# Classification of Actigraphy Records from Bipolar Disorder Patients Using Slope Entropy: A Feasibility Study

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Dataset

#### 2.2. Preprocessing

#### 2.3. Slope Entropy

- WPE. This is one of the PE derived methods. It includes amplitude information on the PE computation. It has demonstrated a very high discriminating power and stability in a recent comparative study [17].
- SlopEn. Recently proposed, it showed a higher discriminating power than PE and WPE [20] for a disparity of records. This was the final choice, since it yielded the best classification performance in an exploratory analysis, as described in Section 3. Therefore, this will be the method described in detail next.

- 2, if $d>\gamma $.
- 1, if $d\le \gamma $ and $d>\delta $.
- 0, if $\left|d\right|\le \delta $.
- $-1$, if $d<-\delta $ and $d\ge -\gamma $.
- $-2$, if $d<-\gamma $.

^{®}source code in Appendix A). The numerical values obtained from the Shannon entropy of the relative frequencies can be normalised using a common reference in order to keep the SlopEn range within desired limits (for example, between 0 and 1). The SlopEn result of each record will be the records’ feature to be used in the classification analysis using a threshold, as described in the next section.

#### 2.4. Performance Evaluation

## 3. Experiments and Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Slopen Source Code

**function**[pe, Psi_Patt, counter] = SlopeEn(data, dim, gamma, delta)

**if**nargin < 1, error(’The data time-series must be included’),

**end**

**if**nargin < 2, dim = 6;

**end**

**if**nargin < 3, gamma = 0.94;

**end**

**if**nargin < 4, delta = 0.001;

**end**

**if**n_dp <= dim || n_dp < 10, error(’The signal is too short’),

**end**

**if**delta < 1e-12, error(’The delta parameter is too small choose number higher than 1e-12’),

**end**

**if**delta >= gamma, error(’The delta parameter has to be larger than the gamma parameter’),

**end**

**for**k = 1:n_dp-(dim-1)

**for**m = 1:dim-1

**if**lg_gamma(m)

**elseif**lg_delta(m)

**elseif**lg_ab_delta(m)

**elseif**lg_n_gamma(m)

**else**

**end**

**end**

**for**m = 1:n_patt

**if**sum(Psi_Patt(m,:) == patt) == dim-1

**break**

**end**

**end**

**if**act_match

**end**

**end**

**for**k = 1:n_patt

**end**

**end**

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**Figure 2.**Example of signals from the three classes in the experimental database. The plots shown correspond to the actigraphy data as they were captured with the monitoring device, no filtering or preprocessing yet. One day (24 h) corresponds to 2880 samples (sampling period 30 s).

**Figure 3.**Examples of the prepocessing stage and the result of activity epoch extraction. (

**a**) Moving average filtered signal from Figure 2 in order to discriminate between periods of activity and no activity. (

**b**) Epochs of activity extracted from each original record according to the threshold applied to the filtered signal. Minimum length obtained was 1000 samples. The activity part was not dependent on the state.

**Figure 4.**Example of ROC curve obtained in the experiments from which a classification threshold is computed according to the nearest point in curve to (0,1).

**Table 1.**Exploratory analysis results using several entropy methods. Significance related to differences between entropy results from each class. Only SlopEn was able to find statistically significant differences between all the signal classes pairs. It is important to note that accuracy has to be understood in terms of p, since groups are unbalanced and a high accuracy can be due to a correct classification of the most populated class, but with a very poor accuracy for the minority class. The significance p accounts for this possible variation and the Matthews Correlation Coefficient (MCC) result was also included for SlopEn with the same purpose.

SampEn | WPE | PE | BE | SlopEn | |
---|---|---|---|---|---|

Classes (dep,man) | Accuracy = 0.80 | Accuracy = 0.70 | Accuracy = 0.73 | Accuracy = 0.77 | Accuracy = 0.77 |

MCC = 0.4614 | MCC = 0.1108 | MCC = 0.3735 | MCC = 0.2548 | MCC = 0.4276 | |

$p=0.0080$ | $p=0.0697$ | $p=0.0059$ | $p=0.0093$ | $p=0.0062$ | |

$m=2,r=0.25$ | $m=6$ | $m=5$ | $m=3$ | $m=6,\gamma =0.20,\delta =1\times {10}^{-3}$ | |

Classes (dep,rem) | Accuracy = 0.67 | Accuracy = 0.65 | Accuracy = 0.67 | Accuracy = 0.65 | Accuracy = 0.65 |

MCC = 0.2535 | MCC = 0.2610 | MCC = 0.2022 | MCC = 0.2475 | MCC = 0.2465 | |

$p=0.0025$ | $p=0.0167$ | $p=0.0108$ | $p=0.0015$ | $p=0.0213$ | |

$m=3,r=0.25$ | $m=7$ | $m=7$ | $m=3$ | $m=6,\gamma =0.30,\delta =1\times {10}^{-3}$ | |

Classes (man,rem) | Accuracy = 0.68 | Accuracy = 0.61 | Accuracy = 0.62 | Accuracy = 0.61 | Accuracy = 0.68 |

MCC = 0.1531 | MCC = 0.0951 | MCC = 0.1323 | MCC = 0.2006 | MCC = 0.2206 | |

$p=0.2995$ | $p=0.4382$ | $p=0.0579$ | $p=0.1490$ | $p=0.0332$ | |

$m=3,r=0.30$ | $m=6$ | $m=7$ | $m=7$ | $m=6,\gamma =0.85,\delta =1\times {10}^{-3}$ |

**Table 2.**Fine tuning of the $\gamma $ parameter for SlopEn using a grid search and trying to maximise the performance in terms of classification accuracy linked to statistical significance. Intermediate results (from 0.30 up to 0.80) are not included, because they were not significant for man–rem until $\gamma =0.80$ was reached. For all cases $m=6$ and $\delta =1\times {10}^{-3}$.

$\gamma =0.10$ | 0.20 | 0.30 | 0.80 | 0.90 | ||

Classes (dep,man) | Se | 0.70 | 0.81 | 0.79 | 0.75 | 0.68 |

Sp | 0.69 | 0.62 | 0.62 | 0.69 | 0.75 | |

Acc | 0.70 | 0.77 | 0.75 | 0.73 | 0.70 | |

p | 0.0089 | 0.0062 | 0.0150 | 0.0053 | 0.0089 | |

Classes (dep,rem) | Se | 0.57 | 0.61 | 0.54 | 0.63 | 0.61 |

Sp | 0.67 | 0.58 | 0.68 | 0.59 | 0.59 | |

Acc | 0.64 | 0.59 | 0.65 | 0.60 | 0.60 | |

p | 0.0099 | 0.0098 | 0.0213 | 0.0357 | 0.0334 | |

Classes (man,rem) | Se | 0.59 | 0.74 | 0.73 | 0.79 | 0.65 |

Sp | 0.69 | 0.62 | 0.62 | 0.56 | 0.62 | |

Acc | 0.68 | 0.63 | 0.63 | 0.58 | 0.62 | |

p | 0.0915 | 0.0680 | 0.1284 | 0.0385 | 0.0420 |

**Table 3.**Results for a final fine tuning of the $\gamma $ parameter value for SlopEn. The optimal value was found to be $0.94$, as highlighted in the corresponding column. For all cases $m=6$ and $\delta =1\times {10}^{-3}$.

$\gamma =0.85$ | 0.86 | 0.94 | 0.95 | ||

Classes (dep,man) | Se | 0.75 | 0.73 | 0.75 | 0.73 |

Sp | 0.69 | 0.69 | 0.75 | 0.75 | |

Acc | 0.73 | 0.72 | 0.75 | 0.73 | |

p | 0.0055 | 0.0084 | 0.0077 | 0.0059 | |

Classes (dep,rem) | Se | 0.63 | 0.61 | 0.66 | 0.63 |

Sp | 0.57 | 0.59 | 0.60 | 0.60 | |

Acc | 0.58 | 0.60 | 0.61 | 0.61 | |

p | 0.0419 | 0.0457 | 0.0221 | 0.0262 | |

Classes (man,rem) | Se | 0.65 | 0.65 | 0.71 | 0.67 |

Sp | 0.69 | 0.69 | 0.62 | 0.62 | |

Acc | 0.68 | 0.68 | 0.63 | 0.63 | |

p | 0.0332 | 0.0358 | 0.0358 | 0.0379 |

Classes (dep,man) | Classes (dep,rem) | Classes (man,rem) | |
---|---|---|---|

Se | 0.74 | 0.65 | 0.66 |

Sp | 0.73 | 0.61 | 0.60 |

Acc | 0.74 | 0.62 | 0.61 |

p | 0.0132 | 0.0200 | 0.1266 |

**Table 5.**Classification accuracy achieved removing subjects with data only in one state (except for the man class).

Classes (dep,man) | Classes (dep,rem) | Classes (man,rem) | |
---|---|---|---|

Se | 0.76 | 0.64 | 0.69 |

Sp | 0.75 | 0.69 | 0.62 |

Acc | 0.76 | 0.67 | 0.64 |

p | 0.0055 | 0.0032 | 0.1316 |

**Table 6.**The results obtained using all epochs found in the experimental set with lengths $250,500,750,1000,1250,1500,1750$ and 2000, instead of only the longest one. At least one representative epoch was found in this experiment for up to length $N=1000$ from each record, whereas it was possible to draw more than one epoch in other records (That is why $n=3198$ for $N=250$, but only $n=149$ for $N=2000$, some records were not included in the experiment in that case). Each column refers to records of the same length, as shown in the N row. For all cases $m=6$, $\gamma =0.94$ and $\delta =1\times {10}^{-3}$. In a few cases Acc coincides with Sp or Se due to value rounding and classes imbalance.

N | 250 | 500 | 750 | 1000 | 1250 | 1500 | 1750 | 2000 | |

n | 3198 | 2853 | 2449 | 2119 | 1846 | 1397 | 668 | 149 | |

Classes (dep,man) | Se | 0.68 | 0.73 | 0.68 | 0.67 | 0.68 | 0.67 | 0.74 | 0.81 |

Sp | 0.54 | 0.55 | 0.64 | 0.70 | 0.67 | 0.69 | 0.61 | 0.60 | |

Acc | 0.64 | 0.68 | 0.67 | 0.68 | 0.68 | 0.67 | 0.70 | 0.75 | |

p | 0.0001 | 0.0001 | 0.0001 | 0.0001 | 0.0001 | 0.0001 | 0.0001 | 0.0268 | |

Classes (dep,rem) | Se | 0.54 | 0.55 | 0.58 | 0.53 | 0.61 | 0.63 | 0.64 | 0.65 |

Sp | 0.53 | 0.54 | 0.54 | 0.62 | 0.56 | 0.58 | 0.57 | 0.63 | |

Acc | 0.53 | 0.55 | 0.55 | 0.60 | 0.57 | 0.59 | 0.59 | 0.64 | |

p | 0.0014 | 0.0001 | 0.0001 | 0.0001 | 0.0001 | 0.0001 | 0.0001 | 0.0134 | |

Classes (man,rem) | Se | 0.68 | 0.64 | 0.68 | 0.64 | 0.61 | 0.60 | 0.61 | 0.56 |

Sp | 0.47 | 0.53 | 0.53 | 0.60 | 0.61 | 0.59 | 0.54 | 0.60 | |

Acc | 0.50 | 0.54 | 0.54 | 0.60 | 0.61 | 0.59 | 0.55 | 0.60 | |

p | 0.0605 | 0.0001 | 0.0001 | 0.0001 | 0.0001 | 0.0040 | 0.0659 | 0.4355 |

**Table 7.**Results obtained using a single epoch of 1000 samples from each record. A different optimal parameter configuration was found, but performance was fairly similar to previous cases.

Classes (dep,man) | Classes (dep,rem) | Classes (man,rem) | |
---|---|---|---|

m | 5 | 5 | 4 |

$\gamma $ | 0.75 | 0.75 | 0.9 |

Se | 0.75 | 0.68 | 0.75 |

Sp | 0.69 | 0.66 | 0.61 |

Acc | 0.73 | 0.67 | 0.62 |

p | 0.0076 | 0.0007 | 0.0432 |

MCC | 0.4014 | 0.2939 | 0.2198 |

**Table 8.**Results of the Leave-One-Out (LOO) classification evaluation in terms of average accuracy and standard deviation.

Classes (dep,man) | Classes (dep,rem) | Classes (man,rem) |
---|---|---|

$0.75\pm 0.0287$ | $0.58\pm 0.0407$ | $0.62\pm 0.0370$ |

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## Share and Cite

**MDPI and ACS Style**

Cuesta-Frau, D.; Schneider, J.; Bakštein, E.; Vostatek, P.; Spaniel, F.; Novák, D. Classification of Actigraphy Records from Bipolar Disorder Patients Using Slope Entropy: A Feasibility Study. *Entropy* **2020**, *22*, 1243.
https://doi.org/10.3390/e22111243

**AMA Style**

Cuesta-Frau D, Schneider J, Bakštein E, Vostatek P, Spaniel F, Novák D. Classification of Actigraphy Records from Bipolar Disorder Patients Using Slope Entropy: A Feasibility Study. *Entropy*. 2020; 22(11):1243.
https://doi.org/10.3390/e22111243

**Chicago/Turabian Style**

Cuesta-Frau, David, Jakub Schneider, Eduard Bakštein, Pavel Vostatek, Filip Spaniel, and Daniel Novák. 2020. "Classification of Actigraphy Records from Bipolar Disorder Patients Using Slope Entropy: A Feasibility Study" *Entropy* 22, no. 11: 1243.
https://doi.org/10.3390/e22111243