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Time-Series Physiological Data Balancing
for Regression
Hiroki Yoshikawa, Akira Uchiyama, Teruo Higashino
Graduate School of Information Science and Technology, Osaka University
{h-yoshikawa, uchiyama, higashino}@ist.osaka-u.ac.jp
Abstract—Many studies have shown the effectiveness of ma-
chine learning in estimating psychological or physiological states
using physiological data as input. However, it is ethically and
physically difficult to collect a large amount of data without
bias in an uncontrolled environment. Specifically, the amount
of data in rare cases is especially small compared to common
data. Therefore, the distribution bias may cause overfitting in
machine learning. In this paper, we propose a SMOTE-based
method to alleviate the distribution bias by data augmentation
in the regression problem using a dataset containing time-series
physiological data. The effectiveness of the proposed method
was confirmed for datasets of thermal sensation and core body
temperature collected in uncontrolled environments. The results
show that our method improves the performance of regression
models for minor cases with a bit of decline in the mean average
error.
Keywords—Machine learning, Data preprocessing, Health care,
Time-series, Regression
I. INTRODUCTION
Machine learning is one of the most commonly used ap-
proaches for a wide variety of applications, including health-
care. Many of the healthcare applications typically use time-
series data such as heart rate and body temperature [1], [2] to
estimate psychological or physiological states of humans using
machine learning algorithms. For training estimators, data
collection through real experiments is essential. The challenge
in data collection, especially in healthcare applications, is data
imbalance, i.e., the distribution of the dataset is non-uniform.
This is natural because minor cases do not frequently happen
in the real world. The imbalanced data causes classifiers to
be naturally biased towards the majority class, leading to the
performance degradation for important and interest minority
samples [3], [4]. This is because standard machine learning
methods usually seek the minimization of training errors. We
may be able to collect data in minor cases by designing exper-
iment protocols carefully for some researches. Nevertheless,
such data collection is limited in controlled environments.
Therefore, it is difficult to collect data in minor cases in
uncontrolled environments for researches in the healthcare
domain.
To address this problem, researchers make use of a part of
the modeling workflow toolkit called data balancing [5]. The
data balancing is a way of pre-processing the data to increase
its size, diversity, and robustness of models. Oversampling and
undersampling are used for balancing the dataset by augment-
ing minor data and discarding major data, respectively. The
former approach is applied based on existing algorithms such
as Synthetic Minority Oversampling Technique (SMOTE) [4].
SMOTE augments the data in minor classes by interpolation
for classification problems.
In the field of physiological sensing, estimations of hu-
man states such as thermal sensation using machine learning
often regard the target problems as classification problems
for simplicity [6], [7]. However, to achieve estimations of
human states with finer granularity, regression is more appro-
priate than classification because regression estimates numer-
ical values. Because regression problems output continuous
numerical values, data balancing algorithms for classification
problems are not suitable for regression problems. For data
balancing in regression problems, some algorithms such as
SMOTER [8] were proposed based on SMOTE. SMOTER
divides the distribution of the numerical target values into the
major and minor values based on the relevance score of the
target value. After that, it applies undersampling for major
cases and oversampling for minor cases. The oversampling
strategy is designed for numerical values based on SMOTE. It
uses the weighted average between the target values of the two
minor cases based on the distance between them. Through the
above steps, the dataset for a regression problem is balanced.
However, SMOTER does not consider time-series feature
values commonly used in psychological or physiological state
estimation.
In this paper, we propose a data balancing method for
regression with time-series feature values based on SMOTER.
To consider the temporal dependency of time-series data, we
extend a distance function. To define the distance between
time-series samples, we use Dynamic Time Warping (DTW)
distance as used in TS SMOTE [9]. TS SMOTE is designed
to extend SMOTE to time-series data. Our method interpolates
synthetic time-series using the weighted average and the
DTW distance. Table I summarizes the difference between
our method and other balancing methods in terms of the
capability to deal with time-series features and target problem
types. As far as we know, our method is the first to achieve
data balancing for regression problems with time-series feature
values.
For evaluation, we apply our method to two imbalanced
datasets with time-series feature values. The first dataset is
the thermal sensation dataset, which consists of time-series
physiological data measured by a wristband sensor as a feature
value and thermal sensation vote (TSV) as a target value.
TABLE I
SUMMARY OF BALANCING METHODS.
Method time-series target problem
SMOTE No classification
TS SMOTE Yes classification
SMOTER No regression
Proposed method Yes regression
The second dataset is the core body temperature dataset. The
core body temperature is measured by a tympanic temperature
sensor during exercise. Feature values are measured by a
wristband sensor, chest strap sensor, and environmental sensor.
The results show that our method improves the performance
of regression models for minor cases with a little decline in
the mean average error.
II. RE LATE D WOR K
A. SMOTE-based Data Balancing
In order to deal with the imbalanced datasets, researchers
proposed data augmentation methods. The basic strategy is
pre-processing the data to increase its size and diversity [10].
SMOTE is a predominant data augmentation for classification.
Chawla et al. [4] showed the advantages of this approach
compared to other alternative sampling techniques on several
real-world problems using several classification algorithms.
Because of the advantage, methods derived from the SMOTE
are proposed [11], such as Adaptive Synthetic sampling ap-
proach (ADASYN) [12] and Borderline-SMOTE [13]. The
SMOTE-based extensions replace the original interpolation
procedure with other more complex ones, such as clustering
and probabilistic functions.
Furthermore, filtering extensions after SMOTE are pro-
posed, such as SMOTE + Tomek [14] and SMOTE +
ENN [15]. To clarify the boundaries between classes, they
remove unnecessary samples from the dataset after the data
augmentation. They are kinds of undersampling techniques.
In this paper, to focus on evaluating the data augmentation of
time-series data, the combination with undersampling is out
of scope. However, those undersampling techniques can be
applied after the data augmentation by the proposed method.
For regression problems, SMOTER [8] and SMOGN [16],
which is an extension of SMOTER with Gaussian noise, are
proposed. These methods extend SMOTE for regression prob-
lems by using the relevance function representing the density
of the training data. In this paper, we extend this algorithm
for regression problems based on SMOTER, which is one
of the SMOTE-based extensions for regression problems. It
separates the minor cases from the distribution by a user-
defined threshold. After the separation, it generates new cases
based on weighted averages between pairs in minor cases.
B. Data Balancing for Time-series classification
For time-series classification, some balancing methods were
proposed by generating the synthetic sample. TS SMOTE [9]
is an extension of SMOTE designed for time-series data.
It introduced DTW in the time-series merging algorithm in
the augmentation. On the other hand, OHIT [17] was pro-
posed as an oversampling method for the imbalanced time-
series classification. OHIT is different from the state-of-the-art
oversampling algorithms because it generates the structure-
preserving synthetic samples. These methods are based on
generating samples using the feature of time-series categorized
as the same class. In contrast, we propose a data balancing
method for time-series regression, which can not use classified
time-series samples.
C. Learning-based Data Balancing
Another approach for data augmentation is known as gen-
erative models [18] which are based on deep learning, such as
Generative Adversarial Networks (GANs) [19] and Variational
Autoencoders (VAEs) [20]. These learning-based approaches
can generate synthetic time-series data and augment training
dataset effectively [21]. The algorithms model the real data
distribution Prby learning a distribution Pθparameterized
by θ. The data is generated by learning a function gθwhich
transform a noise with gaussian distribution Zsuch that Pθ≈
gθ(Z). The approaches generate realistic values in several
domains, such as computer vision and cybersecurity [22].
However, the generative models need training, which means
the generative model may overfit common values when we
use an imbalanced dataset. To deal with the problem, it needs
a specialized loss function, which makes the model more
complicated, or data balancing before the training. Therefore,
we propose the data augmentation method based on the
algorithmic approach, which does not need training.
III. PROP OS ED ME TH OD
A. Problem Definition
Imbalanced regression is a sub-class of regression prob-
lems [23]. In this setting, given a training set D=
{hxi, yii}N
i=1, the goal is to obtain a model m(x)that approx-
imates an unknown regression function Y=f(x)as defined
in Ref. [23]. In the problem we address, xis a feature vector
that contains time-series data from Nfsensors as follows.
xi={f1,...,fNf}(1)
fj={s1, . . . , sNs}(2)
where Nfis the number of time-series features, and Tis the
length of the sample of the time-series fj. In this paper, Ns
is the same constant value for any fj. This is because basic
learning approaches for time-series, such as Recurrent Neural
Network (RNN), assume the same length of time-series as
their input.
B. Data Balancing
The overview of the proposed method is shown in Fig. 1.
The input and output are an imbalanced original dataset with
time-series features and a balanced dataset, respectively. First,
a relevance function φ(y)is generated based on the distribution
of the target value yin the original dataset as proposed in
SMOTER. The relevance function is automatically generated
Relevance function
generation
threshold
common rarerare
Separation into
common and rare Time-series
data generation
( Oversampling )
Undersampling
Proposed method
Original dataset Balanced dataset
Fig. 1. Overview of the proposed method.
Time-series 𝑥"
Time-series 𝑥#
Synthetic data
1 − 𝛼
𝑡
Time-series 𝑥
𝛼
Target value 𝑦
1 − 𝛼
𝛼
𝑦"
𝑦#
Fig. 2. Key idea of time-series data generation for regression.
based on a probability density function (pdf) [24]. Second, the
original distribution is separated into minor data Drand major
data Dcby a user-defined threshold tEas follows.
Dr={hx, yi ∈ D|φ(y)> tE}(3)
Dc=D\Dr(4)
After this separation, oversampling and undersampling are
carried out on Drand Dc, respectively.
Based on Dr, we apply time-series data generation. Figure 2
illustrates our key idea based on SMOTER. A synthetic data
is interpolated between two samples in Drwith a ratio α,
which is determined by the weighted average of them. The
data generation in SMOTER needs to define a distance of
a pair of x. Our main contribution is combining the DTW
distance with SMOTER. The distance can be used for time-
series interpolative generation conserving original time-series
features, such as shape [9]. As shown in Fig. 2, synthetic points
in the generated time-series are interpolated between a pair,
which is given by DTW, using the ratio α.
The pseudocode of the main algorithm for data balancing is
shown in Algorithm 1. First, based on the SMOTER algorithm,
the threshold tEof φ(y)is determined to separate the samples
in the dataset into the major and minor classes. φ(y)is a
function that shows the uniqueness of the target value y. A
larger φ(y)corresponds to a smaller number of samples. The
data generation for minor classes is performed by dividing the
median of yinto smaller and larger samples than ˜y.
The method for generating time-series data is shown in
Algorithm 2. The k-nearest neighbors of the minor class
sample case are extracted based on the distance calculated
by Dynamic Time Warping [25]. A new time-series dataset
Algorithm 1 Main SMOTER algorithm.
Input: D- A data set
tE- Threshold
%o, %u- Percentages of over- and under-sampling
k- Number of neighbors used in case generation
Output: Dnew - A generated data set
1: rareL ⇐ {hx, yi ∈ D :φ(y)> tE∧y < ˜y}
2: newCasesL ⇐GENSYNTHCASES(rareL, %o, k)
3: rareH ⇐ {hx, yi∈D:φ(y)> tE∧y > ˜y}
4: newCasesH ⇐GENSYNTHCASES(rareH, %o, k)
5: newCases ⇐newCasesL ∪newCasesH
6: nrN orm ⇐%uof |newCases|
7: normCases ⇐sample of nrN orm case ∈ D \ {rareL ∪
rareH }
8: return newCases ∪normCases
Algorithm 2 Generating synthetic cases.
Input: D- A dataset
%o- Percentages of oversampling
k- Number of neighbors used in case generation
Output: Dgen - Generated new cases
1: newCases ⇐ {}
2: ng ⇐%o/100
3: for all case ∈ D do
4: nns ⇐KNN(k, case, D \ {case})
5: for i⇐1to ng do
6: n⇐randomly choose one of the nns
7: α⇐randomly choose in [0,1]
8: new[y]⇐min(case[y], n[y]) + α|case[y], n[y]|
9: for all f∈features do
10: pairs ⇐DTW(case[f], n[f])
11: for t⇐1to |pairs|do
12: (tnew, vnew )⇐TIMEPOINT(pairs[t]case ,
pairs[t]n, case[f], n[f], α)
13: new[f, tnew]⇐vnew
14: end for
15: end for
16: newCases ⇐newCases ∪ {new}
17: end for
18: end for
19: return newCases
20: function TIMEPOINT(ta, tb, tsa, tsb, α)
21: tnew ⇐min(ta, tb)+(ta+tb)/2
22: vnew ⇐min(tsa[ta], tsb[tb]) + α|tsa[ta]−tsb[tb]|
23: return tnew, vnew
24: end function
new is generated by TS SMOTE for the neighbor n, randomly
selected from the k-nearest neighbors. After the target number
of samples ng is generated by repeating the above steps, the
new generated dataset newCases is returned.
3210123
TSV
0
100
200
300
400
500
600
700
800
Number of samples
Fig. 3. Distribution of TSV.
35.50 35.75 36.00 36.25 36.50 36.75 37.00 37.25 37.50
Core body temperature [ C]
0
25
50
75
100
125
150
175
200
Number of samples
Fig. 4. Distribution of core body temperature.
IV. EVALUATION
A. Dataset
The first dataset is a thermal sensation dataset collected
from 21 subjects. The target value of the dataset is Thermal
Sensation Vote (TSV). The subjects reported TSV within
the range of [-3.5, 3.5] by moving the seek bar up and
down on our smartphone application. The scale is called
the American Society of Heating, Refrigerating, and Air-
Conditioning Engineers’ seven-point thermal scale [26], which
is widely used as the metrics of human thermal sensation; the
seven levels range from -3 to +3 (Cold, Cool, Slightly cool,
Neutral, Slightly warm, Warm, Hot). In total, we collected
1686 TSV inputs. The distribution of the TSV inputs is
shown in Fig. 3. Red hatched areas in the figure highlight
the minor distribution. Because most of the data are collected
in an air-conditioned environment, most of the TSVs labeled
by the subjects are +1 (Slightly warm), 0 (Neutral), or -
1 (Slightly cool). Three feature values are heart rate, skin
temperature, and electrodermal activity collected by an E4
wristband sensor [27]. They are measured continuously as
time-series data.
The second dataset is a core body temperature dataset
collected from 13 subjects while exercising. The target value
is the core body temperature recorded by a cosinuss° C-
Temp [28], which can measure tympanic temperature. The
feature values are measured by two physiological sensors and
𝒙
(3, 10)
LSTM
ReLU
(16)
FC
ReLU
Dropout(0.25)
FC
(1)
𝑦
(16)
Dropout(0.5)
Fig. 5. TSV estimator.
an environmental sensor. The first one of the physiological
sensors is WHS-3 [29], which is a wearable heart rate sensor
with a chest strap. We use heart rate and in-cloth temperature
from WHS-3 as feature values. The second one is the E4
wristband sensor as used in the TSV dataset. In addition to
the three feature values used in the TSV dataset, we also use
acceleration from it. Also, we use an environmental sensor to
measure air temperature and relative humidity as time-series.
In total, eight features are input to an estimator. We collected
750 pairs of the core body temperature and ten minutes of the
eight time-series data through the experiment. The distribution
of the core body temperature is shown in Fig. 4.
B. Evaluation Metrics
We evaluate the proposed method with evaluation metrics
based on precision Pr, recall Rr, and F-measure Frfor
regression problems as proposed in Ref. [30]. Intuitively, the
metrics become larger (i.e. better) when an estimator outputs
closer values in rarer cases. The definition is given below.
Pr=Pφ( ˆyi)>tEφ( ˆyi)α( ˆyi, yi)
Pφ( ˆyi)>tEφ(ˆy),(5)
Rr=Pφ(yi)>tEφ(yi)α( ˆyi, yi)
Pφ(yi)>tEφ(yi),(6)
Fr=2PrRr
Pr+Rr
,(7)
where yiand ˆyiare an actual value and an estimated value
by inputting xito the estimator, respectively. As defined in
Ref. [30], the function αis defined as follows.
α( ˆyi, yi) = I(L( ˆyi, yi)≤tL)(1 −exp( −k(L( ˆyi, yi)−tL)2
tL2)),(8)
where Iis an indicator function which is one if its argument
is true and zero otherwise. tLis a threshold defining an
acceptable error within the domain a metric loss function
L, e.g., the absolute deviation. kis a positive number that
determines the shape of the function.
C. Estimator Design
To estimate the numerical target value y, we construct a
deep learning-based estimator for each dataset using an LSTM
layer. Figures 5 and 6 show estimators for the thermal sensa-
tion dataset and core body temperature dataset, respectively.
The shape of xis (Nf, Ns)as defined in Section III-A. The
𝒙
(8, 10)
LSTM
ReLU
(32)
FC
ReLU
Dropout(0.25)
FC
(1)
𝑦
(32)
Dropout(0.25)
Fig. 6. Core body temperature estimator.
Time
x
Time-series A
Time-series B
SMOTER
Proposed
Fig. 7. Example of time-series generation by proposed method.
input xconsists of three time-series data whose length Nsis
ten.
D. Effect of Data Balancing
We evaluate the proposed method through comparison with
baseline, which is without any data balancing, and SMOTER-
based time-series interpolation with Euclidean distance. The
latter method generates a time-series sample by interpolating
a synthetic sample between corresponding samples in original
time-series data as shown in Fig. 7. The figure shows an
example of the time-series generation by each method given
two time-series samples. As illustrated in the figure, SMOTER
fails to inherit features of the original time-series samples such
as the maximum and minimum values. On the other hand,
the proposed method generates a synthetic time-series sample
with the features of the original time-series samples such as
the shape, maximum, and minimum values.
Table II and Table III shows the evaluation results of the
TSV dataset and the core temperature dataset, respectively.
We note that in addition to the evaluation metrics defined in
Section IV-B, we evaluate the mean absolute error (MAE). We
set the parameters for Table II as tE= 0.5,tL= 1, and k=
100. For Table III, we set them as tE= 0.5,tL= 1, and k=
10. As shown in the table, the baseline, which is an estimator
learning imbalanced dataset, result in low precision for minor
cases. This result is similar to the imbalanced classification
problem. The result of Frshows that the baseline method fails
to estimate minor cases within the acceptable error. In addition,
TABLE II
EST IMATI ON R ESU LT FOR TSV D ATASET.
Method PrRrFrMAE
Baseline 0.00 0.18 0.00 0.52
SMOTER [8] 0.43 0.31 0.36 0.56
Proposed method 0.75 0.32 0.44 0.56
TABLE III
EST IMATI ON R ESU LT FOR C OR E TEM PE RATUR E DATASE T.
Method PrRrFrMAE
Baseline 0.35 0.51 0.40 0.38
SMOTER [8] 0.45 0.50 0.44 0.38
Proposed method 0.77 0.60 0.67 0.35
the result of SMOTER with Euclidean distance showed lower
improvement than the proposed method in Table II. This is
because the time-series generation based on the DTW distance
can generate time-series samples close to the original time-
series samples. As a result, the proposed method remarkably
enhances the estimator’s performance for minor cases with
a little decline of the MAE compared with the baseline. In
Table III, the result of the proposed method is superior to
the result of the SMOTER. The proposed method’s MAE is
improved from the baseline because the estimator can estimate
in a larger range than the baseline, which is overfitted to a
major value.
V. CONCLUSION
In this study, we proposed a data balancing method for
regression datasets, including physiological time-series data.
We demonstrated that the estimation accuracy improved for
rare cases by balancing datasets, including time-series data
measured by physiological sensors. The result indicated that
the balancing method helps the effective extraction of physio-
logical time-series features to estimate numerical values. Our
future work includes further investigation of the applicable
range of the variety of physiological time-series data using
more datasets.
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