# Advancing Spike Sorting Through Gradient‐Based Preprocessing and Nonlinear Reduction With Agglomerative Clustering

## TL;DR

This paper introduces a new automated method for spike sorting that improves accuracy by combining preprocessing and clustering techniques.

## Contribution

The novel framework combines gradient-based preprocessing with nonlinear dimensionality reduction and agglomerative clustering for spike sorting.

## Key findings

- GSA-Spike and GUA-Spike achieved 100% accuracy for non-overlapping spikes and over 99% for overlapping spikes.
- The models showed a 12% improvement in accuracy on challenging dataset portions.
- The proposed method outperformed state-of-the-art methods in unit detection and spike clustering.

## Abstract

Spike sorting is the process of separating electrical events produced by individual neurons in the nervous system, known as “spikes.” Accurate spike sorting is vital because it significantly impacts the reliability of all future analyses. Although several semi‐automated and fully automated spike‐sorting algorithms have been developed, their classification accuracy often proves insufficient. This has led researchers to resort to manual sorting, despite its time‐consuming and labor‐intensive nature. In certain conditions and for specific neuron populations, manual sorting can also be inefficient due to the presence of visually indistinguishable similarities between spikes. This underscores the necessity for the development of fully automated spike‐sorting methods capable of achieving high accuracy.

Unsupervised mathematical methods in spike sorting possess an advantage over supervised machine learning and deep learning models as they require no training and involve lower computational costs. The spike‐sorting methodology comprises two key steps: data preprocessing and spike classification. In this proposed method, a mathematical technique for data preprocessing is introduced, and nonlinear transformations are incorporated to optimally extract features from spike waveforms. The objective is to extract highly informative features that effectively separate clusters by harnessing advanced transforms, specifically uniform manifold approximation and projection (UMAP) and spectral embedding. The feature extraction process is centered around capturing inherent variations in spike waveforms, assuming that strong signal correlations enable the extraction of optimal features. Finally, a density‐based clustering algorithm is employed for spike sorting.

On Dataset1, GSA‐Spike and GUA‐Spike attained 100% accuracy for non‐overlapping spikes and 99.47% (GSA‐Spike) and 99.21% (GUA‐Spike) accuracy for overlapping spikes on the same dataset. In the challenging portion of the dataset, our models demonstrated a 12% improvement in accuracy. Furthermore, in the synthetic data, the efficacy of our proposed models was evident in both unit detection and spike clustering.

The findings of our research demonstrate unparalleled accuracy, surpassing the performance of other state‐of‐the‐art methods.

We propose an unsupervised spike‐sorting framework combining gradient‐based waveform preprocessing with nonlinear dimensionality reduction (UMAP/spectral embedding) and hierarchical agglomerative clustering. Our method (GSA‐Spike and GUA‐Spike) extracts noise‐robust features via nth‐order temporal derivatives, projects data into optimized low‐dimensional manifolds to resolve overlapping spikes, and clusters using silhouette‐guided merging.