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Analysis of extracellular recordings of neural action potentials (known as spikes) is highly dependent upon the accuracy of neural waveform classification, commonly referred to as spike sorting. Feature extraction is an important stage of this process because it can limit the quality of clustering that is performed in the feature space. Principal components analysis (PCA) is the most commonly used feature extraction method employed for neural spike recordings. To improve upon PCA's feature extraction performance for neural spike sorting, we revisit the PCA procedure to analyze its weaknesses and describe an improved feature extraction method. This paper proposes a linear feature extraction technique that we call graph-Laplacian features, which simultaneously minimizes the graph Laplacian and maximizes variance. The algorithm's performance is compared with PCA and a wavelet-coefficient-based feature extraction algorithm on simulated single-electrode neural data. A cluster-quality metric is proposed to quantitatively measure the algorithm performance. The results show that the proposed algorithm produces more compact and well-separated clusters compared to the other approaches.