responses are often found in neural response data from magnetoencephalography (MEG), electroencephalography (EEG), or multichannel electrophysiological and optical recordings. The instantaneous power of a linear combination of channels can be expressed as a weighted sum of instantaneous cross-products between channel waveforms. Based on this fact, a technique known as Denoising Source Separation (DSS) is used to find the most reproducible "quadratic component" (linear combination of cross-products). The linear component with a square most similar to this quadratic component is taken to approximate the most reproducible evoked activity. Projecting out the component and repeating the analysis allows multiple induced components to be extracted by deflation. The method is illustrated with synthetic data, as well as real MEG data. At unfavorable signal-to-noise ratios, it can reveal stimulus-induced activity that is invisible to other approaches such as time-frequency analysis.