This paper proposed a novel non-contact sleep stage estimation method that ensemble the estimation results of specialized RFs that are trained with each sleep stage, which is unlike the conventional machine learning methods that train each sleep stage at once. Concretely, when ensembling the results of each RF, its estimation probabilities are employed to estimate the most likely sleep stage. Furthermore, the method employs the optimal length for learning with RF at each sleep stage. To deal with individual diferences, this paper compares other probabilities of sleep stage estimation by employing hyperparameter for each sleep stage, which subtracts the largest estimated probability to reduce false positive estimation. Through experiments, the following implications have been revealed: (1) the proposed method contributed to improving the percentage of Accuracy by 70.5% from 62.4% by the conventional machine learning method; (2) the suitable lengths of data for learning with RF were about 2, 4, and 2 min for REM sleep, N12 sleep, and N34 sleep, respectively; (3) hyperparameter is efective in reducing biased sleep stage estimation caused by individual diferences and improving estimation accuracy.
For the facts, it is not suitable for measuring daily sleep quality.
Sleep is one of the most important activities of life and To address the problems, the demand for sleep stage
people spend a third of their lives sleeping. If sleep de- estimation methods by simple sensors (such as mattress
privation (especially 4-6 hours of sleep) persists, people sensors) has increased as an alternative to the PSG test. It
become in a state of sleep debt. In the state of sleep debt, is challenging to estimate sleep stages without biological
the ability to think and make decisions are equivalent to data obtained from PSG test. For example, Watanabe
staying up all night [
© 2023 Copyright for this paper by its authors. Use permitted under Creative Commons License individual diferences.
CPWrEooUrckReshdoinpgs IhStpN:/c1e6u1r3-w-0s.o7r3g ACttEribUutRion W4.0oInrtekrnsahtioonpal (PCCroBYce4.0e).dings (CEUR-WS.org) To overcome these problems, this paper aims to improve the accuracy of sleep stage estimation and proposes WRAEKME a novel non-contact sleep stage estimation method that NREM1 ensemble the estimation results of specialized RFs that NNRREEMM32 are trained with each sleep stage. In addition, this paper 0 90 180 270 360 Time (min) tries to discover a way to adjust sleep stage estimation for individual diferences. Concretely, this paper employs TANITA sleep scan SL511 (Japan) as the mattress sensor Figure 1: Example of the overnight sleep stage. for acquiring bio-vibration data, and prepares several RFs for each sleep stage. When ensembling the results of each RF, its estimation probabilities are employed to called the ultradian rhythm. estimate the most likely sleep stage. Furthermore, since The characteristics of each sleep stage are described some characteristics of each sleep stage appear for a short below. The WAKE stage and N1 sleep occur suddenly in a time and others appear intermittently for a long time, short time, and these sleep stages often occur with large multiple data lengths are employed for training RF. For body movements. The size of body movements tends to example, WAKE and N1 sleep suddenly occur with large be larger in the WAKE stage than in the N1 stage. In addibody movements and other sleep stages (especially REM tion, some WAKE stages are self-aware while others are sleep) intermittently occur for a long time. This paper not. In this paper, WAKE stages longer than 2 minutes investigates the optimal data length for each sleep stage are excluded because their characteristics are diferent and employs it to train RF. For individual diferences, this from WAKE stages that occur suddenly. REM sleep is paper focuses on the other probabilities of sleep stage determined by focusing on “rapid eye movement” and estimation to improve the accuracy of the estimation. “decreased skeletal muscle activity” in the R&K method.
This paper is organized as follows. The next section Other characteristics of REM sleep are increased or unstadescribes the sleep mechanism. Section 3 describes the ble heart rate and respiratory rate. The mattress sensors related works of non-contact sleep stage estimation and only can measure the characteristics related to heart rate RF which is the main ML method in our proposed method and respiratory rate, but these characteristics occur interand Section 4 proposes our sleep stage estimation based mittently, rather than continuously. The characteristics on an ensemble of models trained for each sleep stage. of N2 and N34 are that the heart rate and respiratory rate The experiment is conducted in Section 5 and the results tend to decrease with deeper sleep (N34), and the sleep are analyzed in Section 6. Finally, our conclusion is given stage does not change suddenly but remains in the same in Section 7. sleep stage continuously.
The sleep stage is an indicator of the depth of sleep de- 3.1. Sleep Stage Estimation by mattress
ifned by the R&K method. The depth of sleep is classified sensor
into six stages in each epoch (30 seconds), i.e., WAKE,
REM, Non-REM1 (N1), N2, N3, and N4. N4 is often
included in N3 and is denoted as N34 in this paper. The
proportion of each sleep stage in healthy young adults
per night is as follows: WAKE is 1-5%; REM is 15-25%;
N1 is 5-20%; N2 is 45-75%; and N34 is 10-22%
(depending on age and physical condition on that day). In order
to determine the sleep stage, the R&K method needs
biological data such as electroencephalography (EEG),
electrooculogram (EOG), and electromyogram (EMG)
acquired by the PSG test. Figure 1 shows the example of
the overnight sleep stages, where the vertical axis
indicates the sleep stage and the horizontal axis indicates the
time. As shown in Figure 1, the structure of the sleep
stage in a healthy person repeats deep sleep (N3 sleep) 3.2. Random Forests
and shallow sleep (above N3 sleep) alternately, and the
regular sleep repeats this cycle (about 90 to 120 minutes)
three to five times a night. Each cycle is connected by
about 20 to 30 minutes of REM sleep, and this cycle is
Watanabe et al. tried to extract the relation between
the change in the heart rate and sleep stages through
the frequency band containing the multiple biological
rhythms of a human to build a foundation of sleep stage
estimation from heart rate variability (HRV) [
This study employs Random Forests (RF) [
WAKE Non-WAKE
REM Non-REM
N12 Non-N12
N34 Non-N34 Input data 2500
0 -2500
Time Time Time Time
Time Bio-vibration data (mattress sensor value)
Preprocessing or For WAKE
For other stages
WAKE RF REM RF N12 RF N34 RF New subject data (Unlearned) WAKE_P N12_P
REM_P Time
N34_P Ensemble
Time Estimated sleep stage (ensemble result) branches, and classifies them by the majority rule of those results. In this research, Gini impurity is the splitting condition, it becomes low when all the samples contained in each node of the decision tree are the same. RF processing is as follows: 3. Repeat 1. to 2. times.
data set . Figure 3: The example of bio-vibration data in (a) non-WAKE 2. One-third of the original data is called Out-Of- stage and (b) WAKE stage.
Bug (OOB), and it is used for constructing a decision tree. Each node processing is as follows: a) Extract features randomly with not
allowing duplicate value. b) Choose the feature that minimizes Gini impurity, and divides nodes.
stages by an ensemble of four RFs based on their estimation probabilities. All graphs in Figure 2, the horizontal axis represents “time”, and the vertical axis represents sleep stages, bio-vibration data or estimated probability of RF. where is the number of decision trees. In the classification problem, it is recommended to use the square root of the total number of features for the variable , which is employed to divide the nodes of decision trees.
For training each sleep stage, this paper designs two types
of input data. The first type is the features related to body
movement for the WAKE stage, and the other type is the
logarithmic power spectrum for the non-WAKE stage
(i.e., REM sleep, N12 sleep and N34 sleep).
stage, while that is large in the WAKE stage. From this
fact, it is suitable to estimate the WAKE stage by
designing the features such as the variance of the bio-vibration
data in one epoch from the viewpoint of body movement.
Our previous work designed the following six kinds of
features from the bio-vibration data in one epoch are
designed as shown in (Table 1): standard deviation (SD),
the diference between maximum and minimum (Range),
the summation (SUM), the sum of squares (Square), the
average of variation (Level Change: LC) and the
RootMean-Square (RMS) [
1. Applying the Fast Fourier Transform (FFT) [
the power spectrum above 1Hz because of the high density of frequencies below 1Hz. 2. In order to make it easier to understand above 1Hz and for RF to learn, the power spectrum is converted into a logarithmic spectrum (log10). Figure 4(b) shows the example of the logarithmic spectrum converted from the power spectrum of Figure 4(a), where the vertical axis indicates the density (logarithmic value) of the spectrum and the horizontal axis indicates the frequency. Furthermore, the density of each frequency in the logarithmic spectrum is normalized to 0, 1 based on the value of the density of the overall frequency. 3. This logarithmic spectrum is calculated per 30 seconds (stride size is 30 seconds) and labeled with the correct sleep stage (one sleep stage/others) determined by R&K method for RF to learn. Figure ?? shows the example of strides (window size is 128 seconds) and how to label the sleep stage to the spectrum. When labeling the sleep stage to the spectrum, bio-vibration data often have multiple sleep stages, so that, in this study, the sleep stage which is labeled to the spectrum is determined by a majority vote of the proportions occupied by those sleep stages. Note that, when using RF for the sleep stage estimation (not the learning phase), the logarithmic spectrum is not labeled with the correct sleep stage, and the output of the estimation is for the first epoch.
Each sleep stage is trained by a separate RF, and each RF selects and trains features specific to each sleep stage.
When data is input to each RF, the probability of each sleep stage is output by each RF. Then, the sleep stage with the highest probability is determined as a result of the ensemble. However, it is also possible that the probability of both two sleep stages increases (i.e., the estimated probabilities of WAKE, REM, N12 and N34 indicates the total number of epochs in one night. Note that, the numbers in parentheses for WAKE and Total represent the number of epochs excluding consecutive awakenings of more than 2 minutes (sleep disruption) and are excluded from the calculation of Accuracy rates in this paper. The average number of epochs (30 seconds) of sleep without sleep disruption is 634±136.
The performance of the proposed method is compared with single RF trained with four sleep stages at once.
As evaluation criteria, this study employs the Accuracy rate between PSG-based sleep stages and estimated sleep stages. In addition to Ex.1, Precision, Recall, F-measure and Specificity of each sleep stage estimation are employed. are 90%, 50%, 80%, 30% respectively) due to individual diferences. In particular, the probability of the WAKE 5.1. Experimental Setup stage increases with more body movement, but some The electrodes were attached to the body and head of subjects may not be in the WAKE stage. each subject to acquire EEG, EOG and EMG, and the
To deal with the problem, the method subtracts the hy- mattress sensor was placed under the mattress in the bed perparameter % from the probability of the sleep stage to acquire bio-vibration data in one night. After sleep, with the highest probability before comparing it to the the correct sleep stages for each subject were determined other sleep stages. If subtracting the probability changes according to the R&K method based on the data measured the relationship between the probabilities of each sleep by PSG (helped by a medical specialist), and the biostage, the sleep stage with the highest probability at that vibration data measured by mattress sensor is converted time will be the result of the ensemble. For example, the to “Features for the WAKE stage” or “Features except probabilities of WAKE, REM, N12 and N34 are 90%, 50%, for WAKE stage” that logarithmic spectrums of several 80%, 30% respectively, and the hyperparameter for WAKE scales (i.e., window sizes are = {32, 64, 128, 256, 512}). stage ( ) is set as 20%, the probabilities are changed Each feature is labeled with the correct sleep stage in to 70%, 50%, 80%, 30% respectively. In this case, the en- each epoch. The parameters of RF are set as follows: (i) semble result is changed to N12 sleep from the WAKE the maximum depth of the decision tree is 10; (ii) the stage. number of the decision tree is 50; (iii) the number of features employed to construct the decision tree is 16, 23, 5. Experiments and Results 32, 46 and 64 for window sizes 32, 64, 128, 256 and 512 respectively.
stage estimation based on an ensemble of models trained for each sleep stage, this paper conducted the human subject experiments of nine healthy subjects. The experiments are divided into three parts. The purposes of each experiment are the followings:
Ex.1 is conducted for determining a suitable window 1. To determine a suitable window length of input length of input data for each sleep stage except for the data for each sleep stage.; WAKE stage. As evaluation criteria, Ex.1 employs the 2. To determine the hyperparameter , , Accuracy, Precision, Recall, F-measure and Specificity of 12 and 34 for the highest estimated prob- REM sleep, N12 sleep and N34 sleep respectively. ability of ensembling each of the RFs correspond- Figure 5, Figure 6 and Figure 7 show the averaged ing to the four sleep stages. results of each evaluation criteria for each sleep stage.
The vertical and horizontal axes indicate the percentage 3. Sleep stage estimation with the hyperparameters and each criterion, respectively. The blue, orange, gray selected in Experiment 1. and yellow bars indicate the length of the window (input The information on the subjects is summarized in Table 2. data), i.e., 32 seconds, 64 seconds, 128 seconds and 256 The column “ID (Age)” indicates the ID and the age of seconds. In REM sleep, “128 seconds size of window the subject. The columns from “WAKE” to “N34” indicate length” is the most suitable for REM sleep estimation the number of epochs in each sleep stage (WAKE, REM, because Precision, Recall and F-measure are higher than NREM1, NREM2 and NREM34), and the column “Total” any other window length. In N12 sleep, “256 seconds
80.0% 60.0%
Ex.2 is conducted for determining the hyperparameter , , 12 and 34 for the highest estimated probability of ensembling each of the RFs corresponding to the four sleep stages. In Ex.2 all sleep stages are 67.6% 67.5% estimated by the flow of the proposed method, which 67.4% 67.3% 67.5% ensembles RFs specialized for estimating each sleep stage. 67.2% 67.4% Since the adjustment of the hyperparameter for each 67.0% 67.0% 67.2% sleep stage changes the overall result of sleep stage estimation, the evaluation criterion is the percentage of 66.8% 66.7% Accuracy between the sleep stage from PSG and the pre- 66.6% 0 0.05 0.1 0.15 0.2 0.25 0.3 dicted sleep stage. Hyperparameter for each sleep stage has experimented with values of 0.00, 0.05, 0.10, Figure 11: Ex.2 Averaged accuracy of sleep stage estimation 0.15, 0.20, 0.25 and 0.30. in sensitivity analysis of 34.
Figure 8, Figure 9, Figure 10 and Figure 11 show the results of sensitivity analysis for Hyperparameter for each sleep stage. The vertical and horizontal axes in- 5.4. Ex.3 Single RF vs. Proposed Method dicate the accuracy of sleep stage estimation and the value of hyperparameter . From the results, the most Ex.3 is conducted for validating the efectiveness of the suitable hyperparameter is determined as the follow- proposed method and the method is compared with the ings: = 0.20, = 0.25, 12 = 0.00 and result of RF trained with all sleep stages at once. For the 34 = 0.30. proposed method, hyperparameter has experimented with two patterns, = 0 and with the results of Ex.2. As evaluation criteria, Ex.3 employs the percentage of Accuracy between the sleep stage from PSG and the predicted sleep stage. The vertical and horizontal axes indicate the accuracy of sleep stage estimation and estimation methods respectively.
Figure 12 shows the result of sleep stage estimation by single RF, proposed with = 0 and proposed with the results of Ex.2. The vertical and horizontal axes indicate the accuracy of sleep stage estimation and sleep estimation methods. As shown in Figure 12, the estimation accuracies of RF, proposed method ( = 0) and the proposed method ( with the results of Ex.2) are 62.4%, 66.7% and 70.5% respectively. The proposed method is 8.1% higher than the conventional sleep stage estimation method that classifies 4 sleep stages by s single RF. This paper conducted a paired t-test for the results and found a significant diference between the single RF and the proposed method. This result suggests, the proposed method significantly increases the Accuracy of sleep stage estimation more than conventional single RF.
WAKE REM N12
N34 WAKE REM N12 N34 To discuss the diferences in sleep stage estimation results between single RF and the proposed method, Figure 13 shows the results of each subject. The vertical and 6.2. Efectiveness of Hyperparameter . horizontal axes indicate the accuracy of sleep stage estimation and subject IDs. The blue, orange and gray bars As shown in Figure 13, even with the proposed method, the estimation may not improve the Accuracy as in SubiannddicpartoeptohseedrewsuiltthotfhseinregsleulRtsF,opfrEoxp.o2.seTdhweiathccura=cie0s ject I. The lack of improvement in the Accuracy rate of the estimation for each subject are improved by the is caused by the over-estimating REM sleep as shown proposed method. Figure 14 and Figure 15 show the esti- in Figure 16. This means that subject I, who is elderly, mation result of subject D by single RF and the proposed has over-estimating REM sleep because the bio-vibration data in normal conditions are similar to the bio-vibration cmaetethtohde (slee=ps0ta).gTehaendvetrimticea.lTahnedbhluoeriaznodntoarlaanxgees liinndeis- data during REM sleep in the training data (i.e., the estiindicate the correct sleep stage (obtained from PSG) and mated probability of REM sleep is often greater than 50%). estimated sleep stage. The estimation by single RF has Even if the estimated probability of REM sleep is high, more false REM estimations than the estimation by the the estimation probabilities of other sleep stages (espe
PSG RF PSG proposed method. Such false REM estimations by single RF tend to occur in other subjects, and some subjects also have more false WAKE stage estimations than estimations by the proposed method. Since the proposed method trains a dedicated RF for each sleep stage, it can learn the characteristics of each sleep stage from multiple perspectives. On the other hand, a single RF must learn the characteristics of four sleep stages, which limits the number of characteristics that can be learned. This is the reason why the proposed method has higher estimation accuracy than the single RF. cially N12 sleep) may also be high. Based on this, when only the estimated probability of REM sleep is high, REM sleep is employed as the estimation result, and when the estimated probability of other REM sleep is also high, estimation of other sleep stages can be employed to reduce over-estimating REM sleep estimation. Hyperparameter , which is set for each sleep stage, can deal with this problem because it subtracts X% from the probability of the sleep stage with the largest estimated probability.
Then, Subject I was able to reduce over-estimating REM sleep estimation by setting the hyperparameter obtained in Ex.2.
This suggests that hyperparameter is efective in reducing biased sleep stage estimation caused by individual diferences and improving estimation accuracy.
This paper proposed a novel non-contact sleep stage estimation method that ensemble the estimation results of specialized RFs that are trained with each sleep stage. Concretely, when ensembling the results of each RF, its estimation probabilities are employed to estimate the most likely sleep stage. Furthermore, the method employs the optimal length for learning with RF at each sleep stage. To deal with individual diferences, this paper compares other probabilities of sleep stage estimation by employing hyperparameter for each sleep stage, which subtracts the largest estimated probability to reduce false positive estimation. Through experiments, the following implications have been revealed: (1) the proposed method contributed to improving the percentage of Accuracy by 70.5% from 62.4% by the conventional machine learning method; (2) the suitable lengths of data for learning with RF were about 2, 4, and 2 min for REM sleep, N12 sleep, and N34 sleep, respectively; (3) hyperparameter is efective in reducing biased sleep stage estimation caused by individual diferences and improving estimation accuracy.
The future tasks are the followings: (1) expansion of subject data to improve the accuracy of N34 estimation due to the small amount of N34 sleep data; (2) to improve the estimation accuracy by classifying the individual difference trends from subject sleep data and learning for each similar subject.