Efficient low-rank spectrotemporal decomposition using ADMM

Classical time-evolving spectral analysis techniques utilize a sliding window approach that fails to exploit overarching spectrotemporal structures that are known to occur in many real-world signals. In particular, many biological signals have the distinct quality of having few defining spectral characteristics. We propose an algorithm for efficiently estimating a low-rank spectrotemporal decomposition. While existing approaches yield such representations by penalizing a group norm of successive differences, our insight is that a penalty that promotes low-rank yields more flexible representations and an efficient distributed implementation. We demonstrate on simulated time series data and human electroencephalogram (EEG) recordings that this low-rank spectrotemporal decomposition can provide a spectral representation of time series that highlights salient features and reduces the effects of noise.