# Large scale Lasso with windowed active set for convolutional spike sorting

## TL;DR

This paper introduces a scalable, parallelizable active set algorithm for large-scale convolutional Lasso problems in spike sorting, enabling efficient processing of extensive neural datasets and potential online application.

## Contribution

A novel active set algorithm for convolutional Lasso that is efficient, scalable, and suitable for parallel implementation, advancing large-scale spike sorting capabilities.

## Key findings

- Linear complexity with respect to temporal data size.
- Effective spike recovery demonstrated in experiments.
- Robustness to regularization parameter variations.

## Abstract

Spike sorting is a fundamental preprocessing step in neuroscience that is central to access simultaneous but distinct neuronal activities and therefore to better understand the animal or even human brain. But numerical complexity limits studies that require processing large scale datasets in terms of number of electrodes, neurons, spikes and length of the recorded signals. We propose in this work a novel active set algorithm aimed at solving the Lasso for a classical convolutional model. Our algorithm can be implemented efficiently on parallel architecture and has a linear complexity w.r.t. the temporal dimensionality which ensures scaling and will open the door to online spike sorting. We provide theoretical results about the complexity of the algorithm and illustrate it in numerical experiments along with results about the accuracy of the spike recovery and robustness to the regularization parameter.