International Journal of Innovative
Computing, Information and Control
Volume 15, Number 2, April 2019c
ICIC International ⃝2019
ISSN 1349-4198
pp. 783–791

CONSIDERATION OF HUMAN MOTION’S INDIVIDUAL
DIFFERENCES-BASED FEATURE SPACE EVALUATIONFUNCTION FOR ANOMALY DETECTION
Masaya Mori1 , Yuto Omae2 , Takuma Akiduki3 and Hirotaka Takahashi1
1Department of Information and Management Systems Engineering
Nagaoka University of Technology
1603-1 Kamitomioka, Nagaoka, Niigata 940-2188, Japans183368@stn.nagaokaut.ac.jp; hirotaka@kjs.nagaokaut.ac.jp
2

Department of Electrical Engineering
National Institute of Technology, Tokyo College
1220-2 Kunugida, Hachioji, Tokyo 193-0942, Japan3

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

Received June 2018; revised October 2018
Abstract. There are many researches of various human activity recognitions from thedata of inertial sensors by using machine learning. In these researches, it is important
to consider the individual diﬀerence. Even if the subjects perform the same activity,
the data obtained from each subject are of diﬀerent behaviors. Thus, if we construct
the feature space, there is a possibility that the human activity of each subject does notconcentrate on one region. In this case, if we consider the anomaly detection of thehuman activities by using this space, it is diﬃcult to draw the boundary between thenormal and anomaly activities. Therefore, the evaluation index/function that can searchbetter feature values/space for various people is necessary. In this paper, we propose
an evaluation function named “Consideration of Human motion’s Individual diﬀerencesbased Feature Space (CHI-FS) evaluation function” for the anomaly detection. We also
conﬁrm the eﬀectiveness of the CHI-FS evaluation function by using the simulation data
and the data of inertial sensors during car driving.
Keywords: Machine learning, Feature space, Human activity recognition, Anomaly
detection, Mathematical optimization

1. Introduction. Recently, various human activity recognitions from the data of inertial
sensors by using machine learning are investigated, e.g., Khan et al. [1] used a neuralnetwork to classify such motions as walking, running, sitting down and standing up;
Lester et al. [2] classiﬁed the human activities such as walking, running, brushing teeth
and riding an elevator with the Hidden Markov Model (HMM); He and Jin [3] classiﬁed
the walking, running and jumping with the support vector machine; Ward et al. [4] used
HMM to classify such motions as assembly work (using drills and vises); Omae et al. [5]classiﬁed the swimming styles (backstroke, breaststroke, butterﬂy and front crawl) withthe random forest.
If we consider the human activity recognitions, the data of inertial sensors (such as
acceleration and gyro data) are of diﬀerent behaviors since there are individual diﬀerences in human activities by the height, body weight, habits, length of leg and so on.
Therefore, if we investigate the various human activity recognitions by using machine
DOI: 10.24507/ijicic.15.02.783
783

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

learning, it is important to consider the individual diﬀerences and search the importantfeature values for various people [6]. To achieve it, the evaluation index/function that cansearch better feature values/space for various people is necessary. However, the existing
index/evaluation function (e.g., between-class and within-class variance [7] and minimum
reference set [6, 8]) cannot be considered for such individual diﬀerences. Khan et al. [1]and Ward et al. [4] selected the feature values by using the linear-discriminant analysis;
Lester et al. [2] selected the feature values by using a modiﬁed version of AdaBoost proposed by [9]; He and Jin [3] performed the feature extraction by using the discrete cosine
transform and the principal component analysis and composed the feature space. Thesemethods also cannot be considered for individual diﬀerences.
The human activity recognition in machine learning is mainly classiﬁed into the classiﬁcation and anomaly detection. Let us focus on the human activity recognition during
car driving as an example. Figure 1 shows the schematic plot of each activity during car
driving operations in each feature space, respectively. Each legend corresponds to eachdriving activity. Figure 1(a) shows the feature space that can classify between normal andother dangerous driving operations. Figure 1(b) shows the feature space that can classify
normal, one-handed, distracted driving, use of smartphone and other anomaly driving,
respectively. In Figure 1(c), it is diﬃcult to draw the boundary of each operation because
the plots of each driving operation are mixed. The anomaly detection discriminates between the normal and anomaly plots. Therefore, the desirable evaluation index/function
is to search the feature space like Figure 1(a). On the other hand, the classiﬁcation classiﬁes each plot. Therefore, the desirable evaluation index/function is to search for thefeature space like Figure 1(b).

Figure 1. The diﬀerence of better feature space of anomaly detection and classiﬁcation
The classiﬁcation is highly convenient if the discriminated activity is determined beforehand. However, if there are various types of the anomaly activities such as Figure 1(b)and we cannot determine the discriminated activities beforehand, it is diﬃcult to give thelabels of all activities and obtain the learning data of all activities [10]. In addition, it
is more relatively diﬃcult to ﬁnd the optimal space in the classiﬁcation like Figure 1(b)than that in the anomaly detection like Figure 1(a). In most of the cases, we need toclassify the normal and other dangerous activities.

CHI-FS EVALUATION FUNCTION FOR ANOMALY DETECTION

785

Moreover, if we construct the feature space, there is a possibility that the human activityof each subject does not concentrate on one region. In this case, it is also diﬃcult todraw the boundary between the normal and anomaly activities. Therefore, the evaluationindex/function that can search better feature values/space for various people is necessary.
Therefore, in this paper, we propose an evaluation function named “Consideration of
Human motion’s Individual diﬀerences-based Feature Space (CHI-FS) evaluation function” for the anomaly detection.
The paper is organized as follows. In Section 2, we explain our proposed feature space evaluation function named “Consideration of Human motion’s Individual diﬀerences-based
Feature Space (CHI-FS) evaluation function”. In Section 3, we conﬁrm the eﬀectivenessof the proposed CHI-FS evaluation function by using the simulation data and the data ofinertial sensors during car driving. Section 4 is devoted to a summary.
2. Consideration of Human Motion’s Individual Diﬀerences-Based Feature Space Evaluation Function.
2.1. Overview. In this paper, since we consider the anomaly detection, we assume thatthe obtained data set from individual subject consist of many normal data and a few
anomaly data.
The feature space composed of the feature values x is denoted by ⟨x⟩. We also deﬁne
the following sets:
xn , xm ∈ X := {x1 , x2 , . . . , xFmax },i ∈ I := {1, 2, . . . , Nsub },c ∈ C := {nor, ano},m, n = 1, . . . , Fmax ,m ̸= n,

(1)
(2)
(3)

where X is the set whose elements are feature values and its size is Fmax , where Fmax isthe number of the considered feature values, I is the set whose elements are the subject’s
label, Nsub is the number of the considered subjects, and C is the set whose elements are
the labels: normal or anomaly.
We aim to search for the eﬀective/optimal feature space ⟨xopt1 , . . . , xoptu ⟩ to judge
normal and anomaly from the Nsub subjects data. To search for the optimal feature
space, (i) we calculate the function to evaluate the eﬀectiveness of the feature space foranomaly detection in each subject, (ii) we check the values of the function of all subjects
and if the values of all subjects show uniformly eﬀective then we adopt this feature spaceas the optimal feature space.
The overview of the construction of the evaluation function is shown in Figure 2. For
simplicity, we consider u = 2 case in this paper and the feature space in Figure 2 canbe denoted by ⟨xn , xm ⟩. The method of the construction of the evaluation function is
explained step by step.
2.2. Probability density function of the normal data. It is natural that the normal
data concentrate on the one region of the feature space like the top left panel of Figure 2
since the normal data consist of the data of the only speciﬁed activity. Therefore, we assume the multivariate normal distribution as the shape of the probability density function.
Let the feature vector be x = (xn xm )T . The mean value of the feature value xn , xm in the()Tsubject i is deﬁned as xin , xim and the mean vector is denoted by µi (xn , xm ) = xin xim .
The variance-covariance matrix of the normal data of the feature values xn , xm in subject
i is deﬁned as V i (xn , xm ). Then the probability distribution of the normal data on thefeature space ⟨xn , xm ⟩ of subject i is given by:

786

M. MORI, Y. OMAE, T. AKIDUKI AND H. TAKAHASHIi
Pc=nor(xn , xm ) =

2π

√

1
|V i (xn , xm )|
{

}
)T i
(
)
1(
i
−1
i
× exp − x − µ (xn , xm ) V (xn , xm )x − µ (xn , xm ) . (4)2
From the probability distribution of Equation (4), we can estimate the distribution of thenormal data of the subject i on the feature space, like the top middle panel of Figure 2.

Figure 2. Overview of the construction of the evaluation function in feature space ⟨xn , xm ⟩ of subject i (anomaly detection)
2.3. Probability density function of the anomaly data. The anomaly data do notconcentrate on the one region of the feature space like the bottom left panel of Figure 2
since the anomaly data consist of the data deviated from the speciﬁed activity. Therefore,
we assume the multivariate kernel distribution as the shape of probability density function.
The number of anomaly data in the feature values ⟨xn , xm ⟩ in a certain subject i
is N i and the bandwidth in feature values ⟨xn , xm ⟩ of subject i is deﬁned as hin andhim , respectively {[11]. Additionally,
if the kernel function is used to the Gaussian kernel:}
K(a) = √12π exp − 12 a2 and l-th anomaly data in feature values xz of subject i is denoted
as xi(z)l , then the probability distribution of the anomaly data on the feature space ⟨xn , xm ⟩of the subject i is given by:
(
)
Ni
i
∑
∏ 1
x
−
x
z
1
(z)l
i
Pc=ano(xn , xm ) = i
K
.
(5)
i
i
N l=1
hz
hz
z∈{n,m}From the probability distribution of Equation (5), we can estimate the distribution of
anomaly data of the subject i on the feature space, like the bottom middle panel of
Figure 2.
2.4. Constitution of overlap function. The evaluation function of the feature spaceis introduced by using the probability distribution of the normal and anomaly data.
In the feature space ⟨xn , xm ⟩ of subject i, the probability distributions of the normal
and anomaly data are compared. If the coordinate of the high probability of each feature

CHI-FS EVALUATION FUNCTION FOR ANOMALY DETECTION

787

space overlaps, it is natural that we consider this coordinate causes the misclassiﬁcation.
Thus, in each coordinate of the feature space, the following overlap function is calculated:∏
Di (xn , xm ) =Pci (xn , xm ).
(6)c∈CNote that it takes 0 ≤ Di (xn , xm ) ≤ 1 by the deﬁnition of the probability density functionsof Equations (4) and (5). Moreover, Di (xn , xm ) takes a higher value if the coordinate ofnormal and/or anomaly is the higher probability of its occurrence. This schematic viewis in the right middle panel of Figure 2.
2.5. Error risk. The error risk is deﬁned as the function integrating the overlap function
Di (xn , xm ) of subject i:∫ 1∫ 1i
I (xn , xm ) =Di (xn , xm ) dxn dxm .
(7)
0

0

i

The error risk I (xn , xm ) corresponds to the volume of the overlap function Di (xn , xm ).
Being a one-dimensional real-valued function, it has a higher value if the coordinates ofnormal and anomaly with the higher probabilities of their occurrence overlap. Therefore,
it is found that the feature space whose error risk is smaller is the important feature spacefor subject i.
2.6. Optimization of the feature space. Two optimal features ⟨xopt1 , xopt2 ⟩ for the
anomaly detection can be obtained by solving the following optimization problem:⟨xopt1 , xopt2 ⟩ = arg min [α mean{I(xn , xm )}′ + β std{I(xn , xm )}′ ] ,(8)xn ,xmwhere mean{I(xn , xm )} and std{I(xn , xm )} represent the mean and standard deviationof the error risk of all subjects, respectively. The prime ′ means the standardization. The
standardization is deﬁned as:v{I(xn , xm )} − min(v{I(xn , xm )})v{I(xn , xm )}′ =,(9)
max[v{I(xn , xm )} − min(v{I(xn , xm )})]
where v indicates the mean or std, and α and β represent the weight parameters which
satisfy: α+β = 1, α, β ∈ [0, 1]. If the value of α is higher than 0.5, it treats the mean valueof all subjects as important. In contrast, if β is higher than 0.5, it treats the standard
deviation of all subjects as important. We call Equation (8) “Consideration of Human
motion’s Individual diﬀerences-based Feature Space (CHI-FS) evaluation function”.
3. Evaluation of the Eﬀectiveness of CHI-FS Evaluation Function.
3.1. Evaluation by using the simulation data.
3.1.1. Outline. To conﬁrm the eﬀectiveness of the CHI-FS evaluation function discussed
in Section 2, we prepare the feature space of 14 types of simulation data assumed to beobtained from 5 subjects. We also prepare 4 patterns in the 2-dimensional feature space
plot: ‘Very Good’, ‘Good’, ‘Bad’ and ‘Very Bad’, which mean the degree of mixing of thenormal and anomaly data for each individual subject (the left side of Table 1).
The normal data are prepared of 50 plots by using the normal distribution:()
0.12 0Tu = (0.5 0.5) ,
S=
,
(10)
0 0.12where u is the mean vector of the normal data and S is the variance-covariance matrix ofthe normal data. The anomaly data is prepared 20 plots by using the uniformly random
number.

788

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

Table 1. Evaluation results for feature space of each method

Feature
space

case1
case2
case3
case4
case5
case6
case7
case8
case9
case10case11
case12
case13
case14

Subjects
1
Very
Good
Good
Bad
Very
Bad
Very
Good
Very
Good
Very
Good
Very
Bad
Very
Bad
Very
Bad
Good
Bad
Very
Good
Very
Good

2
Very
Good
Good
Bad
Very
Bad
Very
Good
Very
Good
Very
Good
Very
Bad
Very
Bad
Very
Bad
Good
Bad

3
Very
Good
Good
Bad
Very
Bad
Very
Good
Very
Good
Very
Good
Very
Bad
Very
Bad
Very
Bad
Good
Bad

Good

Bad

Good

Bad

4
5
Very Very
Good Good
Good Good
Bad
Bad
Very Very
Bad
Bad

Between
CHI-FS
CHI-FSevaluation evaluation -class andExpected
within MRS
functionfunction
ranking-class(α, β) =(α, β) =(0.5, 0.5)
(0.7, 0.3) variance
1

1

3

1

1

2
6

3
7

11
8

6
14

3

9

12

12

7

Good Good

3

2

9

2

2

Bad

7

4

2

4

4

12

10

10

5

13

11

14

13

Good Good

14

14

1

11

Bad

Bad

11

13

7

9

Bad
Bad
Good Good
Very
Good
Bad
Very
Bad
Bad

4
5

5
6

13
6

3
10

10

9

5

8

8

8

4

12

Bad

Very Very
Bad
Bad
Very Very
Good Good

5

The ‘Very Good’ is the feature space satisfying the following condition: the anomaly
data do not exist within 1σ region from the mean value of the normal data. This feature
space can divide clearly between the normal and anomaly data. The ‘Good’ is feature
space: 5 anomaly data exist within 1σ region from the mean value of the normal data.
The ‘Bad’ is feature space: 10 anomaly data exist within 1σ region from the mean value ofthe normal data. The ‘Very Bad’ is feature space: 5 anomaly data exist within 1σ region
from the mean value of the normal data. It is diﬃcult to divide between the normal data
and anomaly data in ‘Very Bad’ feature space.
The 14 cases obtained from 5 subjects we assumed are summarized in the left side ofTable 1. The robust feature space means the feature space that can clearly distinguishbetween the normal and anomaly data of various subjects, i.e., case1, case2, case5. The
case8 (‘Very Bad’ is 3 subjects, ‘Very Good’ is 2 subjects) is considered as the eﬀective
feature space for a few subjects. In contrast, the case11 (‘Bad’ is 2 subjects, ‘Good’ is 3
subjects) can be considered as the eﬀective feature space for various subjects. Thus, inthis paper, we should consider that case11 is also important. The expected top 5 ranking
is shown in the right side of Table 1.
For comparison, the between-class and within-class variance [7] and Minimum Reference
Set (MRS) [6, 8] are also used to evaluate the future space.
3.1.2. Results and discussion. The results obtained for the CHI-FS evaluation function,
the between-class and within-class variance and Minimum Reference Set (MRS) are summarized in the right side of Table 1. The number from 1 to 14 represents the ranking

CHI-FS EVALUATION FUNCTION FOR ANOMALY DETECTION

789

in each evaluation method of the 14 feature spaces. The expected top 5 ranking is also
shown in Table 1.
In the case of (α, β) = (0.5, 0.5) in the CHI-FS evaluation function of Equation (8),the evaluation results were: the ﬁrst eﬀective feature space was case1, the second one
was case2 and the third one was case5. The case1 was the feature space prepared as the
optimum, i.e., all are ‘Very Good’. Thus, the desirable result was obtained. However, it
was evaluated that case5 (3 ‘Very Good’ and 2 ‘Good’) was the third one and case2 (all‘Good’) was the second one. This evaluation result was reversed in our expectation. In thecase5, the mean of all subjects is better than that of case2. However, the distribution of
the data is very deviated. As the result, the case2 ranking became higher than case5. Fromthe point view of the proposed CHI-FS evaluation function of Equation (8), we conﬁrmedthat the second term tended to be emphasized. The same tendency was conﬁrmed, e.g.,
between case4 and case7, between case4 and case8.
As one solution, we changed the weight parameters: increase the α and decrease theβ, i.e., we considered the case of α > β. In the case of (α, β) = (0.7, 0.3), the evaluation
results are also shown in the right side of Table 1. We found that the desirable result was
obtained in the case of (α, β) = (0.7, 0.3).
In the case of the between-class and within-class variance, the ﬁrst eﬀective feature
space was case9, the second one was case6 and the third one was case1. The evaluationof the between-class and within-class variance is suited for class classiﬁcation problem [7].
Thus, we found that this evaluation result was not desirable for our purpose.
In the case of MRS, the ﬁrst eﬀective feature space was case1, the second one was case5
and the third one was case11. Although the ﬁrst and second one was obtained in thedesirable result, the third one or later could not be obtained in the desirable result. For
example, the case6 and case7 were not more robust than the case2, but the case6 andcase7 have higher ranking than the case2.
These results suggest there is a possibility that we can search for the eﬀective feature
space considering the human motion’s individual diﬀerences for anomaly detection byusing the proposed CHI-FS evaluation function.
3.2. Evaluation by using the data of the inertial sensors during car driving.
3.2.1. Outline. In Section 3.1, we conﬁrmed an eﬀectiveness of the proposed CHI-FS
evaluation function. In this section, we conﬁrm more eﬀectiveness of the proposed CHIFS evaluation function by using the data of the inertial sensors during care driving [12].
Nagasawa et al. [12] tried to detect the aimless driving including the drowsy driving byusing inertial sensors worn on the left and right wrists. By using these data and the
proposed CHI-FS evaluation function, we search for the eﬀective feature space to detect
the aimless driving. From the inertial sensors worn on the left and right wrists, the dataof X/Y/Z-axis acceleration, its composited acceleration and X/Y/Z-axis angular velocity
are obtained with sampling frequency 100Hz. We set the 60sec window and 1sec slide
width. To downsample the data, within 60sec window, we calculate the mean values ofthese data in 1sec sub-window. After that, the dynamic changes of these values are also
calculated. The dynamic change represents the amount of the diﬀerential value from justbefore and current measurements. The mean, standard deviation, variance, skewness andkurtosis of the dynamic change within 60sec window are calculated. After that, we slide
the window with 1sec slide width and repeat this procedure.
We use the mean, standard deviation, variance, kurtosis and skewness of the dynamicchanges as the feature values. As the result, the 70 feature values are obtained. We also
gave the label of normal and anomaly to the data. More details were explained in [12].

790

M. MORI, Y. OMAE, T. AKIDUKI AND H. TAKAHASHIThe number of the constructed feature spaces in this paper is 70 C2 = 2415. We evaluate
and rank each feature space by using the CHI-FS evaluation function. Moreover, weevaluate the F -measure [12] as the anomaly detection quality of each subject by using
the obtained each feature space and One Class Support Vector Machine (SVM).
3.2.2. Results and discussion. The results of the evaluation and the F -measure of eachsubject by using the obtained each feature space and One Class SVM are shown in Table 2.
To conﬁrm the eﬀectiveness of CHI-FS evaluation function for various people, we calculate
the mean and standard deviation of F -measure for all subjects. By deﬁnition of them,
the large mean value of F -measure and the small standard deviation value of F -measure
have to be selected at higher rank. We show the results of these values to the ninth line
and tenth line of Table 2.
Table 2. Evaluation results by CHI-FS evaluation function and the qualityof anomaly detection by using its space and One Class SVM
CHI-FS
F -measure (Individual subject)∗∗ F -measure
Feature space∗evaluation value
Sub 1 Sub 2 Sub 3 Sub 4 Sub 5 Mean Std.0056 (1st rank)(gy-r-sd, ax-l-ku) .846 .076 .381 .528 .485 .463 .277
.0060 (2nd rank)(gx-r-sd, am-r-sd) .488 .572 .694 .167 .439 .472 .196
.0061 (3rd rank)(am-r-sd, az-l-ku) .241 .515 .527 .264 .496 .409 .143
Evaluation .0062 (4th rank)(gx-r-sd, az-l-ku).258 .076 .502 .426 .504 .353 .184
value of.0063 (5th rank)(gx-r-sd, ax-l-ku) .789 .133 .574 .496 .538 .506 .237
the top.0063 (6th rank)(az-l-sd, am-r-sd).318 .615 .324 .247 .641 .429 .185
10 ranks.0064 (7th rank)(gx-r-sd, gz-l-sd).390 .578 .131 .469 .503 .414 .172.0069 (8th rank)(am-r-sd, ax-l-ku) .377 .199 .510 .340 .508 .387 .130.0070 (9th rank)(gx-r-sd, ax-l-sk).431 .236 .539 .394 .621 .444 .147
.0071 (10th rank)(gx-r-sd, am-l-sd) .588 .000 .231 .711 .595 .425 .298
Evaluation .1001 (2061st rank) (gx-r-sk, gy-l-sk).000 .047 .267 .288 .549 .230 .220
value.1002 (2062nd rank) (ax-r-me, ax-r-sk) .000 .503 .117 .604 .446 .334 .261
∼ 0.10.1006 (2063rd rank) (gy-r-me, am-r-va) .417 .016 .414 .076 .043 .193 .204
Evaluation .2000 (2341st rank) (gx-l-me, ay-l-va).000 .000 .006 .211 .310 .105 .146
value
.2002 (2342nd rank) (gx-l-me, am-r-ku) .000 .000 .008 .168 .022 .040 .072
∼ 0.20.2031 (2343rd rank) (gz-r-me, am-l-me) .491 .016 .057 .494 .280 .267 .229
Evaluation .6251 (2413th rank) (gx-l-me, gy-l-me) .284 .000 .000 .146 .064 .099 .120
value of the .7340 (2414th rank) (gz-r-me, gx-l-me) .283 .031 .003 .088 .279 .137 .135
lowest ranks .9316 (2415th rank) (gx-l-me, gz-l-me) .000 .000 .000 .123 .104 .045 .063∗
1st-digit: (ax/ay/az/am, x/y/z/composited acceleration) (gx/gy/gz, x/y/z angular velocity), 2nddigit: (r/l, inertial sensor of the right/left wrist), 3rd-digit: (me/sd/va/sk/ku, mean/standard deviation/variance/skewness/kurtosis of the dynamic change)∗∗
Boldface means F -measure ≥ .400 and the underline means the maximum of F -measure in its space.

In case of the top 10 ranks, the mean value of F -measure for all subjects is .353 ∼ .506,
and the F -measure of each subject is large overall (Especially, the 4 out of 5 F -measuresof the feature spaces of the 2nd and 5th rank exceed .400.). Moreover, about the standard
deviation value of F -measure of all subjects, there are no extremely large dispersion in
the feature space of top 10 ranks.
If the CHI-FS evaluation value becomes larger, then the mean of F -measure also tends
to become worse. On the other hand, the standard deviation of F -measure is overall
smaller dispersion, but this is because of extremely small F -measure of each subject if theevaluation value becomes larger. If the evaluation value of the CHI-FS evaluation function
shows good value (small value), the detection accuracy for the normal and anomaly datais good. Note that even if the feature space is evaluated as the top rank, there are somecases that F -measure of subject 2 is low. There is a possibility that the subject 2 has the
speciﬁc individual diﬀerence.

CHI-FS EVALUATION FUNCTION FOR ANOMALY DETECTION

791

These results also suggest even if we use the real data of the inertial sensors, there
is a possibility that we can search for the eﬀective feature space considering the humanmotion’s individual diﬀerences for anomaly detection by using the proposed CHI-FS evaluation function. However, we emphasize that we need more veriﬁcation.
4. Summary. We proposed the feature space evaluation function named “Considerationof Human motion’s Individual diﬀerences-based Feature Space (CHI-FS) evaluation function”. We also conﬁrmed the eﬀectiveness of the proposed CHI-FS evaluation function byusing the simulation data and the data of the inertial sensors during car driving. However, the validation is not suﬃcient because the number of subjects is low. We need more
veriﬁcation.
As the future work, we will perform more veriﬁcation of the eﬀectiveness and reliability
to other case studies. In this paper, for simplicity, we discuss the case of the 2-dimensionalfeature space. The extension of Equation (8) for the n-dimensional feature space is not
so diﬃcult. However, it is easy to notice that the calculation cost becomes high. Thus,
the reduction of calculation cost is also an important issue.
Acknowledgments. 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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