Table 3 Neurophysiological features of each spike characterizing the process of creating objects (24D feature-vectors).

From: Spike sorting based on shape, phase, and distribution features, and K-TOPS clustering with validity and error indices

 

Number

Name

Algebraic definition

Shape

F1

Waveform duration of the FD of the action potential

tP5 − tP1

F2

Peak-to-valley amplitude of the FD of the action potential

\({{\rm{a}}}_{{{\rm{FD}}}_{{\rm{P}}4}}-{{\rm{a}}}_{{{\rm{FD}}}_{{\rm{P}}2}}\)

F3

Valley-to-valley amplitude of the FD of the action potential

\({{\rm{a}}}_{{{\rm{F}}{\rm{D}}}_{{\rm{P}}6}}-{{\rm{a}}}_{{{\rm{F}}{\rm{D}}}_{{\rm{P}}2}}\)

F4

Correlation coefficient between the FD of the action potential (ap) and the reference spike-waveform (ref), considering their corresponding standard deviation σFD

\(\frac{{\sigma }_{{{\rm{FD}}}_{\mathrm{ap},\mathrm{ref}}}^{2}}{{\sigma }_{{{\rm{FD}}}_{{\rm{ap}}}}\cdot {\sigma }_{{{\rm{FD}}}_{{\rm{ref}}}}}\,\,\)

F5

Logarithm of the positive deflection of the FD of the action potential

\(\mathrm{log}(\frac{{{\rm{a}}}_{{{\rm{FD}}}_{{\rm{P}}4}}-{{\rm{a}}}_{{{\rm{FD}}}_{{\rm{P}}2}}}{{{\rm{t}}}_{{\rm{P}}4}-{{\rm{t}}}_{{\rm{P}}2}})\)

F6

Negative deflection of the FD of the action potential

\(\frac{{{\rm{a}}}_{{{\rm{FD}}}_{{\rm{P}}6}}-{{\rm{a}}}_{{{\rm{FD}}}_{{\rm{P}}4}}}{{{\rm{t}}}_{{\rm{P}}6}-{{\rm{t}}}_{{\rm{P}}4}}\)

F7

Logarithm of the slope among valleys of the FD of the action potential

\(\mathrm{log}(\frac{{{\rm{a}}}_{{{\rm{FD}}}_{{\rm{P}}6}}-{{\rm{a}}}_{{{\rm{FD}}}_{{\rm{P}}2}}}{{{\rm{t}}}_{{\rm{P}}6}-{{\rm{t}}}_{{\rm{P}}2}})\)

F8

Root-mean-square of pre-event amplitudes of the FD of the action potential

\(\sqrt{\frac{{{\rm{a}}}_{{{\rm{FD}}}_{{\rm{P}}1}}+{\sum }_{i\,=\,m-1}^{1}\,{{\rm{a}}}_{i}}{m}}\)

F9

Negative slope ratio of the FD of the action potential

\((\frac{{{\rm{a}}}_{{{\rm{FD}}}_{{\rm{P}}2}}-{{\rm{a}}}_{{{\rm{FD}}}_{{\rm{P}}1}}}{{{\rm{t}}}_{{\rm{P}}2}-{{\rm{t}}}_{{\rm{P}}1}})/(\frac{{{\rm{a}}}_{{{\rm{FD}}}_{{\rm{P}}3}}-{{\rm{a}}}_{{{\rm{FD}}}_{{\rm{P}}2}}}{{{\rm{t}}}_{{\rm{P}}3}-{{\rm{t}}}_{{\rm{P}}2}})\)

F10

Positive slope ratio of the FD of the action potential

\((\frac{{{\rm{a}}}_{{{\rm{FD}}}_{{\rm{P}}4}}-{{\rm{a}}}_{{{\rm{FD}}}_{{\rm{P}}3}}}{{{\rm{t}}}_{{\rm{P}}4}-{{\rm{t}}}_{{\rm{P}}3}})/(\frac{{{\rm{a}}}_{{{\rm{FD}}}_{{\rm{P}}5}}-{{\rm{a}}}_{{{\rm{FD}}}_{{\rm{P}}4}}}{{{\rm{t}}}_{{\rm{P}}5}-{{\rm{t}}}_{{\rm{P}}4}})\)

F11

Peak-to-valley ratio of the FD of the action potential

\(\frac{{{\rm{a}}}_{{{\rm{FD}}}_{{\rm{P}}2}}}{{{\rm{a}}}_{{{\rm{FD}}}_{{\rm{P}}4}}}\)

Phase

F 12

Amplitude of the FD of the action potential relating to P1

\({{\rm{a}}}_{{{\rm{FD}}}_{{\rm{P}}1}}\)

F13

Amplitude of the FD of the action potential relating to P3

\({{\rm{a}}}_{{{\rm{FD}}}_{{\rm{P}}3}}\)

F14*

Amplitude of the FD of the action potential relating to P4

\({{\rm{a}}}_{{{\rm{FD}}}_{{\rm{P}}4}}\)

F 15

Amplitude of the FD of the action potential relating to P5

\({{\rm{a}}}_{{{\rm{FD}}}_{{\rm{P}}5}}\)

F16

Amplitude of the FD of the action potential relating to P6

\({{\rm{a}}}_{{{\rm{FD}}}_{{\rm{P}}6}}\)

F17

Amplitude of the SD of the action potential relating to P1

\({{\rm{a}}}_{{{\rm{SD}}}_{{\rm{P}}1}}\)

F 18 *

Amplitude of the SD of the action potential relating to P3

\({{\rm{a}}}_{{{\rm{SD}}}_{{\rm{P}}3}}\)

F19*

Amplitude of the SD of the action potential relative to P5

\({{\rm{a}}}_{{{\rm{SD}}}_{{\rm{P}}5}}\)

Distribution

F20

Inter-quartile range (Q3 − Q1) of the FD of the action potential, considering the percentiles \({{\rm{P}}}_{{75}_{{\rm{FD}}}}\) and \({{\rm{P}}}_{{25}_{{\rm{FD}}}}\)

\({{\rm{P}}}_{{75}_{{\rm{FD}}}}-{{\rm{P}}}_{{25}_{{\rm{FD}}}}\)

F21

Inter-quartile range (Q3 − Q1) of the SD of the action potential, considering the percentiles \({{\rm{P}}}_{{75}_{{\rm{SD}}}}\) and \({{\rm{P}}}_{{25}_{{\rm{SD}}}}\)

\({{\rm{P}}}_{{75}_{{\rm{SD}}}}-{P}_{{25}_{{\rm{SD}}}}\)

F22

Kurtosis coefficient of the FD of the action potential, considering the fourth sampling moment of n amplitudes \({{\rm{a}}}_{{{\rm{FD}}}_{i}}\) about its mean \(\overline{{{\rm{a}}}_{{\rm{FD}}}}\), and the standard deviation σFD

\(\,\frac{{\sum }_{i=1}^{n}\,{({{\rm{a}}}_{{{\rm{FD}}}_{i}}-\overline{{{\rm{a}}}_{{\rm{FD}}}})}^{4}}{n\cdot {\sigma }_{{\rm{FD}}}^{4}}\)

F23

Fisher asymmetry of the FD of the action potential, considering the third sampling moment of n amplitudes \({{\rm{a}}}_{{{\rm{FD}}}_{i}}\) about its mean \(\overline{{{\rm{a}}}_{{\rm{FD}}}}\), and the standard deviation σFD

\(\frac{{\sum }_{i=1}^{n}\,{({{\rm{a}}}_{{{\rm{FD}}}_{i}}-\overline{{{\rm{a}}}_{{\rm{FD}}}})}^{3}}{n\cdot {\sigma }_{{\rm{FD}}}^{3}}\)

F24

Fisher asymmetry of the SD of the action potential, considering the third sampling moment of n amplitudes \({{\rm{a}}}_{{{\rm{FD}}}_{i}}\) about its mean \(\overline{{{\rm{a}}}_{{\rm{FD}}}}\), and the standard deviation σSD

\(\frac{{\sum }_{i=1}^{n}\,{({{\rm{a}}}_{{{\rm{SD}}}_{i}}-\overline{{{\rm{a}}}_{{\rm{SD}}}})}^{3}}{n\cdot {\sigma }_{{\rm{SD}}}^{3}}\)

  1. List of shape (F1–F11), phase (F12–F19), and distribution (F20–F24) features and their algebraic definition (see graphic representation in Fig. 3), considering the first derivative (FD) and the second derivative (SD) of each action potential. The three common features (F14, F18 and F19) proposed also by other authors19,20 (see Table 1) are marked with an asterisk.
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