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Spike sorting technologies support neuroscientists to access the neural activity with single-neuron or single-actionpotential resolutions. However, conventional spike sorting technologies perform the feature extraction and the clustering separately after the spikes are well detected. It not only induces many redundant processes, but it also yields a lower accuracy and an unstable result especially when noises and/or overlapping spikes exist in the dataset. To address these issues, this paper proposes a unified optimization model integrating the feature extraction and the clustering for spike sorting. Unlike the widely used combination strategies, i.e., performing the principal component analysis (PCA) for spike feature extraction and the K-means (KM) for clustering in sequence, interestingly, this paper finds the solution of the proposed unified model by iteratively performing PCA and KM-like procedures. Subsequently, by embedding the K-means++ strategy in KM-like initializing and a comparison updating rule in the solving process, the proposed model can well handle the noises and overlapping interference as well as enjoy a high accuracy and a low computational complexity. Finally, an automatic spike sorting method is derived after taking the best of the clustering validity indices into the proposed model. The extensive numerical simulation results on both synthetic and realworld datasets confirm that our proposed method outperforms the related state-of-the-art approaches.

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