Spike sorting plays an irreplaceable role in understanding brain codes. Traditional spike sorting technologies perform feature extraction and clustering separately after spikes are well detected. However, it may often cause many additional processes and further lead to low-accurate and/or unstable results especially when there are noises and/or overlapping spikes in datasets. To address these issues, in this paper, we proposed a unified optimisation model integrating feature extraction and clustering for spike sorting. Interestingly, instead of the widely used combination strategies, i.e., performing the principal component analysis (PCA) for spike feature extraction and K-means (KM) for clustering in sequence, we unified PCA and KM into one optimisation model, which reduces additional processes with fewer iteration times. Subsequently, by embedding the K-means++ strategy for initialising and a comparison updating rule in the solving process, the proposed model can well handle the noises and/or overlapping interference. Finally, taking the best of the clustering validity indices into the proposed model, we derive an automatic spike sorting method. Plenty of experimental results on both synthetic and real-world datasets confirm that our proposed method outperforms the related state-of-the-art approaches.
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