Elsevier

Journal of Neuroscience Methods

Volume 238, 30 December 2014, Pages 43-53
Journal of Neuroscience Methods

Computational Neuroscience
Spike sorting using locality preserving projection with gap statistics and landmark-based spectral clustering

https://doi.org/10.1016/j.jneumeth.2014.09.011Get rights and content

Highlights

  • An automatic unsupervised spike sorting method is proposed.

  • The method uses locality preserving projection (LPP) algorithm for feature extraction.

  • LPP features serve as inputs for the landmark-based spectral clustering (LSC) method.

  • LPP–LSC is highly accurate and computationally inexpensive spike sorting.

  • LPP–LSC can be applied into real-time spike analysis.

Abstract

Background

Understanding neural functions requires knowledge from analysing electrophysiological data. The process of assigning spikes of a multichannel signal into clusters, called spike sorting, is one of the important problems in such analysis. There have been various automated spike sorting techniques with both advantages and disadvantages regarding accuracy and computational costs. Therefore, developing spike sorting methods that are highly accurate and computationally inexpensive is always a challenge in the biomedical engineering practice.

New method

An automatic unsupervised spike sorting method is proposed in this paper. The method uses features extracted by the locality preserving projection (LPP) algorithm. These features afterwards serve as inputs for the landmark-based spectral clustering (LSC) method. Gap statistics (GS) is employed to evaluate the number of clusters before the LSC can be performed.

Results

The proposed LPP–LSC is highly accurate and computationally inexpensive spike sorting approach. LPP spike features are very discriminative; thereby boost the performance of clustering methods. Furthermore, the LSC method exhibits its efficiency when integrated with the cluster evaluator GS.

Comparison with existing methods

The proposed method's accuracy is approximately 13% superior to that of the benchmark combination between wavelet transformation and superparamagnetic clustering (WT–SPC). Additionally, LPP–LSC computing time is six times less than that of the WT–SPC.

Conclusions

LPP–LSC obviously demonstrates a win–win spike sorting solution meeting both accuracy and computational cost criteria. LPP and LSC are linear algorithms that help reduce computational burden and thus their combination can be applied into real-time spike analysis.

Introduction

Neuroscience practice extracellularly records the activity of single neurons using thin electrodes implanted in the brain. Neurons in the vicinity of the electrode tip are picked up by the extracellular recordings and thus there is a demand to determine which spike corresponds to which neuron (Fig. 1).

Neurons, which are picked up by the same electrode, can fire in response to different activities. Even when nearby neurons have similar responses, it is important to distinguish them and observe their individual tuning properties, firing characteristics, and relationship with other neurons. Spike sorting refers to the process that assigns the detected spikes of a multichannel signal into clusters based on the similarity of their shapes.

In the literature, there exist a number of methods from machine learning or statistical mechanics dealing with neural spike analysis in general or spike sorting in particular. Lewicki (1998) and Brown et al. (2004) reviewed state-of-the-art techniques and challenges in analysing neural spike training data.

Alternatively, a method that combines wavelet transformation (WT) with superparamagnetic clustering without assumptions such as low variance or Gaussian distributions was proposed in Quiroga et al. (2004). Vollgraf et al. (2005) presented a spike sorting application that uses an optimal linear filter to reduce the distortions of the peak amplitudes of action potentials in extracellular multitrode recordings.

Hill et al. (2011) on the other hand recommended that four quality metrics of false-positive and false-negative errors should accompany spike sorting regardless of the algorithm used to sort. These metrics would facilitate the assessment regarding the performance of the sorter relative to the level of contamination of the data. Oliynyk et al. (2012) constructed a new tool for fast and robust online classification of single neuron activity based on the fuzzy c-mean clustering. The method is particularly useful for the analysis of large parallel recordings, which are practically impossible or inconvenient for human supervision, and thus is helpful in the decoding of neural ensembles or other clinical applications.

An algorithm for automatic unsupervised detection of action potentials in extracellular recordings was introduced in Shalchyan et al. (2012). A new manifestation variable for detection is defined based on the combination of denoised wavelet coefficients over selected scales. Tiganj and Mboup (2012) used an iterative application of independent component analysis and a deflation technique in two nested loops for spike sorting with multi-channel recordings. Each loop of the algorithm improves the final sorting results and thus significantly increases the overall spike sorting performance.

More recently, Pillow et al. (2013) investigated the geometry of failures of traditional spike sorting algorithms and developed a sorting model, which explicitly accounts for the superposition of spike waveforms. Otherwise, a divide and conquer approach for spike sorting, which uses a modified gradient ascent clustering algorithm, was examined in Swindale and Spacek (2014). Ekanadham et al. (2014) in another approach investigated a unified sparse estimation methodology for spike sorting that iteratively optimizes both the waveform shapes and their respective spikes.

Though various methods have been suggested, obtaining high accuracy in spike sorting is always a big challenge in neuroscience and biomedical engineering. Furthermore, the computational burden in spike sorting is massive. This paper presents an integrated approach, which combines locality preserving projection (LPP) (He and Niyogi, 2004), gap statistics (GS) (Tibshirani et al., 2001), and landmark-based spectral clustering (LSC) (Chen and Cai, 2011), for a computationally inexpensive unsupervised spike sorting method. According to our best knowledge, this is the first proposal on application of the LPP for spike feature extraction, GS in determining the number of clusters, and LSC for clustering spike sorting data. The accuracy of the proposed approach is compared to the renowned benchmark spike sorting method that is a combination between the wavelet transformation (WT) and the superparamagnetic clustering (SPC) in Quiroga et al. (2004).

The arguments are organized as follows. The next section describes details of steps in the proposed methodology. Section 3 is devoted for experiments and results whilst discussions and concluding remarks are presented in Sections 4 Discussions, 5 Conclusions respectively.

Section snippets

Spike sorting methodology

The proposed methodology is graphically illustrated in Fig. 2 where LPP method is employed for spike feature extraction. The automatic unsupervised clustering is deployed by a combination of GS and LSC.

The first step in the methodology is spike detection, which aims to identify data points that form an action potential. The voltage threshold detection is utilized where the automatic threshold (Thr) is set to:Thr=4median|x|0.6745where x is the bandpass-filtered signal. For each detected spike,

Experiments and results

Datasets used for experiments in this paper are identical to those published in Quiroga et al. (2004) for ease of comparisons. Twenty datasets with different noise levels, from 0.05 to 0.2 (or 0.4 for easy clustering datasets), are simulated for experiments. Three distinct spikes having a Poisson distribution of interspike intervals with a mean firing rate of 20 Hz are presented in all datasets. The background noise reproduces spike shape variability although spikes are originated from the same

Discussions

From the experimental results, we find some cases where application of datasets with higher background noise level yields greater accuracy than those with lower noise level. For instance, in Example 1 at noise level 0.05 (0.4), accuracy of the WT–SPC method is 58.56% (87.21%) (see Table 1). Note that the noise levels may not be as important as the shape of the spikes. Although the noise levels are low but there are the cases that the shapes of clusters are difficult to cluster. This declines

Conclusions

This paper presents the integrated approach of LPP, GS and LSC for spike sorting. As per obtained results, the proposed method significantly dominates the popular existing combination of WT and SPC.

The LSC clustering method demonstrates its advantage when combined with the cluster evaluator GS. Under the automatic perspective, the comparison is absolutely convincing as the challenge to find the correct number of clusters in the proposed LPP–LSC method is as difficult as to find the appropriate

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