Main disease classification of intermittent claudication via
L1-regularized SVM
Tetsuyou Watanabe1 , Takeshi Yoneyama1 , Yasumitsu Toribatake2 and Hiroyuki Hayashi2
Abstract— There are multiple diseases that cause intermittent
claudication, including lumber spinal canal stenosis (LSS) andperipheral arterial disease (PAD). LSS is categorized on thebasis of the diseased part: L4 and L5. The medical treatment
for these groups is totally different and the differentiation isimportant. With this in mind, we examined walking-motion
data for patients and derived several features for the differentiation in previous studies. However, these features were notspecialized for classification, and there is no guarantee that thefeatures are effective for real differentiation. The present study
investigates the possibility of differentiation by gait analysis, via
use of an L1-regularized support vector machine (SVM). An
L1-regularized SVM can execute both classification and feature
selections simultaneously. On the basis of this method, ourpaper presents the methodology for classifying the underlying
disease of the intermittent claudication with an accuracy of
79.7%. In addition, new effective features for the differentiation
are extracted.

I. INTRODUCTION
There is a walking symptom called intermittent claudication [1], in which patients experience severe pain in thelower limbs while walking. However, they can walk again
after taking a break. The main diseases that cause thispain are lumber spinal canal stenosis (LSS) and peripheralarterial disease (PAD). Toribatake et al. [1] pointed out
the similarity between PAD and LSS groups. The medical
treatment for both these groups is totally different. Then,
it is very important to differentiate these diseases. LSS canbe divided into L4, L5, and S1 radiculopathies based on
the stenosis area. Among the 3 radiculopathies, S1 is rare
and sometimes does not require any treatment. This paper
focuses on L4 and L5. Herein, the differentiation of healthy
controls (Normal), PAD, L4, and L5 patients is considered.
Generally, to identify the main disease, several tests suchas angiography, myelography, magnetic resonance imaging(MRI), and ankle brachial index (ABI) [2] are conducted.
These tests are precise but are invasive and expensive. In
addition, highly skilled professionals are required to conduct
the tests. These drawbacks make it difficult to conduct thesetests at small hospitals. Moreover, at-home differentiation
might be useful. The best differentiation method would use
the minimum number of simple instruments that could be
easily used by even non-professionals.The affected area of*This work was not supported by any organization
1 T. Watanabe and T. Yoneyama are with the School of MechanicalEngineering, Kanazawa University, Kakuma-machi, Kanazawa, 920-1192,
Japan (corresponding author to provide phone: +81-76-234-4682; fax: +8176-234-4682; e-mail: twata@t.kanazawa-u.ac.jp)
2 Y. Toribatake and H. Hayashi are with the Department of Orthopedic
surgery, Kanazawa University

legs are different from the diseases. Then it is possible thatgait pattern is also kinematically different from the disease.
With this in mind, we developed another examination
method for analyzing two-dimensional walking motion measured by commercially available cameras [5], and we derived
several differentiation factors [6]. However, classification
was not taken into account in the factor deviation, and thefactors are not always suitable for classification. There areseveral studies on gait analysis of intermittent claudication
by other groups [3], [4]. However, differentiation has notbeen considered in any study thus far.
This paper presents an approach for a classification
methodology with L1-regularized SVM that extracts relevant
features with the classification and the differentiation. L1regularized SVM is a classifier for linear classification with alarge number of instances/features, and can select the relevant
instances/features simultaneously with the classification. On
the basis of information obtained in previous studies [5], [6],we define candidates of the features (such as fundamental
statistics), and make the features sparse with a Gaussian basis
function. The sparseness of the input instances/features gives
a highly accurate classification of the Normal, PAD, L4 andL5 groups of patients. The main difference of the extracted
features with the differentiation features from the previous
studies is that those are valid for not the entire group but apart of the group, and can deal with individual differences.
II. M ETHODOLOGY
A. Participants
The participants were 13 healthy individuals (Normal;
5 men and 8 women), 13 PAD patients (12 men and 1
woman), 11 LSS (L4) patients (7 men and 4 women), and
22 LSS (L5) patients (9 men and 13 women). Diagnosesof the participants were made by conducting MRA, ABI,
MRI, contrast-enhanced CT, selective nerve root blocks,
and radiological examinations, and considering any clinicalfeatures and surgical findings.
B. Motion capture
The following is the goal of the proposed system. People measure their walking by using a commercially available camera, although the obtained gait pattern is twodimensional. Upon sending the data to the server, the server
determines which disease most likely causes the intermittent
claudication and which the individual should go to, vascularsurgery or orthopedics. The system would be available atsmall hospitals and at home. The requirements for the walking measurement system are easy setup, easy measurement,

Subjecteasy calibration, available for use in small spaces, and shortmeasurement time. With these in mind, we set up the simple
walking measurement system (Fig. 1). Participants attached
LED makers and walked on the treadmill in semidarkness
such that the LED lights can be easily seen. The positionsof the markers are the acromion, anterior superior iliac, headof the fibula, lateral malleolus and the 5th metatarsal headof the participant (Fig. 2a). Note that the right side is facing
forward, as shown in Fig. 2. The markers were attached to theimpaired leg. To determine a safe treadmill speed for normal
walking, the participants practiced walking on the treadmill
before the actual experiment. During the experiment, if theparticipant felt pain, we stopped the measurement. For safety,
doctors watched the participants to help in the event of an
accident. As described later, we used only angles for the
analysis, and did not do any calibrations (for example, forestimating leg length). For recording the gait pattern, weused a commercially available camera with a frame rate of
30 [frame/s].

5 LED Markers
Camera800~900mm
TripodTreadmillFig. 1.

2300~3000mm

Walking measurement systemyyAcromion(Marker 1)(x1,y1)

Upper body angle(x2,y2)=(0,0)

xxAnterior superior
iliac (Marker 2)

Femur angle

Head of the fibula (Marker 3)(x3,y3)Knee angle
Ankle angle

Lateral malleolus (Marker 4)(x4,y4)(x ,y )
5

5

The fifth metatarsal head (Marker 5)(a) Marker positions(b) Angles

C. Analysis
The angles used for analysis are shown in Fig. 2b. We
detected the marker positions by our own algorithm [5]based on an LK filter [7]. We derived the angles from themarker positions. Note that the angles are not identical tothe actual angles because they are mapped on the sagittal
plane; we also gave them arbitrary names. The accuracy ofthis system depends on the resolution of the camera and the
distance between the treadmill and camera. The resolution
was 0.007∼0.04 [rad].
III. D IFFERENTIATION VIA L1- REGULATED SVM
A. L1-regulated SVM
Here, L1-regulated SVM [8] is introduced. Consider the
given pairs of instances and labels (x1 , y1 ), · · · , (xm , ym )where xi ∈ Rn and yi ∈ {−1, 1} is the label for xi .
We consider the following problem.
min  w 1 +C
w

m


ξi2

(1)

i=1

ξi = max(0, 1 − yi wT xi )Here  · 1 expresses L1 norm. Note that  w 1 is theregularization term and ξi is the hinge loss. The original
SVM [9] can be regarded as the problem that minimizes
the error (loss) with the regularization term expressed by L2
norm. By using the regularization term expressed by L1 norm
instead of the original L2 norm, the problem can becomea type of least absolute shrinkage and selection operator(LASSO) [10]. Thanks to the characteristic of the constraints,
the part of the components of w is perfectly identical to zero.
Then, LASSO can automatically select relevant instances(features), and can handle a large number of instances (n)compared to the number of the data pairs (m). Therefore,
we can define a large number of candidates of features as
the components of instance xi , without considering whether
or not the candidates are relevant or irrelevant.

Fig. 2.

The coordinate frame, the marker positions, and the angles

Let di ∈ Rl be the original data corresponding to xi . The
relationship between di and xi can be represented by
xi = φ(di )(2)where φ = [φ1 φ2 · · · ]T is the basis function. Note that ingeneral, n  l. Different from the original SVM, for φ, it is
not necessary to construct kernel function like K(xi , xj ) =φ(xi )T φ(xi ). Any type of nonlinear functions can be used
as φ.
Given test data dt , the decision of the classifier is donebysgn(f (dt )) = sgn(wT φ(dt ))(3)

Note that we can add a bias term such as f (d) =wT φ(d) + b by letting one component of φ be 1.
The goal of the differentiation is that given a (test) dataset, we appropriately judge which group among the Normal,
PAD, L4 and L5 groups the data belongs to. Then, a 4class classifier is needed, although L1-regularized SVM isa binary classifier. A one-versus-the-rest (OVR) approachis used for constructing the 4-class classifier. OVR is used
to train k independent binary classifiers where at every ithclassifier, we split the data set into two classes: one is thedata belonging to the ith class and the other is the remaining
data. Letting the label for the former data set be positive andthe label for the latter data set be negative, we conduct thetraining. Then, the ith classifier decision is done bysgn(fi (dt )) = sgn(wTi φ(dt ))(4)

The overall decision is done by
i = argmax fi (d)i(5)

TABLE IC OMPONENTS OF DATA (d) FOR INPUT OF THE L1- REGULARIZED SVM.
N OTE THAT WE CONSIDERED THE LISTED VALUES WITH REGARD TO

Predicted class
Normal PAD
L500
Normal12
Actual
PAD
1
8
3
class
L5
0
0
20
L4
1
2
1

EVERY ANGLE SHOWN IN F IG .2 B AND THE ANGLES CORRESPONDING TO
THE QUADRICEPS AND GASTROCNEMIUS MUSCLES .

averageof angle at
maximum
1 cycleminimumswing phase
medianstance phase
range
Average of 10/20 points before swing phase starts
Average of 10/20 points after swing phase starts
Average of 5/10 points before and after stance phase starts
Average of 5/10 points before and after the maximum point
Average of 5/10 points before and after the minimum point

L4
1
1
2
7

Fig. 3. Confusion matrix of the L1-regulated SVM classifier. Total accuracy
was 79.7%
TABLE II
T HE AVERAGE NUMBER OF SELECTED FEATURES FOR EVERY
CLASSIFIERClassifier for Normal vs others
Classifier for PAD vs others
Classifier for L5 vs others
Classifier for L4 vs others

175.4
255.3
324.0
245.4

B. Application methodology
We took the first 10 cycles per participant from therecorded data. We approximated the gait pattern for every
angle by spline curves and took 101 equally spaced data
points (with respect to time) from one cycle of the gait
pattern. Then, all of the data obtained for every angle wasmade into a 101 dimensional vector. Utilizing the data vector,
we calculated the average, maximum, minimum, and medianvalues with respect to 1 cycle and the swing and stancephases. Note that we focused on the motion of the marker
attached on the 5th metatarsal head. We regard the time
when the x component of the marker position is maximum
as the stance phase start time. Similarly, we regarded thetime when the marker position is minimum as the swing
phase start time. In addition, we considered the stance phasestart time, swing phase start time, the time when the angle ismaximum and minimum as the special points, and calculated
the average values around the special points. The details of
the calculated values are shown in Table I. We calculated
these values with regard to every angle shown in Fig. 2b, andAngle 5 = Upper body angle + Femur angle − Knee angle
and Angle 6 = −Knee angle + Ankle angle. In our previous paper [6], we showed that with regard to the factors
associated with the quadriceps and gastrocnemius muscles(biarticular muscles), there are statistically significant differences between some groups. Then, we additionally calculated
the feature values with regard to Angle 5 corresponding to
the quadriceps muscle and Angle 6 corresponding to thegastrocnemius muscle. These listed values are regarded asdata d ∈ Rl (= R150 ).
L1-regularized SVM is normally for the case when thenumber of instances is much larger than the number of data,
and the instances are supposed to be sparse. Then, in order toobtain the sparseness of the instances and good classification,
we considered the following basis function
 dj − djkavg 2)
φjk (d) = exp(−
2
2σjk(j = 1, · · · , 59, k = 1, · · · , 150)

(6)where djkavg and σjk are respectively the average and variance values for the jth original instance dj (jth componentof d) of the kth participant. In total, 90000(= 150+59×150)
instances were used where the number of participants is 59
and d itself is included (φ(d) = d).
In order to investigate the possibility of differentiation,
the one subject-leave-out method was used. Data for one
participant were used as test data and the remaining data wereused as training data. We had 59 participants, and repeatedthe analysis 59 times while changing the test data. Because
there were 10 data sets for every participant, we had 10
results at every test. We decided which group the participant
belongs to by a majority vote.
C. Results
Fig. 3 shows the results of the classification in the formof a confusion matrix. The total classification accuracy
was 79.7%, which confirms the efficiency of the present
approach.
The L1-generized SVM classifier can select relevant features. In order to see the effect, we investigated the numberof selected relevant features for every classifier that is forclassifying one specified group and the other groups. The
results are shown in Table II. It can be seen that the relevant
features are effectively selected, and the number of therelevant features are definitely much smaller than the numberof the input features (instances).
In order to see which kinds of features are effective
for classification and selection, we investigated the relevant
selected features. Regarding the features/instances expressedby (6) as the jth component (feature) of di , we counted
the number of relevant features. Table III shows the relevant
features for each classifier, which are the features selectedmost often.
D. Discussion
Although the total accuracy for classification was good,it should be improved. The classification accuracy for theNormal and L5 groups was very high while that for the
PAD and L4 groups was not high. L1-regularized SVM
is not suitable for dealing with the correlation between
instances/features. In the present approach, we did not define
the instances/features φ considering the correlation between

TABLE III
T HE RELEVANT FEATURES SELECTED MOST OFTENClassifier
Normal vs others
PAD vs others
L5 vs others
L4 vs others

Relevant features
Minimum value at stance phase of Femur angle
Range at swing phase of the angle
corresponding to the gastrocnemius muscle
Average of 20 points before the swing phase of
the Ankle angle starts
Median of the Femur angle at 1 cycle

90
80
70

Frequency

60
50

L4

40

L5

30

PAD

20

Normal

10
78.9
80.2
81.5
82.9
84.2
85.5
86.9
88.2
89.6
90.9
92.2
93.6
94.9
96.3
97.6
98.9
100.3
101.6
102.9
104.3

0

Median of the Femur angle during one cycle [degree]

Fig. 4. Distribution of the median values of the Femur angle during one
cycle. This feature is for classifying L4 and the other groups.
90
80
70

Frequency

60
50

L4

40

L5

30

PAD

20

Normal

10
89.1
92.4
95.7
99.1
102.4
105.7
109
112.4
115.7
119
122.3
125.7
129
132.3
135.6
139
142.3
145.6
149
152.3

0

Average of 20 points before the swing phase of the Ankle angle starts

Fig. 5. Distribution of the average values of 20 points before the swing
phase of the Ankle angle starts. This feature is for classifying L5 and theother groups.

the components of data d, because the number of all possible combinations of the correlation is extremely large andconsequently untreatable. This might be one reason why theclassification accuracy for the PAD and L4 groups is nothigh. How to deal with the correlation is part of our future
work. As shown in Table II, the number of relevant features
for classification of the L5 group is the largest, which might
affect the good classification result shown in Fig. 3. Note
that, in general, classifying the Normal group is easier thanclassifying the other groups, and then the required numberof relevant features was small.
Among the features listed in Table III, we focus on thefeatures for classifying the L4 and L5 groups because thatfor the PAD group is close to the features presented in [6].
In order to see the details of the features, we investigated the
distribution of the features, as shown in Fig. 4 and Fig. 5. We
made 20 equally spaced intervals for the feature values. The
scale of the horizontal axis shows the center value of eachinterval. We counted the elements/features included in every
interval and showed the counted frequency in the figures.

The vertical axis shows the frequency. From Fig. 4, it canbe seen that most of the elements distributed around thelowest values belong to the L4 group. These elements are
considered to have effectively worked for classification. The
instances given by (6) are for every participant. This is thetrick that gives features valid for not the entire group but forpart of the group. Then, the present approach can deal withindividual differences, which is the main difference from theprevious studies. This discussion is true of the feature forclassification of the L5 group, as shown in Fig. 5. Froma clinical perspective, a low femur angle is indicative of alow hip position; this is considered to be the strategy forcompensating the decrease of the quadriceps’ muscle powerin the L4 group. As for the feature shown in Fig. 5, it isrelated with the drop foot. The decrease in power of thetibialis anterior muscle can be seen in the L5 group, andtheir toes are likely to drop especially during the swing
phase, which could cause stumbling. Then, for safe landing,they took the strategy of keeping the ankle angle as small as
possible just before takeoff.
IV. C ONCLUSION
This paper presented an approach for classifying the maindisease of intermittent claudication via an L1-regularized
SVM. The accuracy of the approach was 79.7%, and relevant
differentiation features could be extracted with the classification. The main characteristics of the extracted features arethat they are valid for not the entire group but for part of
the group, and are able to deal with individual differences.
Although the classification accuracy is high, it is not enoughfor practical differentiation. Improving the classification is
our future work.
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