# Plant Electrical Signal Classification Based on Waveform Similarity

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## Abstract

**:**

## 1. Introduction

^{−}, Ca

^{2+}, K

^{+}, H

^{+}) through a cell membrane by voltage-dependent ion channels and the activity of electrogenic pump within the plasma membrane, and the ionic mechanism makes an AP an identifiable waveform within the various plant species. In theory, once a membrane potential threshold is exceeded, APs propagate with defined amplitudes, propagation speed, and a refractory period [1,2,3,4,5,6]. Unlike APs, VPs are induced by damaging stimulation—e.g., cutting, burning—and they are slower propagating than APs, having a speed of 0.5–5 mm/s in general. They are varied in diverse distance-dependent waveforms, which show longer, delayed repolarizations and a large range of variation with attenuation of amplitude and velocity. In 2009, Zimmermann and his coworkers defined a novel electrical long-distance apoplastic signal in plants—i.e., SP. They suggested that hyperpolarization events of a plasma membrane are systemically transmitted via propagating SPs (2009) [7]. For higher plants, Sukhov and Vodeneev’s research group established mathematic models to describe action potential and variation potential based on ions kinetics [8,9].

^{2+}[16] and (or) H

^{+}influxes [17,18]. In addition, electrical signals can affect physiological processes [11], e.g., respiration [18,19], changes of ATP content [20], transpiration [21], plant resistance to heating [22].

^{−}, Ca

^{2+}, K

^{+}, H

^{+}) through a cell membrane. Ions move via different ion channels and pumps in the plant, under the control of concentration and electric gradients [8,24].

## 2. Related Works

#### 2.1. Plant Electrical Signal Recognition and Classification

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_{3}16 ppm for a minute, 5 mL 3 M NaCl, and 10 mL 3 M NaCl. Eleven statistical features were extracted from plant electrical signal by linear and nonlinear methods. Then the features were trained by five classifiers including Fisher linear discriminant analysis, quadratic discriminant analysis, naive Bayes classifier (diaglinear classifiers and diagquadratic classifiers), and Mahalanobis classifier. Using the five classifiers, then the average accuracy of classification was 70%, and the best individual accuracy was 73.67% [47]. The forward and inverse modelling approaches for prediction of light stimulus from electrophysiological response in plants were established by Chatterjee and his coworkers [48].

#### 2.2. Time Series Waveform Recognition and Classification

#### 2.2.1. Artifacts Reduction

#### 2.2.2. Recognition of Waveform in Time Series

#### 2.2.3. Features Extraction and Classification

## 3. Materials and Methods

#### 3.1. Our Proposed Method

#### 3.1.1. Data Preprocessing

#### 3.1.2. Recognizing Algorithm for Plant Electrical Signals

Algorithm 1: AP extraction. |

Input: Raw signal is represented by ST Output: Waveforms similar to AP |

BEGIN |

1. DS = Take derivative of ST by a five order central difference algorithm // Derivative. |

2. Noise_Threshold = 0.1 // Initialize noise threshold. |

3. PV = findpeaks(DS) // A search algorithm to find the peaks and valleys in DS. |

4. For i=1:N // N is the number of peaks or valleys in PV. |

5. IF amplitude of PV(i) < Noise_Threshold THEN N_Peaks = PV(i); // If peak amplitude is below Noise_Threshold, then add it into N_Peaks. |

6. Else S_Peaks = PV(i); // If peak amplitude is above Noise_Threshold, then add it into S_Peaks. |

7. ENDIF |

8. END |

9. Noise_Threshold = 0.75×Noise_Threshold + 0.25×mean(N_Peaks) // Update noise threshold |

10. For i=1:NS //NS is the number of peaks in S_Peaks |

11. S_Peaks_left_Position(i) = Search the left part of S_Peaks(i) //Search for start point on the left of S_Peaks(i) |

12. S_Peaks_right_Position(i) = Search the right part of S_Peaks(i) // Search for end point on the right of S_Peaks(i) |

13. END |

14. For i=1:NS-1 //NS is the number of peaks in S_Peaks |

15. IF S_Peaks_left_Position(i+1) < S_Peaks_right_Position(i) // For overlap AP signals, separate them by resetting the end position of last AP and start position of next AP. . |

16. THEN L = S_Peaks_right_Position(i) - S_Peaks_left_Position(i+1); L1 = L –$\lfloor L/2\rfloor $; L2 = $\lfloor L/2\rfloor $; S_Peaks_right_Position(i) = S_Peaks_right_Position(i) − L1; S_Peaks_left_Position(i+1) = S_Peaks_left_Position(i+1) + L2 ; |

17. ENDIF |

18. END |

19. For i=1:NS-1 //NS is the number of peaks in S_Peaks |

20. IF Amplitude(S_Peaks(i)) < 5 mv&&Duration(S_Peaks(i))<1s // remove the s_peak point if they meet these conditions |

21. THEN Remove S_Peaks(i) |

22. ENDIF |

23. END |

24. For i=1:NS’-1 // NS’ is the number of peaks in S_Peaks |

25. IF S_Peaks_left_Position(i+1) == S_Peaks_right_Position(i)|| S_Peaks_left_Position(i+1) == S_Peaks_right_Position(i) + 1 // For adjacent monophasic AP signals, merge them into one APs. |

26. THEN // Merge the two APs into one AP S_Peaks_right_Position(i) = S_Peaks_right_Position(i+1); Delete S_Peaks(i+1), S_Peaks_left_Position(i+1) and S_Peaks_right_Position(i+1). |

27. ENDIF |

28. END |

29. END |

#### 3.1.3. Template Matching Algorithm to Classify AP

Algorithm 2: Template matching algorithm to classify AP. |

Input: Raw signal represented by ST, AP template represented by AT in database |

Output: AP, non-AP |

1. Normalize ST and AT // Normalize ST and AT by Equation (2) |

2. Align ST with AT // STs are properly aligned with templates |

Append-Threshold = 0.91; // |

Update-threshold = 0.95; // |

3. corr = Pearson correlation coefficient between ST and AT // Computing PCC |

4. IF corr < Append-Threshold |

ST is not an AP signal, reject it. |

Return FALSE; |

ENDIF |

5. IF corr> = Append-Threshold && corr < Update-threshold |

Add ST into APTemp // Add ST into AP Template library |

Return TURE; |

ENDIF |

6.IF corr >Update-threshold |

Merge ST with APTemp; |

Return TURE; |

ENDIF |

#### 3.1.4. Features Extraction from AP

#### 3.2. BP-ANNs

#### 3.3. SVM

#### 3.4. Deep Learning Algorithm

## 4. Results

#### 4.1. Classification Results of Our Proposed Method

#### 4.1.1. Experimental Data

#### 4.1.2. AP Waveform Recognition Results

#### 4.1.3. Template Matching Results

#### 4.1.4. Features of AP waveforms

#### 4.2. Classification Results of BP-ANNs

#### 4.3. Classification Results of SVM

#### 4.4. Classification Results of Deep Learning Method

## 5. Discussion

## 6. Conclusions

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 5.**Extracellular recording sketch. S1 and S2 are stimulating electrodes; S1 is the anode. E1, E2, E3, and E4 are measuring electrodes; R represents reference electrode and is placed in the node of stem, with respect to the ground. The distance between S2 and E1 is 2 cm, and there is 0.2–0.3 cm between adjacent measuring electrodes.

**Figure 6.**AP of cucumber (

**a**) Raw signal; (

**b**) Frequency spectrum of raw signal; (

**c**) Frequency spectrum of raw signals in log scale; (

**d**) Signal after filtering.

**Figure 8.**Electrical signals induced by electrical stimulation. Green circle indicates artifact, blue rectangle indicates sub threshold response, and red rectangle indicates AP.

**Figure 9.**(

**a**) First two principle components scatter plot; (

**b**) First three principle components scatter plot.

Expression | Definition | Advantages | Disadvantages |
---|---|---|---|

Euclidean distance $D(X,Y)=\sqrt{{\displaystyle \sum _{i=1}^{N}{({x}_{i}-{y}_{i})}^{2}}}$ | Calculating the distance of two time series in N-dimensional space | Simple, and supports high-dimensional data | Sensitive to data shift and noise. The length of two time series must be same |

DTW $\begin{array}{l}D({x}_{i},{y}_{i})=DISTANCE({x}_{i},{y}_{j})+\\ \mathrm{min}[D({x}_{i-1},{y}_{j}),D({x}_{i},{y}_{j-1}),D({x}_{i-1},{y}_{j-1})]\end{array}$ | DTW is an algorithm for measuring the similarity between two temporal sequences with different length | Estimate the similarity of two time series with unequal length | O(N^{2}) for computing complexity |

Classification | Feature Parameters |
---|---|

Time-domain features (seven items) | Amplitude, Duration, Rising duration, Decline duration, Rising slope, Decline slope, Area |

Statistics characteristics (five items) | Skewness, Kurtosis, Hjorth: Hjorth activity, Hjorth mobility, Hjorth complexity |

Frequency-domain features (two items) | Average power, Energy |

Nonlinear features (five items) | Permutation entropy, Sample entropy, Correlation dimension (CD), LLE, Hurst exponent |

Append-Threshold | Update-Threshold | Accuracy | The Number of New Templates |
---|---|---|---|

0.89 | 0.95 | 95.4% | 38 |

0.9 | 0.95 | 95.4% | 27 |

0.91 | 0.95 | 96.0% | 24 |

0.92 | 0.95 | 95.7% | 21 |

0.93 | 0.95 | 92.1% | 19 |

0.94 | 0.95 | 87.5% | 13 |

0.95 | 0.96 | 85.4% | 13 |

Features | Non-AP (Mean ± S.E.M.) | AP (Mean ± S.E.M.) |
---|---|---|

Amplitude * (mV) | 14.33 ± 9.90 | 20.57 ± 12.55 |

Durations * (s) | 8.01 ± 4.35 | 9.75 ± 5.05 |

Rising duration * (s) | 2.36 ± 1.31 | 3.00 ± 1.62 |

Decline duration * (s) | 5.75 ± 3.61 | 6.85 ± 4.22 |

Rising slope * (mv/s) | 6.78 ± 6.19 | 8.42 ± 7.47 |

Decline slope (mv/s) | 2.64 ± 2.13 | 2.90 ± 2.61 |

Area | 4749.01 ± 7728.3 | 6078.16 ± 11,038.49 |

Skewness | −0.57 ± 0.71 | −0.50 ± 0.65 |

Kurtosis | 2.80 ± 1.33 | 2.70 ± 0.82 |

Hjorth activity * | 27.27 ± 34.44 | 48.82 ± 54.37 |

Hjorth mobility * | 0.16 ± 0.10 | 0.14 ± 0.07 |

Hjorth complexity * | 1.89 ± 0.71 | 2.17 ± 0.91 |

Energy * | 740,601.4 ± 1,415,709 | 1,207,443 ± 2,076,630 |

Average power * | 8065.49 ± 15,968.75 | 11,440.17 ± 18,881.54 |

Permutation entropy | 0.83 ± 0.25 | 0.82 ± 0.19 |

Sample entropy | 0.05 ± 0.05 | 0.05 ± 0.05 |

Correlation dimension | 0.75 ± 0.24 | 0.74 ± 0.22 |

LLE * | −0.07 ± 0.07 | −0.05 ± 0.04 |

Hurst | 0.99 ± 0.07 | 0.99 ± 0.04 |

First Principle Component | Second Principle Component | Third Principle Component | Fourth Principle Component | Fifth Principle Component | |
---|---|---|---|---|---|

Eigenvalue | 0.2700 | 0.0770 | 0.0285 | 0.0128 | 0.0078 |

Percentage | 65.89% | 18.80% | 6.96% | 3.13% | 1.91% |

Accumulated percentage | 65.89% | 84.68% | 91.65% | 94.78% | 96.69% |

Units Number | Accuracy | Run Time |
---|---|---|

20 | 79.7% | 2704 s |

16 | 84.8% | 5340 s |

12 | 81.5% | 34,727 s |

8 | 84.1% | 65,664 s |

4 | 83.5% | 20,687 s |

First Principle Component | Second Principle Component | Third Principle Component | Fourth Principle Component | Fifth Principle Component | |
---|---|---|---|---|---|

Accuracy | 55.6% | 66.7% | 75.8% | 76.7% | 77.3% |

Kernel Function | Range of Parameters | Interval | Selected Parameters | Highest Accuracy |
---|---|---|---|---|

Quadratic kernel ${\left[\left({x}_{i}\cdot {x}_{j}\right)+1\right]}^{b}$ | b = 2 | 0 | b = 2 | 62.96% |

Polynomial kernel ${\left[\left({x}_{i}\cdot {x}_{j}\right)+1\right]}^{b}$ | b = 3 | 0 | b = 3 | 74.07% |

Gaussian Radial Basis Function $\mathrm{exp}(-\frac{|{x}_{i}-{x}_{j}{|}^{2}}{2{\sigma}^{2}})$ | $\sigma =[0.1,3]$ | 0.1 | $\sigma =1.9$ | 77.59% |

Sigmoid kernel $\mathrm{tanh}(\gamma \times ({x}_{i}-{x}_{j})+c)$ | $\gamma =[0.1,5]$ $c=[-5,-0.1]$ | 0.1 | $\gamma =0.1$ c = −0.3 | 78.17% |

Number of Second Hidden Units | Number of Third Hidden Units | Number of Fourth Hidden Units | Selected Parameters | Highest Accuracy | |
---|---|---|---|---|---|

Range | [40, 200] | [8, 24] | [4, 8] | Multiple selections | 77.4% (3 hidden layers) |

Interval | 40 | 4 | 4 | Multiple selections | 77.4% (4 hidden layers) |

Classifier | Accuracy | Average Running Time | Sensitivity | Specificity | Positive Predictive Value (PPV) | Negative Predictive Value (NPV) |
---|---|---|---|---|---|---|

Template matching | 96.0% | 3.20 s | 96.6% | 94.8% | 97.8% | 91.9% |

BP neural network | 84.8% | 5340 s | 74.9% | 52% | 89.7% | 27.1% |

SVM | 78.2% | 2.1 s | 89.5% | 95.8% | 98.7% | 7.2% |

DBN | 77.4% | 112.06 s | 100% | 0 | 70.8% | 0 |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Chen, Y.; Zhao, D.-J.; Wang, Z.-Y.; Wang, Z.-Y.; Tang, G.; Huang, L.
Plant Electrical Signal Classification Based on Waveform Similarity. *Algorithms* **2016**, *9*, 70.
https://doi.org/10.3390/a9040070

**AMA Style**

Chen Y, Zhao D-J, Wang Z-Y, Wang Z-Y, Tang G, Huang L.
Plant Electrical Signal Classification Based on Waveform Similarity. *Algorithms*. 2016; 9(4):70.
https://doi.org/10.3390/a9040070

**Chicago/Turabian Style**

Chen, Yang, Dong-Jie Zhao, Zi-Yang Wang, Zhong-Yi Wang, Guiliang Tang, and Lan Huang.
2016. "Plant Electrical Signal Classification Based on Waveform Similarity" *Algorithms* 9, no. 4: 70.
https://doi.org/10.3390/a9040070