Keywords

1 Introduction

We often take various actions according to past experience in the same situation. For example, when we decide a menu of the dinner, the choice of the meal of the dinner is affected by the meal of several days. This example describes the conscious action, but it is unclear whether it is true in the unconscious action such as sleep. Concretely, we do not know how the sleep of the current day is affected by the sleep of several past days. If some kinds of relationship are found between the sleep of the current day and that of the past days, the sleep stage (which indicates the deepness/lightness of the sleep) can be estimated by using such a relationship. More importantly, if the current sleep stage is estimated by the past sleep data, the accuracy of the real-time sleep stage estimation can be improved. From this fact, this paper focuses on the real-time sleep stage estimation and proposes the method which appropriately selects the past sleep data as the prior knowledge for improving accuracy of the sleep stage estimation.

This paper is organized as follows. The next section introduces the real-time sleep stage estimation method. The method of personalized the prior knowledge is described in Sect. 3. Section 4 conducts the experiment and discusses the results. Finally, our conclusion is given in Sect. 5.

2 Real-Time Sleep Stage Estimation

2.1 Overview

The sleep that is the action that we take much time and do routinely, but many people will spend it whether own sleep is healthy without knowing it. If we want to know own sleep, we are necessary many processes [4]. Because to know own sleep is difficult unlike knowing the numerical value like the weight, blood pressure, temperature. Specifically, we obtain sleep data by attaching innumerable electrodes to the head, and we can finally know the sleep for the day by the specialists diagnose the provided data. To reduce those impossibility with the metering equipment of the unconstraint type, the technique that estimates for a sleep stage by using fast Fourier transform is devised by provided data [2, 3, 6, 8]. However, we know own sleep of the day after having got up and are not provided in real time. If the sleep stage is obtained in real time, the sound and the smell to lead a deep sleep using the real-time sleep stage, and am applicable to the monitoring in the nursing facility. In late years the study of the estimate attracts attention elsewhere for a real-time sleep stage because it is applicable to many fields.

2.2 Using Trigonometric Function Regression Model Parameters Express the Wave Which Assumes the Full Time of Heartbeat Data Letting Be Similar from One Period to n Period

Harada proposed the real-time sleep stage estimation method using trigonometric function regression model [1]. This method approximates the shape of heartbeat data acquired in real time by the expression (1), and estimates the sleep stage. In the expression (1), a n and b n are the parameters to show the wave of heartbeat data are similar, and those parameters express the wave which assumes the full time of heartbeat data letting be similar from the wave of one period to the wave of n period. In addition, c is a parameter to express the relative numerical high value of wave, and takes around 60 values if it is heartbeat data of healthy adults. N is a parameter to decide the frequency ingredient of the wave to use for approximation, and usually uses the parameter with N = 13 for the real-time sleep stage estimation. Because the frequency ingredient is approximated by the parameter of N = 13 shows the middle frequency of heart beat, and the middle frequency is tended to similar to the figure of the sleep stage [7].

$$ {\text{f}}\left( {\text{t}} \right) = c + \sum\limits_{n = 1}^{N} {\left( {a_{n} *cos\frac{2\pi t}{L/n} + b_{n} *sin\frac{2\pi t}{L/n}} \right)} $$
(1)

The Fig. 1 shows the sleep data of the phrase subject. In the Fig. 1, the cross axle shows the sleep time, and the vertical axes show the heart rate numerical value and the sleep stage. The number 5 of the sleep stage value shows wake of the sleep stage, the number 4 shows REM of the sleep stage, the number 3 to 0 show stage 1 to 4 of the sleep stage. The solid line (color is blue) shows the heart rate value which measured with measuring instrument, and the small dotted line (color is red) shows the approximate value which it was similar to by this method. In addition, the rough dotted line (color is green) shows the value which is discretized the approximate value, and it also shows the sleep stage.

Fig. 1.
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Heart rate approximation using trigonometric function regression model (Color figure online)

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This method can get the sleep stage using heart rate data. But this method needs quantity of enough heart rate data which is from the time of falling sleep to the time of the getting up. Therefore, when there is less heart rate data as immediately after the beginning of sleep, there is the problem that is too difficult to have the good approximation.

2.3 Real-Time Sleep Stage Estimation Using the Prior Knowledge

In order to solve the problem in the previous chapter, expression (1) is added the approximate expression such as expressions (2) and (3). Those parameters that are \( \hat{a}_{n} ,\,\hat{b}_{n} ,\,\hat{c}_{n} \) in expression (2) are correction parameter called “the prior knowledge”, those prevent excessive approximation in less heart rate data and has the effect to promote to the appropriate approximation. \( \lambda \) is a parameter of indicating the correction degree, and the value of the parameter shows the approximate degree. Further, \( \Delta {\text{T}} \) is a parameter that shows setting a time to function correction, and it is set at 1.5 h in the general real-time sleep stage estimation. This means that there is no correction to the prior knowledge after 1.5 h. This equation makes it possible to estimate the sleep stage in real time only by the heartbeat data.

$$ {\text{P}}\left( \phi \right) = \frac{\lambda s\left( t \right)}{N}\left\{ {\left( {c - \hat{c}} \right)^{2} + \sum\limits_{n = 1}^{N} {\left\{ {\left( {a_{n} - \hat{a}_{n} } \right)^{2} + \left( {b_{n} - \hat{b}_{n} } \right)^{2} } \right\}} } \right\} $$
(2)
$$ {\text{s}}\left( {\text{t}} \right) = \left\{ {\begin{array}{*{20}l} { - \frac{{T\left[ {hour} \right]}}{{2\varDelta T_{s} \left[ {hour} \right]}} + 1} \hfill & {T < 2*\varDelta T_{\gamma } } \hfill \\ 0 \hfill & {otherwise} \hfill \\ \end{array} } \right. $$
(3)

2.4 Problems

There are the problems that are not decided which should use the prior knowledge on day for a real-time sleep stage estimation. Figure 2 shows the estimated rate of the real-time sleep stage of one certain subject. There is no prior knowledge from the left and is the figure where used the knowledge which is obtained from the different day for as prior knowledge. The stick of each figure expresses the rate of agreement of the sleep stage in each time called 0–5 min, 5–10 min, 10–20 min… The rate of agreement is the numerical value in comparison with the sleep stage measured by an electroencephalograph (wake, REM, stage1–4). The result of using the prior knowledge no. 1 shows the real-time estimated rates always become higher than the result of not using the prior knowledge. However, the rate of agreement falls in the figure of using the prior knowledge no. 2 than using the prior knowledge no. 1 same way as a case of not using the prior knowledge. Therefore it is necessary to choose the prior knowledge that can appropriately attain a high rate of agreement, but there are ignorance and problems to say which standard we should choose it in.

Fig. 2.
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The concordance rate in having the prior knowledge parameters or not (Color figure online)

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3 Selection of Personalized the Prior Knowledge

3.1 Overview

The appropriate selection of the personalized data as prior knowledge is important because estimated precision drastically changes down as spoke in the second sections when the appropriate choice of the prior knowledge is not selected do the choice that various, is appropriate by not only the individual but also the estimated day. We pay our attention on the shape of heartbeat data provided in real time and employ the subsequent knowledge on a day to resemble the heartbeat data provided from the past sleep as prior knowledge. The prior knowledge is implemented by the parameter of the heartbeat data which a shape resembles most for an estimate. When the shape of the heartbeat is different from the estimated heartbeat shape in real time from past prior knowledge, we can follow it quickly and it is big with estimate precision and becomes able to in this way prevent that I fall down.

3.2 Determination of Similarity of Heartbeat Data

We calculate the difference degree with the heart rate at the time to measure a heartbeat and the similarity with heartbeat data in past sleep estimating and demand the mean. Specifically, we find similarity by a flow to show in Fig. 3. At first we find the heartbeat data between 60 s and the data which it was similar to for the past sleep data number. By a well-thought value, we use the small prior knowledge of the value for choice as a thing having high similarity and estimate it at that point. The next does a similar calculation between 120 s and decides prior knowledge. We become able to choose appropriate prior knowledge in real time by performing this for a sleep.

Fig. 3.
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Calculation flow of the similarity

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4 Experiment

4.1 Experiment Setting

I inspect whether you can choose appropriate prior knowledge using sleep data for 9th for three adult male *3 day in total in an estimate for a real-time sleep stage. The sleep data use the thing which converted the data which I obtained from an apparatus and the electroencephalograph apparatus which can acquire a heartbeat, the body movement data of the unconstraint type for a sleep stage.

4.2 Evaluation Criteria

The rate of agreement for a sleep stage provided by a sleep stage and the electroencephalograph which estimated by choice of the prior knowledge for a real-time sleep stage becomes higher; watch it whether can choose it. More specifically, the estimated rate that is calculated by the prior knowledge having good fitness which is selected by the proposed method is compared with the estimated rate that is calculated by the other prior knowledge. Here evaluation value in the means is the difference the heart rate that is approximated using the selected prior knowledge and the heart rate is measured, and this lower value is high similarity.

4.3 Results

Figures 4, 5 and 6 are estimated results about subject A. The left figure shows the value of the gap with the approximate heartbeat, and the right figure is the result estimated for a sleep stage in real-time. In addition, the result of having been surrounded in a red line is the result which is chosen the prior knowledge of being calculated lower fitness as a thing having high similarity. Subject A knows what can choose the prior knowledge to start the estimated percentage that is higher that there is no knowledge in than this. Figures 7, 8 and 9 are estimated results about subject B. It can attain the estimated percentage that is higher that there is no the prior knowledge in subject B. Figures 10, 11 and 12 are estimated results about subject C. In subject C, the result not to use the prior knowledge for improves, and the estimated precision becomes low even if I use either the past prior knowledge.

Fig. 4.
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Result of Subject A in 140930 (Color figure online)

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Fig. 5.
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Result of Subject A in 141001 (Color figure online)

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Fig. 6.
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Result of Subject A in 141002 (Color figure online)

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Fig. 7.
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Result of Subject B in 141003 (Color figure online)

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Fig. 8.
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Result of Subject B in 141009 (Color figure online)

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Fig. 9.
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Result of Subject B in 141010 (Color figure online)

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Fig. 10.
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Result of Subject C in 140821 (Color figure online)

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Fig. 11.
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Result of Subject C in 140823 (Color figure online)

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Fig. 12.
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Result of Subject C in 140830 (Color figure online)

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4.4 Discussion

In subject C, the result of estimating is not higher than the result of not using the prior knowledge, because we thought that it is different from the past heartbeat shape in the heartbeat shape of the day. In other words precision has worsened because the heartbeat shape of the day was not similar the heartbeat shape of estimating. It is necessary to estimate in real-time without using the prior knowledge from the past sleep data when there is not similar thing to solve this problem. Also the estimated rate in each times (0–5 min, 5–10 min, 10–20 min…) are different in each subject. It is shown that it is necessary to change to other the prior knowledge or no need to use the prior knowledge. Therefore, to tackle the problem is necessary to change the value of the some prior knowledges in the real-time estimation or to use the weighted average value of the some prior knowledges.

5 Conclusion

This paper focused on the real-time sleep stage estimation and proposes the method which appropriately selects the past sleep data as the prior knowledge for improving accuracy of the sleep stage estimation. The prior knowledge in this paper is represented as the parameters for estimating the sleep stage. Concretely, these parameters are acquired from the heartbeat data of a certain past day, and they are used to estimate the heartbeat data of a current day, which data is finally converted to the sleep stage. The role of the proposed method is to select the appropriate parameters of the heartbeat data of a certain past day, which is similar to the heartbeat data of a current day. Such a role clarifies the relationship of the past sleep (and heartbeat) and the current sleep (and heartbeat), which contributes to estimating the current sleep stage from the heartbeat data of a different past day which is similar to the data of the current day. To investigate the effectiveness of the proposed method, we conducted the human subject experiment which investigated the accuracy of the real-time sleep stage estimation of two adult males (whose age are 20 and 40) and one adult female (whose age is 60) by employing the appropriate parameters of the different day from three days. The experimental results revealed that the accuracy of the real-time sleep stage estimation with the proposed method is higher than that without it.

What should be noticed here is that the effectiveness of the proposed method has been shown in only two adult males and one adult female with three days. Therefore, further careful qualifications and justifications, such as an increase of the number of human subjects or sleep days, are needed to generalize our results. Such important directions must be pursued in the near future in addition to the following future research: (1) an investigation of the accuracy of the sleep stage estimation in the case of not finding appropriate parameters; and (2) a classification of the relationship with the current and past sleep data.