# Nonparametric collective spectral density estimation with an application to clustering the brain signals

## TL;DR

This paper introduces a nonparametric method for jointly estimating spectral density functions of multiple time series, enabling improved estimation, visualization, and clustering of brain signals based on their spectral features.

## Contribution

It proposes a collective spectral density estimation technique using basis functions and a low-dimensional manifold, enhancing efficiency and enabling clustering of brain signals.

## Key findings

- Improved spectral density estimation accuracy.
- Effective clustering of EEG signals based on spectral features.
- Visualization tools for spectral density analysis.

## Abstract

In this paper, we develop a method for the simultaneous estimation of spectral density functions (SDFs) for a collection of stationary time series that share some common features. Due to the similarities among the SDFs, the log-SDF can be represented using a common set of basis functions. The basis shared by the collection of the log-SDFs is estimated as a low-dimensional manifold of a large space spanned by a pre-specified rich basis. A collective estimation approach pools information and borrows strength across the SDFs to achieve better estimation efficiency. Also, each estimated spectral density has a concise representation using the coefficients of the basis expansion, and these coefficients can be used for visualization, clustering, and classification purposes. The Whittle pseudo-maximum likelihood approach is used to fit the model and an alternating blockwise Newton-type algorithm is developed for the computation. A web-based shiny App found at "https://ncsde.shinyapps.io/NCSDE" is developed for visualization, training and learning the SDFs collectively using the proposed technique. Finally, we apply our method to cluster similar brain signals recorded by the electroencephalogram for identifying synchronized brain regions according to their spectral densities.