Jean-Philippe Thivierge Google Meet link: meet.google.com/naa-bidm-gue Neocortical activity is characterized by the presence of low-dimensional fluctuations in firing rate that are coordinated across neurons [1]. Despite a wealth of experiments and models, the role of low-dimensional fluctuations remains unclear, in part due to limited data analysis techniques. While several approaches exist to perform dimensionality reduction [2], there is a lack of methods designed to extract frequency-specific, low-dimensional fluctuations from neural signals. This is true even with methods aimed at finding rotational structure in PCA [3], as these approaches suffer from a lack of frequency‐specific separation of components.
Here, we describe a technique termed frequency-separated principal components analysis (FS-PCA) that addresses this issue. This talk is organized as a tutorial where we first show toy examples that apply FS-PCA to artificial signals. Then, we provide an application of FS-PCA to both spontaneous and evoked cortical activity. Finally, we discuss the interpretation, limitations, and possible extensions of this technique to problems in systems neuroscience.
FS-PCA is based on recent theoretical advances on the eigenspectrum of Hankel matrices [4]. As a first example, we consider a sine wave with added zero-mean Gaussian noise (Fig.1a). We show that this signal can be converted to a Hankel matrix (Fig.1b) whose eigenspectrum contains 2 _f_ +1 largest eigenvalues, where _f_ is the number of characteristic frequencies of the original signal. The reconstructed signal obtained from FS-PCA closely matches the amplitude, phase, and frequency of the original signal (Fig.1c).
Next, we apply FS-PCA to population recordings from macaque V1 cortex. We show that the first dimension of the reconstructed signal captures the slow, low- frequency fluctuations in mean population activity observed over time (Fig.1d, red line). Adding further dimensions markedly improves the reconstruction of population activity (Fig.1d, blue line). Overall, ranked eigenvalues obtained from FS-PCA followed an approximate power-law where the highest ranked dimensions captured a large proportion of the data (Fig.1e). In turn, highest- ranked dimensions had a lower characteristic frequency than lower dimensions (Fig.1e, inset). In sum, these results suggest that while a broad spectrum of frequencies contributed to population activity, fluctuations in spontaneous activity were dominated by low-frequency components.
