International Journal of Innovative
Computing, Information and Control
Volume 15, Number 1, February 2019c
ICIC International ⃝2019
ISSN 1349-4198
pp. 199–208

A NOVEL DEEP LEARNING OPTIMIZATION ALGORITHM
FOR HUMAN MOTIONS ANOMALY DETECTION
Yuto Omae1 , Masaya Mori2 , Takuma Akiduki3 and Hirotaka Takahashi2
1

Department of Electrical Engineering
National Institute of Technology, Tokyo College
1220-2, Kunugida, Hachioji, Tokyo 193-0942, Japanyuto.omae@gmail.com
2

Department of Information and Management Systems Engineering
Nagaoka University of Technology
1603-1, Kamitomioka, Nagaoka, Niigata 940-2188, Japanhirotaka@kjs.nagaokaut.ac.jp
3

Department of Mechanical Engineering
Toyohashi University of Technology
1-1, Hibarigaoka, Tenpakucho, Toyohashi, Aichi 441-8580, Japan

Received May 2018; revised September 2018
Abstract. Recently, there are many researches to detect the anomaly of human motions
by using the machine learning and inertial sensors. In general, the individual diﬀerences
exist in human motion by the height, body weight, habits and so on. Classiﬁcation models
based on the deep learning have often high quality. However, the general deep learning
optimization algorithms do not consider the individual diﬀerences in human motions.
By the reason, classiﬁcation model based on the algorithms does not guarantee to take
into account the individual diﬀerences. Therefore, we propose a novel deep learning optimization algorithm for human motions’ anomaly detection from the data of the inertial
sensor. The reliability of the proposed algorithm is also conﬁrmed by the collected dataset.
Keywords: Inertial sensor, Human motion, Deep learning, Mathematical optimization,
CHI-FS evaluation function

1. Introduction. By using the machine learning and inertial sensors, many researchesof human activity recognition exist. For example, Morris et al. [1] developed a muscle
training motion recognition system by using a linear support vector machine. Bao andIntille [2] developed an ordinal activities recognition (e.g., walking, sitting, and running)by using C4.5 decision tree. Omae et al. [3] developed a swimming style classiﬁcation
model (butterﬂy, front crawl, backstroke and breaststroke) by using random forest classiﬁer. Jensen et al. [4] and Kobayashi et al. [5] developed a swimming motion (stroke
and turn motion) recognition model. Moreover, there are the human activity recognition
models based on the deep learning from the data of the inertial sensors (e.g., Alsheikh et
al. [6], Ordonez and Roggen [7] and Ravi et al. [8]). In general, human motions include
the individual diﬀerences among the humans, such as the height, body weight, and habits.
Thus, the signals from the inertial sensors include these diﬀerences.
Omae and Takahashi [9] pointed out that we should consider the individual diﬀerences
if we use the machine learning algorithm. However, general feature selection algorithms(e.g., out-of-bug error method [10], reliefF [11] and minimum reference set [12]) to develop
high quality classiﬁer do not consider them. Thus, Omae and Takahashi proposed a
DOI: 10.24507/ijicic.15.01.199

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Y. OMAE, M. MORI, T. AKIDUKI AND H. TAKAHASHI

feature selection algorithm considering them for the classiﬁcation problems [9]. Moreover,Mori et al. extended their algorithm [9] for the anomaly detection problems [13, 14, 15].
As their results, the classiﬁcation quality had higher score than that using other feature
selection algorithms. The algorithm was developed to search for the eﬀective featuresfrom many features of the time and/or frequency domain of inertial sensors. It cannot
use the optimization of deep learning-based classiﬁcation or anomaly detection model.
Therefore, in this paper, we propose a deep learning optimization algorithm considering
the individual diﬀerences by extending previous algorithm. Our target problem is thehuman motions’ anomaly detection and target model is the Convolutional Neural Network(CNN) as the deep learning.
The paper is organized as follows. In Section 2, we brieﬂy explain the CNN-based
feature extraction from the inertial sensors and its model parameters. In Section 3, we
explain our proposed method of the CNN learning algorithm considering the individual
diﬀerences of human motions. In Section 4, we show the results of the experiment to
conﬁrm the reliability of the proposed algorithm. Section 5 is devoted to a summary.
2. CNN-Based Feature Extraction and Its Model Parameters. Figure 1 shows
the schematic view of the CNN-based feature extraction from the inertial sensors and its
model parameters.

...

Fully connected layer

Fully connected layer...

Fully connected layer

Sliding
window

Convolution layer...

Inertial
sensorConvolution layer

3-Acceleration and Gyro
Signals (6 axis)

Convolution layer

Human Activity

Featureextractionʹʹ ʹʹʹ ˕˕ ˕ʹ ˕˕ʹ˕ ʹ ʹ
Feature space

CNN model parameters:
The located point of a sensor isdecided by analysts (e.g.: left wrist).

˕: Normal motion, ʹ: Anomaly motion

Kernel filters, weight and bias parameters

Figure 1. CNN-based feature extraction and model parameters θ
Initially, we attach the sensors to a subject’s body. The located points are the backwaist, wrist, and so on (e.g., the located point of the subject in Figure 1 is the left wrist).
The inertial sensors measure the signals (X, Y, Z-axes acceleration and gyro data) fromhuman motions. The signals processed by the sliding window [16] are inputed into the
CNN. They are transformed into the low dimensional matrix based on the kernel ﬁlters.
After that, the feature extraction is performed via the fully connected layers. The CNN
has many model parameters to carry out the feature extraction (e.g., kernel ﬁlter, weightand bias parameters). We line up model parameters θα and make the column vector thatis expressed by,θ = [θ1 · · · θn ]T ,(1)

where n is the number of model parameters. Then, the feature vector based on the CNN
is expressed by,f (θ) = [f1 (θ) · · · fm (θ)]T ,(2)

where m is the number of output neurons of the CNN. By deﬁnition of Equation (2), thefeature vector f (θ) depends on model parameter θ.

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3. Optimization Algorithm. In this section, we describe our proposed method of the
CNN learning algorithm considering the individual diﬀerences of human motions. The
algorithm aims to detect the anomaly motion, which is independent of the individual
diﬀerences, from many subjects. In the proposed algorithm, we use a Variance and Correlation (VC) evaluation function and a Consideration of Human motion’s Individual
diﬀerences-based Feature Space (CHI-FS) evaluation function [13, 14, 15]. By using the
VC and CHI-FS evaluation functions, the CNN model parameters θ are optimized basedon the Gradient Descent (GD).
3.1. Variance and correlation evaluation function. We explain the VC evaluation
function. It evaluates the variances of the features and correlations among the featuresof i-th subject in the feature space based on the CNN. The schematic view of the VC
evaluation function is shown in Figure 2(a). Initially, we deﬁne,( i)∑ Var fj,nor
(θ)
i
( i
)
oδ1 (θ) =
Var
f
(θ)
j,ano
j∈{1,...,m}
∑
∑
∑
( i
)
1
i
+
Cor fj,l(θ), fk,l(θ) − m,(3)
2
2m − mj∈{1,...,m} k∈{1,...,m} l∈{nor,ano}()
iwhere Var fj,{nor,ano}(θ) means the variance of i-th subject’s feature fji (θ) of class label{nor, ano}. “nor” and “ano” show the normal and anomaly motions, respectively (e.g.,ii“nor”: walking, “ano”: falling down, stumbling and so on). Moreover, Cor(fj,l(θ), fk,l(θ))
iimeans the correlation of i-th subject’s feature fj (θ) and fk (θ) of class label l ∈ {nor, ano}.
The range of oiδ1 (θ) is [0, ∞). Equation (3) represents the evaluation value of i-th subject’s
feature space. The ﬁrst term of Equation (3) consists of the variance of the normal andanomaly data in the feature space. If the variance of normal data is small and thevariance of anomaly data is high, the ﬁrst term achieves small value. The second term

Figure 2. The relationship between the evaluation functions and the feature space

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Y. OMAE, M. MORI, T. AKIDUKI AND H. TAKAHASHI

of Equation (3) consists of the correlation of the normal and anomaly data in respective
features value. Note that the number of the correlation in the second term except for thecorrelation between the same features is 2m2 − m, then the reason of division 2m2 − m inthe second term is the normalization. It is desirable that we do not have the correlation
relationship between the respective features for the feature space. If the correlation issmall, the second term is small. The third term has an eﬀect to remove the correlation
between the same feature. In the case of the correlation between the same feature, thisvalue is one. Since the number of their cases in the second term is m, we subtract m in
the third term. Therefore, if oiδ1 (θ) has small value, it means a good feature space. In
contrast, if oiδ1 (θ) has high value, it means a bad feature space.
From the calculation of Equation (3), the evaluation values of the respective subject
can be obtained. After that, we transform them into the evaluation value of all subjectsby,Oδ1 (θ) = w1 Mean(oδ1 (θ)) + (1 − w1 )Std(oδ1 (θ)), w1 ∈ [0, 1],(4)where Mean(oδ1 (θ)) and Std(oδ1 (θ)) are all subjects’ mean and standard deviation ofoiδ1 (θ), ∀i, respectively. w1 is a weight parameter that is range from zero to one. If thevalue of w1 is higher than 0.50, it treats the mean value of all subjects as important.
In contrast, if w1 is smaller than 0.50, it treats the standard deviation of all subjects asimportant. In other words, the role of w1 is an adjustment parameter between the meanvalue and standard deviation. The evaluation value Oδ1 (θ) achieves good value if thevariances of the normal data of all subjects are low, the variances of anomaly data of all
subjects are high and the correlations of the respective features of all subjects are low.
3.2. CHI-FS evaluation function. The CHI-FS evaluation function is developed byMori et al. [13, 14, 15] and evaluates the integrated error risk between the normal andanomaly data in the feature space. The schematic view of the CHI-FS evaluation function is shown in Figure 2(b). The CHI-FS evaluation function considers the individual
diﬀerences of the respective subject and the output value is good if the error risk of many
subjects achieves small error risk. In other words, if the error risk of only some subjects
achieves small, the evaluation value is not small. In this case, the output of the CHI-FS
evaluation function should be bad value. Therefore, we can search for a good feature
space for many subjects by using this function. For example, Mori et al. [14, 15] searched
for the best feature space for the aimless detection from the acceleration and gyro dataof inertial sensors attached on the right and left wrists. However, in this case study, they
did not use deep learning. In other words, the CHI-FS evaluation function in previous
research was used to perform the feature selection.
In this paper, we extend this CHI-FS evaluation function to use in deep learning. We
calculate the class overlapping function expressed by,∏(5)
Di (f (θ)) =Pji (x; f (θ)),
j∈{nor,ano}

where,
i(x; f (θ))
Pnor
1
√
=
(2π)m/2 |Cov(f i (θ))|{}( i ))T( i )−1 (( i ))
1(
× exp − x − Mean f (θ)
Cov f (θ)
x − Mean f (θ)
.
2

(6)

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203

Cov(f i (θ)) is(the m)× m size variance-covariance matrix of i-th subject’s feature vectorf i (θ). Mean f i (θ) is the m dimensional mean vector of i-th subject’s feature vectorf i (θ). And,
(
)
{
}
Ni
xz − fzi,l (θ)
1
1 ∑ ∏
1
1 2
i
Pano (x; f (θ)) = i
K, K(a) = √ exp − a , (7)N l=1
hiz (θ)hiz (θ)22π
z∈{1,...,m}where fzi,l (θ) is the l-th real obtained data of i-th subject’s feature fzi (θ), N i is the numberof i-th subject’s samples of anomaly data and K(a) is the kernel function, and we use
Gaussian kernel. hiz (θ) is the i-th subject’s bandwidth [17] of z-th feature fzi (θ) and
expressed by,()
hiz (θ) = 1.06 Std fzi (θ) (N i )−1/5 ,(8)where Std (fzi (θ)) is the i-th subject’s standard deviation of feature fzi (θ). This bandwidthhiz (θ) is deﬁned by Sheather [18].
Di (f (θ)) of Equation (5) means the overlapping amount on the feature space by theifeatures f (θ) of i-th subject. Pnor
(x; f (θ)) of Equation (6) means the probability distribution of the data labeled by “nor” of i-th subject. We assume the Gaussian distributionii
as Pnor(x; f (θ)) because of the normal human motion (e.g., walking). Pano(x; f (θ)) of
Equation (7) means the probability distribution of the data labeled by “ano” of i-th subi
ject. We assume the non-parametric distribution as Pano(x; f (θ)) because of the anomaly
human motion (e.g., falling down, stumbling and so on).
After that, we calculate the error risk of i-th subject expressed by,∫∫ioδ2 (θ) = · · · Di (f (θ)) df (θ),(9)
Lwhere L is an integration range and we set L = [0, 1]. It is required the standardizationof the feature vector’s range from zero to one. As the result, we can get the risk of themiss-classiﬁcation on the features f (θ) of i-th subject.
After we obtain oiδ2 (θ) of all subjects, we calculate the evaluation value deﬁned by,Oδ2 (θ) = w2 Mean(oδ2 (θ)) + (1 − w2 )Std(oδ2 (θ)), w2 ∈ [0, 1],(10)where Mean(oδ2 (θ)) and Std(oδ2 (θ)) are the all subjects’ mean and standard deviation ofoiδ2 (θ), ∀i, respectively. w2 is a weight parameter that is range from zero to one. Notethat Equation (10) has the same meaning of Equation (4).
3.3. Optimization. We carry out the optimization of the CNN model parameters basedon the VC and CHI-FS evaluation functions. If the value of evaluation functions achieves
low score, the CNN performs the good feature extraction such as the right side ﬁgures of
Figure 2. Therefore, as the best model parameters θ opt , we deﬁned,
θ opt = argmin Oδc (θ), c ∈ {1, 2}.
(11)θHowever, there are many model parameters (i.e., n is very large value). Because we cannot
ﬁnd a minimum value of it, we adopt the suboptimal solution as the CNN model parameters by using the GD method. In other words, we update the CNN model parameters
by using,
]T
[
∂
∂
t+1
t
,
(12)
···
θ
= θ − γ∇Oδc (θ), ∇ =∂θ1∂θnwhere θ t means the t-th parameters of θ, and γ means the learning coeﬃcient.

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Y. OMAE, M. MORI, T. AKIDUKI AND H. TAKAHASHI

Initially, we use the VC evaluation function (c = 1) to obtain the CNN model parameters for the feature extraction such as the right side ﬁgures of Figure 2(a). After theconverged VC evaluation function, we use the CHI-FS evaluation function (c = 2). By
switching the evaluation functions, the CNN aims to extract the features such as the rightside ﬁgures of Figure 2(b).
4. Experiment.
4.1. Outline. We perform an experiment to conﬁrm the reliability of the proposed algorithm. We use the data form the swimming situation. The number of subjects is six
who are the university students. A single inertial sensor is attached on the back waist.
We used an inertial sensor made by Sports Sensing Co., Ltd with the following speciﬁcations: accelerations (±5 G); angular velocities (±1500 dps); sampling frequency (100Hz); weight 20 g; size 67 × 26 × 8 mm [19]. After starring measurement of inertial sensor
data, the subject performs walking and jumping and so on (various human motions).
After that, they carry out the butterﬂy as swimming with the full force (distance: 50m). Finally, they leave from the pool and perform walking, jumping, and so on (various
human motions).
We took the movie of their motions by using video camera (30 fps). Then, we gave thelabel “nor” to butterﬂy motions and label “ano” to those except butterﬂy motions. In
other words, the normal motion means the butterﬂy and the anomaly motions mean thevarious motions (walking, jumping, leaving motion from the pool and so on).
4.2. Result and discussions. The six subjects were divided into two groups. One ofthem is the training data for the CNN and the other is the test data. The training datais the dataset for the parameter optimization and consists of three persons’ data. The
test data is the dataset for the evaluation of the proposed method and consists of three
persons’ data. We set γ = 0.1 in Equation (12) and optimized the CNN model parameters
by using the training dataset. The CNN is constructed by: the convolution layer on 50×1
kernel ﬁlter as the ﬁrst layer, the convolution layer on 50 × 1 kernel ﬁlter as the second
layer, the fully connected layer of ﬁve neurons as the third layer and the fully connected
layer of two neurons as the fourth layer. Thus, the role of the fourth layer is the feature
extraction.
First, Oδ1 (θ) was used as evaluation function. The number of updating by the GD
method is 500. As the result, the evaluation value Oδ1 (θ) converged. We called it “optimization of Oδ1 (θ) model”. Next, we switched from Oδ1 (θ) to Oδ2 (θ). As the result of
the GD method for the optimization Oδ2 (θ), the evaluation value declined many times.
We stopped the updating model parameters at the 104 times. We called it “optimizationof Oδ1,2 (θ) model”.
The optimization of Oδ1 (θ) model and optimization of Oδ1,2 (θ) model are optimized
by our proposal evaluation functions. To compare their models and general models ofdetection quality, we developed other two CNN models. One of them is non-learningmodel. It uses initial model parameters and we call it “initial model”. The other isthe CNN model optimized by cross entropy cost function. As the result of parameters
updating of thirty thousand times, mini-batch error rate converged. Since it is general
optimization algorithm of CNN, we called it “normal model”.
After that, we developed the anomaly detection models based on the One Class-SVM(OC-SVM) in the feature spaces of the four CNN models (initial model, normal model,
optimization of Oδ1 (θ) model and optimization of Oδ1,2 (θ) model). The kernel function of
the OC-SVM we used was the Gaussian kernel. The parameter learning of the OC-SVM

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was performed by the normal data of the training dataset. In other words, this is thenon-supervised learning.
After that, we evaluated anomaly detection quality based on F -measure. F -measure isexpressed by,
F =

2N A
,
N +A

(13)

where N is the accuracy of the normal data detection and A is the accuracy of the anomaly
data detection. The range of F -measure is from 0 to 1. If F -measure achieves high value,
it means high quality detection model.
We show the results of F -measure in Table 1. Sub 1, 2 and 3 are the subjects assigned
to the training dataset. Sub 4, 5 and 6 are the subjects assigned to the test dataset.
In the case of initial model, F -measures are below .500 to all subjects. It means badanomaly detection quality. In the case of normal model, anomaly detection qualities oftraining dataset are high. However, the values of test dataset are middle. In the caseof optimization of Oδ1 (θ) model, the F -measures are similar values to all subjects andrange from .612 to .782. The mean values of train and test are .718 and .699, respectively.
In the case of optimization of Oδ1,2 (θ) model, the F -measures are similar values to all
subjects and range from .685 to .837. The mean values of train and test are .776 and.761, respectively. As the results of calculating F -measure to the test dataset, it achieved
a good score in order of optimization of Oδ1,2 (θ) model, optimization of Oδ1 (θ) model,
normal model, and initial model. Therefore, the CNN optimized our proposed algorithm
which can extract the features for human motions anomaly detection.
Table 1. F -measure of the anomaly detection models
Training dataset
Test dataset
Mean
Model nameSub:1 Sub:2 Sub:3 Sub:4 Sub:5 Sub:6 Train Test
Initial model.142 .160 .215 .481 .390 .375 .172 .415
Normal model.819 .880 .878 .651 .552 .642 .859 .615
Optimization of Oδ1 (θ) model .733 .649 .772 .703 .782 .612 .718 .699
Optimization of Oδ1,2 (θ) model .805 .837 .685 .767 .791 .724 .776 .761
We also survey the boundary line by the OC-SVM on the CNN-based feature space.
We show the results in Figure 3 (the training data: sub 1, 2 and 3) and Figure 4 (the test
data: sub 4, 5 and 6). The light gray area means the normal motions area and the darkgray area means the anomaly motions area. The white circles mean the normal motions’plot and the black circles mean the anomaly motions’ plot. The left side of the ﬁguresmeans 0 times updating, i.e.: “initial model”. The center or right sides of the ﬁguresmeans 500 or 104 times updating. These correspond to the optimization of Oδ1 (θ) and
optimization of Oδ1,2 (θ), respectively. In the case of not suﬃcient learning, the detection
areas were not appropriate. In contrast, they were properly formed in the cases of thelearned CNN model parameters. However, there are some anomaly plots in the normal
area even in the case of learned parameters. Therefore, it is required more learning to
reduce the miss-detection.
These results suggest that the CNN has acquired the robustness to human motions’individual diﬀerences by our proposal optimization algorithm because the variances of F measure among all subjects are low in the case of optimization. However, the validation
is not suﬃcient because the number of subjects is low. We need more veriﬁcation of thereliability.

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Y. OMAE, M. MORI, T. AKIDUKI AND H. TAKAHASHI

Figure 3. The boundary line of the OC-SVM (training data). The left side
ﬁgures are “initial model”, the center ﬁgures are “optimization of Oδ1 (θ)
model” and the right side ﬁgures are “optimization of Oδ1,2 (θ) model”.
5. Conclusion. In this paper, we proposed a deep learning optimization algorithm considering the individual diﬀerences of human motions from the data of inertial sensors. In
our proposed algorithm, we use the Variance and Correlation (VC) evaluation functionOδ1 (θ) and Consideration of Human motion’s Individual diﬀerences-based Feature Space(CHI-FS) evaluation function Oδ2 (θ). By using VC and CHI-FS evaluation functions, the
CNN model parameters are optimized based on the Gradient Descent (GD).
We performed the experiment to conﬁrm the reliability of our algorithm. We use
the data from the swimming situation. We set the butterﬂy as the normal motion andthe various motions (walking, jumping, leaving motion from the pool and so on) as theanomaly motions. The four CNN based-feature extraction models are (1) initial model, (2)normal model, (3) optimization of Oδ1 (θ) model and (4) optimization of Oδ1,2 (θ) model.
As the result of comparing their F -measures, we veriﬁed that the CNN-based feature
optimized Oδ1,2 (θ) achieved most high quality as the anomaly detection models. These
results suggest that by using our proposed algorithm, we can develop the human motions’anomaly detection considering the individual diﬀerences via inertial sensors based on the
CNN and the OC-SVM, although the previous CNN optimization algorithms did notconsider it.
As the future works, we will perform more veriﬁcation of the reliability to other casestudies, the reduction of the number of calculation.

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Figure 4. The boundary line of the OC-SVM (test data). The left side
ﬁgures are “initial model”, the center ﬁgures are “optimization of Oδ1 (θ)
model” and the right side ﬁgures are “optimization of Oδ1,2 (θ) model”.
Acknowledgment. This work was supported in part by JSPS Grant-in-Aid for Young
Scientists (B) (Grant No. JP17K13179; Y. Omae) and by JSPS Grant-in-Aid for ScientiﬁcResearch (C) (Grant Nos. JP16K06156 and JP17K05437; T. Akiduki and H. Takahashi).
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