Journal of Robotics, Networking and Artificial Life
Vol. 7(1); June (2020), pp. 41–47
DOI: https://doi.org/10.2991/jrnal.k.200512.009; ISSN 2405-9021; eISSN 2352-6386
https://www.atlantis-press.com/journals/jrnal

Research Article

Verification of a Combination of Gestures Accurately
Recognized by Myo using Learning Curves
Kengo Kitakura, Hideyuki Tanaka*
Graduate School of Education, Hiroshima University, Kagamiyama 1-1-1, Higashi-hiroshima, Hiroshima 739-8524, Japan

ARTICLE INFOABSTRACT

Article History

This paper studies verification of a combination of hand gestures recognized by using the Myo armband as an input device.
To this end, relationship between data distribution and learning curves is investigated for binary classification and multi-classclassification problems. A verification method is then proposed for finding a combination of gestures accurately classified.
Experiments show effectiveness of the proposed method.

Received 31 October 2019
Accepted 25 February 2020
Keywords
Learning curve
data distribution
Myo armband
American signreliable gesture recognition© 2020 The Authors. Published by Atlantis Press SARL.
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

1. INTRODUCTION
A technique for hand gestures recognition from surface
ElectroMyoGraphy (sEMG) is useful for extending means of humancommunication. To find the rule of sEMG that corresponds to thestate of hand gestures, machine learning is often used (e.g. Savur and
Sahin [1] and Galea and Smeaton [2]). Recently, the Myo armband[3] is one of the most popular sEMG acquisition systems, because
it is relatively inexpensive and easy to remove. The Myo armband isbeing regarded as one of the tools for operating virtual reality (VR)[4] and for communicating with hearing impairment [1], and so on.
In developing various applications of Myo as an input device, it
is important to verify a combination of gestures learned from theMyo data, because we cannot develop a reliable application withoutfinding a combination of gestures accurately classified. To find sucha combination, we need to confirm that the number of the data
used for learning is sufficient, but we cannot from a single matrixof classification accuracy.
There is a method for confirming that the number of the data used
for learning is sufficient; that is using a learning curve [5]. The
meaning of the learning curve in the context of machine learning
is mainly divided into two [6]. One is a graph that is created byplotting performance measure against the training iteration on thecondition that the number of training data is fixed. The other is agraph that is created by plotting performance measure against the
number of the data used for training. In this study, we mean thelearning curve by the second graph; it is created by plotting classification accuracy of training or test against the number of data fortraining.
Corresponding author. Email: tanakalpha@hiroshima-u.ac.jp*

In several studies, the learning curve has been used for predicting the data required for DNA classification [7] and for comparing
the methods of machine learning algorithms [8], and so on. Thesestudies have used the averaged learning curve, which is an averageof the discrimination accuracy of all classes. In contrast, Wahba
et al. [9] proposed to use the learning curve for individual classes.
Learning curves are useful for verifying a combination of gestures
accurately classified, because they possibly offer information on theboundary and data distributions. Learning curves indeed indicate
accuracy of a classifier, and accuracy depends on the boundary anddata distributions. However, the relationship between learning curves
and data distributions has not been clear. If the relationship is clarified,
it would be useful for inferring them in a high dimensional space.
There are a lot of studies on gesture recognition using the Myoarmband [1,2,10]. But research has not been done for finding a
combination of gestures accurately classified in the light of learning
curves.
In this paper, we study relations between learning curves and data
distribution. We then verify a combination of gestures accurately
classified using a Myo armband.

2. MYO ARMBAND AND GESTURES
Myo (Figure 1) is an armband type gesture controller developedby Thalmic Labs. It measures sEMG of the arm (Figure 2). Myo
has sEMG sensors of eight channels and its sampling frequency is
200 Hz. The sEMG measured by each channel is converted fromanalog to digital and is sent to the PC as an integer value between−128 and 128 by Bluetooth. The signal indicates the amount ofactive muscle fibers and is a dimensionless value.

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42

We deal with the sEMG data of 24 gestures except “j” and “z” inASL, because we classify the hand gestures by using only the sEMG
data and the gestures of “j” and “z” include motion of fingers. To
conduct experiments, we make training and test dataset. The sizeof each dataset is 24 × 100. We use K-nearest neighbor of the scikitlearn toolkit for classification.

3. LEARNING CURVE AND
DATA DISTRIBUTION
Figure 1 | Myo armband it has eight channels.

In this section, given the training and test data sets, we study characteristics of learning curves. We first consider a binary classification problem given the uniformly distributed data, and then amulti-class one given the normally distributed data. Suppose thatthe training data x1 ,¼, x N Î  d are given.
We construct the learning curve by increasing the training data
one-by-one chosen from the given data. We compute the learning
curve by taking the average, because the learning curve depends on
how to increase the training data. We will show how to increase thedata in Appendix A.

Figure 2 | Wearing Myo armband.

3.1. Binary Classification Problem
Suppose that the dimension f of the feature space is 1 and consider
a binary classification problem (c = 2). Assume that the training
data belonging to A and B are given and are uniformly distributed
as follows:		 0.1 £ x A (k) £ 0.5, 0.6 £ x B (k) £ 1.0, 
where ξA(k) and x B (k ) Î  are respectively the k-th training data(k = 1, …, N). We hence have training data:
xk = [x A (k), x B (k)]T Î  d(k = 1,¼, N ),where d = fc = 2. We moreover suppose that the test data corresponding to A and B are given, and that they are respectively labeled
as A′ and B′. The test data are uniformly distributed as follows:
0.3 £ x A¢ (k ) £ 0.7, 0.4 £ xB¢ (k) £ 0.8,
where ξA′(k) and x B¢ (k ) Î  are respectively the k-th test data(k = 1, …, M).

Figure 3 | American sign language [12].

Let us represent the sEMG by vl(t), where l is the number of channel(l = 1, …, 8) and t is the time index (t = 1, …, Nv). We use the average of the absolute value wl(t) for each channel in 1 s as features forclassification and define as follows:		 wl ( j) =1 200
å vl (200( j - 1) + t ) , 
200 t =1

(1)

where j = 1, …, Nw and l = 1, …, 8. It should be noted that the features(1) were used by Donovan et al. [11] as the mean absolute value (MAV).
American Sign Language (ASL) is a sign language mainly used in
North America. It is published by National Institute on Deafness
and Other Communication Disorders [12] and shown in Figure 3.

We show the distribution of training and test data in Figure 4. The
classification boundary is 0.55, if the number of the training data
is sufficiently large, because the boundary is between 0.5 and 0.6 in
the training data set and the boundary 0.55 maximizes the marginof classification. If the number of training and test data, N and M,
are sufficiently large, the percentage of the blue area in Figure 4
represents the misclassification rate:e=(0.7 - 0.55) + (0.55 - 0.4)
= 0.375(0.7 - 0.3) + (0.8 - 0.4)

The misclassification rate e is obtained by the volume of the misclassification areas of A′ and B′ (blue areas), supposing that thedata of A′ and B′ are uniformly distributed. The accuracy rate ismoreover given by 1 − e for large M and N.

K. Kitakura and H. Tanaka / Journal of Robotics, Networking and Artificial Life 7(1) 41–47

		 1 - eN =Figure 4 | The distribution of training and test data. The first row represents
the training data, and the second and third rows the test data. The data inthe blue area is misclassified by the classification boundary 0.55.

1 m M A ¢ ( p) + M B¢ ( p)
å 2M ( p) . 
m p =1

43(2)

The left hand side of (2) is related to the learning curve at N, andthe right hand side depends on the test data and the boundary
set by the N training data. In other words, the right hand side
represents the percentage of data that does not violate the boundary. It should be noted that the test data are uniformly distributed, but the right hand side of (2) can be calculated regardlessof the distribution, by just counting the number of not violating
the boundary.

3.2. Multi-class Classification Problem

Figure 5 | Learning curves. Blue and red curves respectively represent thelearning curves for the training and test data. The value of the learning
curve for the test data at i = 300 is approximately 62.5%.

The learning curve is created by plotting the classification accuracy 1 − ei against the number of training data i, where ei is misclassification rate for i. The accuracy of the learning curve 1 − eN
approaches 1 − e, as the number of the training data N becomeslarge. We therefore see that the accuracy rate 1 − e of the classification for the test data (Figure 4) is related with that for sufficiently
large data in the learning curve (Figure 5). This fact implies thatthe accuracy rate of K-nearest neighbor is 1 − 0.375 (62.5%), if N
and M are sufficiently large.
Let us consider the case where N and M are finite. We draw the learning curves of training and test data by averaging m learning curves
obtained by the m maps (SN,k); see Appendix A. We use p as an identifier (p = 1, …, m). We describe the number of the test data for p as
M(p) and suppose that the classifier sets a classification boundary atz(N), given N training data. We express the total numbers of k satis ¢ ( p) :fying the following inequalities respectively by MA′(p) and M
A

We study a multi-class classification problem. Let us consider datain feature space of f = 2 dimensions and classify them into c = 3
classes. Suppose that normally distributed data wA(n), wB(n), andwC (n) Î  f (n = 1, ¼, N ) are given as training data and labeled
as A, B, and C, respectively. We then construct vector variables
xn Î  d for (n = 1, …, N):		 xn = [ wA (n)T , wB (n)T , wC (n)T ]T . 
Assume that normally distributed data wA′(n), wB′(n), andwC¢ (n) Î  f are given and corresponding to the labels of A, B, andC, respectively. Figures 6 and 7 respectively show the training data
A, B, and C, and test data A′, B′, and C′. The green lines in Figures
6 and 7 are the classification boundaries trained by all the data A,
B, and C. The results of drawing individual learning curves for the
training and test data are shown in Figures 8–10. Averaged learning
curves for test and training data are shown in Figure 11.
From the individual learning curves of training and test data in
Figures 8–10, we examine the relationship between the classification boundary and the distribution of the training and test data in
Figures 6 and 7.

0.3 £ x A¢ (k) £ z (N ), z (N ) £ x A¢ (k) £ 0.7,
meaning that the number of data correctly classified is MA′(p) and ¢ ( p) ; i.e. the following equation isthat the one misclassified is M
Asatisfied: ( p) .
M ( p) = M ( p) + M
A¢A¢Figure 6 | Training data indicating three classes of A, B and C. The green
line is the boundary of the classes.

In the same way, we express the total numbers of k satisfying the ( p):
following inequalities respectively by MB′(p) and M
B¢z (N ) £ x B¢ (k) £ 0.8, 0.4 £ x B¢ (k) £ z (N ),meaning that the number of data correctly classified is MB′(p) and ( p); i.e. the following equation isthat the one misclassified is M
B¢established: ( p) .
M ( p) = M B¢ ( p) + M
B¢The accuracy rate 1 − eN is then given by averaging the accuracy calculated from the number of correctly classified data (Appendix A):

Figure 7 | Test data indicating three classes of A′, B′ and C′. The green
line is the boundary of the classes.

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K. Kitakura and H. Tanaka / Journal of Robotics, Networking and Artificial Life 7(1) 41–47

Figure 8 | Learning curves (A, A′). Red line is the learning curve oftraining, and blue line is that of test.

We can obtain the ratio of misclassification caused by changes of
distribution between training and test, from the gap between thelearning curves of training and test data. For example, there is a gap
between A and A′ in Figure 8. In this case, the ratio of test data correctly classified is lower than that of training data. This is because
the test data A′ violates the boundary defined by the training data
A in Figure 7. On the other hand, the data B′ is correctly classified
by the boundary set by the training data. In this way, we can findtest data seriously affected by distribution changes, by constructing
individual learning curves.

4. EXPERIMENTS
We investigate characteristics of the data of Myo in Section 4.1 andpropose a method for finding a combination of gestures accurately
classified in Section 4.2.

Figure 9 | Learning curves (B, B′). Red line is the learning curve oftraining, and blue line is that of test.

Let us consider data in a feature space of f = 8 dimensions and classify them into c = 24 classes; they corresponds to characters of thealphabet except “j” and “z”. Using wl(j) in (1), we define the dataof Myo in the feature space as w( j) = [w1 ( j), w2 ( j),¼, w8 ( j)]T Î  f .
Suppose that the training data for the label “a” to “y” except “j” arerespectively given by wa(n) to wy(n) except wj(n) (n = 1, …, N). We
moreover construct vector variables:
xn = [wa (n)T , wb (n)T , ¼, w y (n)T ]T Î  d ,where d = fc.

Figure 10 | Learning curves (C, C′). Red line is the learning curve oftraining, and blue line is that of test.

4.1. Visualization of Myo Data
We visualize the features extracted from the data of Myo to see thecharacteristics of the data distribution. Figures 12 and 13 indicate theresults of principal component analysis showing eight-dimensionalfeature values obtained from Myo by reducing the dimensions to
2. Each of the three classes corresponds to a, b, and f gestures. Even
if Myo is not removed between training data acquisition and test
data acquisition, the data distribution changes between training
and test data acquisition, and it makes learning difficult. This is

Figure 11 | Learning curves (averaged). Red line is the learning curve oftraining, and blue line is that of test.

In the same way as deriving (2), we see that the accuracy of the test
data B′ is equal to the ratio of the data B′ that does not violate theboundary determined by the training data A, B and C. The label
B′ is indeed classified with 100% accuracy as shown in Figure 9,
indicating that all test data of B′ are not outside of the trained areaof B (Figure 7). The label B is also classified with 100% accuracy(Figure 9), showing that all training data of B can be trained correctly (Figure 6). We observe that the labels C and C’ are also classified with almost 100% accuracy. On the other hand, we see from thelearning curve in Figure 8 that accuracy of classification of A′ at 300
sets of data is about 70%. This fact implies that the test data of A′
cross the classification boundary and that some of them are outsideof the classification area of A as shown in Figure 7.

Figure 12 | Training data of Myo.

Figure 13 | Test data of Myo.

K. Kitakura and H. Tanaka / Journal of Robotics, Networking and Artificial Life 7(1) 41–47

true for the case where Myo is removed as well. We will therefore study verification of a combination of gestures using learning
curves based on the investigation of the boundary and the test data
in Section 3.

4.2. Method for Verification
We verify a combination of gestures that can be classified withhigh accuracy. We first acquire 24 training and test data labeled“a” to “y” except “j”. We then make verification, using individual
learning curves and averaged ones and conducting experiments
for acquiring data.
Suppose that the numbers of training and test data are the same
(N = M). Let us draw individual learning curves of training and test
data. If accuracy is low for a label (e.g. “k”) in both training and test
data at N and if the gap between them are very small, then there
is a possibility that accuracy of the classifier for the label (e.g. “k”)
may be enhanced by excluding another label that makes conflict forclassification. We should therefore keep such a label (e.g. “k”), if thegap between learning curves of training and test data is small. On
the other hand, if there is a large gap between the training and test
data in learning curves of a label (e.g. “f ”), then the label (e.g. “f ”)
should be excluded from the classification target.
We show an example of learning curves for a gesture to be excludedin Figure 14. Even if the learning curve of training is seen thatclassification is possible, the gesture should be excluded from theclassification target in case that the learning curve of test data at
N indicates low accuracy because of the gap between the training
and test data. We show another example of the gesture regarded asa classification target in Figure 15. Accuracy for training and test
data are both high, and there is almost no gap between them.
Let us reduce the number of the combination of gestures from cs
to ce for finding a reliable one. Based on the above consideration,
the combination of gestures is verified by the following verification
algorithm.

Figure 14 | Example of learning curves for a gesture (“f ”) to be excluded.

45[Verification algorithm]:
Step 1: Draw individual learning curves and an averaged one for thenumber of classes cs.
Step 2: Exclude the gesture that has a large gap between learning
curves of the training and test data. If there are no more gestures tobe excluded, then go to Step 5.
Step 3: Re-acquire data for gestures that are not excluded in Step 2
and draw the individual and averaged learning curves.
Step 4: Repeat Steps 2 and 3 until there are no more gestures thatcan be excluded in Step 2.
Step 5: Re-acquire data for not excluded gestures and draw the individual and averaged learning curves. Check if an averaged learning
curve has a satisfactory discrimination accuracy. If it is unsatisfied,
go to Step 2.
In Step 2, excluded gestures are determined by referring the accuracy indicated by the learning curve as shown in Figures 14 and 15.
Suppose that the number of the training data is a. In this experiment, a is 20. The value of a depends on the user who allows how
much time for learning. The more a is increased, the more time isneeded for learning. Of course, the user can reduce the value of aby seeing the learning curve.
We make experiments and apply the proposed method to thedata. Since data distribution depends on removal of Myo between
experiments, we investigate verification by taking the interval
time between test and training data acquisition into account. We
thus consider two cases: For the first case we do not remove Myo
between data acquisition (Case 1), and for the second case we do it.
We moreover consider two cases in the second case: There is little
time in the interval (Case 2), and there are several days (Case 3).
We apply the verification algorithm and conduct experiments inthe order of Cases 1–3, since the number of the reliable combination is decreased in the order of them.

4.3. Results of Experiments
We determined the threshold γ for the gap of accuracy between training and test data as 20%. We obtained a combination of gestures withhigh accuracy for each of Cases 1–3, extracting a combination of gestures that was not in a trade-off relationship. As a result, we found thefollowings. In Case 1, five gestures “e”, “k”, “q”, “r”, and “y” can be classified with 100% accuracy. Also, in Case 2, the classifier obtained by
the verification algorithm can classify the four gestures “e”, “k”, “q”, and“y” with 99% accuracy. But in Case 3, only two gestures “k” and “q” areclassified with 99% accuracy.

5. CONCLUSION

Figure 15 | Example of learning curves for a gesture (“k”) not to be
excluded.

In this study, we investigated the relationship between data distribution and learning curves, and we then verified a combination of
ASL that is accurately classified using a Myo armband. In addition, asa result of investigating the characteristics of the data acquired from
Myo, it was found that the distribution of data changes between theinterval of training and test data acquisition, and verifications werehence carried out for the cases of different intervals. It remains a future
topic how to determine the threshold γ for the gap to ensure accuracy.

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46

APPENDIX A. APPENDICESCONFLICTS OF INTEREST

Suppose that the data x1 ,¼, xN Î  d are given. We pick up the datafrom them and increase the training data from 1 to n(n ≤ N). There
are many combinations in increasing training data via picking up
them one-by-one. We construct the learning curve of a classifierby averaging them for different combinations, because the learning
curve depends on how to increase the data.

The authors declare they have no conflicts of interest.

We explain how to construct the learning curve. Let us consider apermutation map sN: {1, …, N} → {1, …, N}. Since there exist N!
maps for sN, we describe them by sN,k (k = 1, 2, …, N!), where sN,i ≠s (i ≠ j). For s , define x1, k , x 2, k , ¼, x N, k Î  d as:
N,j

N,k

é x1, k ùé x1 ù
ê
ú
ê ú

:
S
=
ê
ú
N , k ê  ú , SN , k : = s N , k Ä I d ,ê úê xN úë û
êë x N, k úû
where Id is the identity matrix of d × d, and ⊗ is the symbol
for the Kronecker product [13]. Since x1, k ,¼
� , x N, k are given bychanging the order of x1, …, xN, the following equation holds fork = 1, …, N!

{ x , ¼, x } = { x , ¼, x },
1, k

N ,k

N

1

meaning that the set of x1, …, xN and that of x1, k , x 2, k , ¼, x N , k aresame. Define a set D = x1, k , ¼, x i , k and let h be the classii,k

{

}

i,k

fication accuracy of the classifier learning from the training dataDi,k(i = i0, …, N), where i0 is the minimum number of data required
for the classifier. Let us randomly choose m maps from the maps
sN,k (k = 1, 2, …, N!) and take an average for accuracy hi,k for the
training data Di,k:m

 = 1 h .
hi
å i,km k =1 construct a learning curve
The index i and averaged accuracy hifor the training data. Given the test data, let qi,k be accuracy of theclassifier for the training data Di,k and take an average for qi,k forthe training data Di,k:m

1qi = åqi , k ,m k =1 construct a learning curve for the test data.
where i and hi

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47

AUTHORS INTRODUCTION
Mr. Kengo Kitakura

Dr. Hideyuki Tanaka
He graduated Department of Electrical andInformation Engineering National Instituteof Technology, Kure College in 2016. He
graduated Program in Technology andInformation Education, school of education, Hiroshima university in 2018. He has
been a student of master course of Graduate
school of Education, Hiroshima university
and will graduate in March 2020.

He graduated master course at graduate school of engineering in Kyoto
University and received Dr. (Eng.) from
Kyoto University. He is now a memberof Graduate School of Education in
Hiroshima University. He is a member ofIEEE, SICE, and ISCIE.