Elsevier

Neurocomputing

Volume 69, Issues 7–9, March 2006, Pages 975-978
Neurocomputing

Letters
Solving alignment problems in neural spike sorting using frequency domain PCA

https://doi.org/10.1016/j.neucom.2005.06.006Get rights and content

Abstract

The principal component analysis (PCA) is a popular projection method in neural spike sorting. When the waveforms extracted from a spike train are aligned incorrectly, however, the projection performance of the PCA deteriorates drastically, and the clustering errors multiply. This drawback is taken care of by the frequency domain PCA in this paper. By experiments, it is shown that the proposed approach maintains good projection performance under considerable alignment errors of the waveforms.

Introduction

Various techniques have been proposed for neural spike sorting. Most of them share the common structure shown in Fig. 1 (without “Transform to Frequency Domain”) for unsupervised cases, that is, when no prior information is available. The raw neural signal from the electrode first goes through an action potential detector, and the detected waveforms are cut out for further processing. The resulting waveforms are then mapped to lower-dimensional feature vectors for clustering and classification. The principal component analysis (PCA) [9] and the fuzzy c-means (FCM) algorithm [5] are widely used as the projection and the clustering method, respectively, mainly because of their good performance and fastness. As a reference point for the waveform extraction, conventional methods use mainly the dominant extrema of action potentials. In noisy environments, which are becoming more important when considering prosthesis applications, however, the extrema of the waveforms are often damaged and cause significant misalignment problems. The effect of noise on the projection process can be divided into two. One is the changes in the amplitude of the waveforms and is called the “amplitude error”. The other is the “alignment error” which is caused by shifted reference points for the waveform extraction due to the damaged extrema. Since the alignment affects the projection bases in the PCA, the performance of the PCA and the subsequent FCM heavily depends on the accuracy of the waveform alignment.

We therefore propose two frequency domain PCAs that are robust to the alignment errors. The proposed algorithms use the frequency domain representations of the waveforms to eliminate the dependency on the alignment errors. Note that our method therefore includes an extra block, called “Transform to Frequency Domain” in Fig. 1. Experiments show that the proposed approaches give good projection performance and noticeably reduce clustering errors.

Section snippets

Frequency domain PCA

The PCA is a method of transforming a set of vectors into those of a lower dimension such that the latter are as widely separated as possible [9]. In the spike sorting problem, each input vector is a sampled waveform of length N corresponding to an action potential and is cut out from a longer waveform containing multiple action potentials and noise. When it is cut out, the reference point for aligning the action potential is usually its dominant extremum. The position of an extremum can be

Simulation results and conclusions

To evaluate the proposed methods, computer simulations are performed on spikes derived from real neural signals. Seventy real action potential templates are collected both from real recordings and from the literature, and three from the collection are used in each simulation. The noise is generated by AR modeling of the background noise obtained from real recordings. The signal to noise ratio (SNR) is defined as follows:SNR(dB)=20log10Peak to peak of signalσNoise.

The MTEO [1], PCA, and FCM are

Acknowledgements

This work was supported by Brain Korea 21 Project in 2004 and by the Nano Bioelectronics and Systems Research Centre of Seoul National University, which is an ERC supported by the Korean Science and Engineering Foundation (KOSEF).

Hae Kyung Jung received his B.S. and M.S. degrees in Electrical Engineering and Computer Science from the Seoul National University, Seoul, Korea, in 1999 and 2001, respectively, where he is currently pursuing his Ph.D. degree in the School of Electrical Engineering and Computer Sciences.

His research interests include multimedia signal processing, digital watermarking and biomedical signal processing.

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Hae Kyung Jung received his B.S. and M.S. degrees in Electrical Engineering and Computer Science from the Seoul National University, Seoul, Korea, in 1999 and 2001, respectively, where he is currently pursuing his Ph.D. degree in the School of Electrical Engineering and Computer Sciences.

His research interests include multimedia signal processing, digital watermarking and biomedical signal processing.

Joon Hwan Choi received his B.S. and M.S. degrees in Electrical Engineering and Computer Science from the Seoul National University, Seoul, Korea, in 2001 and 2003, respectively, where he is currently pursuing his Ph.D. degree in the School of Electrical Engineering and Computer Sciences.

His research interests include biomedical signal processing and pattern recognition.

Taejeong Kim received his B.S. degree from the Seoul National University, Seoul, Korea, in 1976, his M.S. degree from the Korea Advanced Institute of Science and Technology in 1978, and his Ph.D. degree from the University of Michigan, Ann Arbor, in 1986, all in Electrical Engineering.

From 1978 to 1981, he was a Researcher at the Electronic Telecommunications Research Institute, Daejon, Korea. From 1986 to 1988, he was a member of the technical staff at AT&T Bell Laboratories, Murray Hill, NJ. Since 1988, he has been with the Seoul National University, where he is currently a Professor in the School of Electrical Engineering and the Institute of New Media and Communications. His research interests include source coding and statistical signal processing.

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