On the Instability of Sensor Orientation in Gait Veriﬁcation on Mobile

Phone

Thang Hoang

, Deokjai Choi

and Thuc Nguyen

Faculty of Information Technology, Saigon Technology University, Ho Chi Minh City, Vietnam

Department of Electronics and Computer Engineering, Chonnam National University, Gwangju, South Korea

Faculty of Information Technology, University of Science VNU-HCMC, Ho Chi Minh City, Vietnam

thang.hoangminh@stu.edu.vn, dchoi@jnu.ac.kr, ndthuc@ﬁt.hcmus.edu.vn

Keywords:

Gait Recognition, Pattern Recognition, Behavioural Biometrics, Implicit Authentication, Accelerometer,

Mobile Security.

Abstract:

Authentication schemes using tokens or biometric modalities have been proposed to ameliorate the security

strength on mobile devices. However, the existing approaches are obtrusive since the user is required to

perform explicit gestures in order to be authenticated. While the gait signal captured by inertial sensors is

understood to be a reliable proﬁle for effective implicit authentication, recent studies have been conducted

in ideal conditions and might therefore be inapplicable in the real mobile context. Particularly, the acquiring

sensor is always ﬁxed to a speciﬁc position and orientation. This paper mainly focuses on addressing the

instability of sensor’s orientation which mostly happens in the reality. A ﬂexible solution taking advantages

of available sensors on mobile devices which can help to handle this problem is presented. Moreover, a novel

gait recognition method utilizes statistical analysis and supervised learning to adapt itself to the instability of

the biometric gait under various circumstances is also proposed. By adopting PCA+SVM to construct the gait

model, the proposed method outperformed other state-of-the-art studies, with an equal error rate of 2.45% and

accuracy rate of 99.14% in terms of the veriﬁcation and identiﬁcation aspects being achieved, respectively.

1 INTRODUCTION

Over recent years, mobile devices have greatly

evolved from primitive machines for voice and text

communication to personal intelligent assistants and

are becoming more familiar to everybody. A survey

of the mobile market forecasted that mobile subscrip-

tions will reach 9.3 billion by 2019, 5.6 billion of

which will be for smart phones. Mobile facilities in-

clude not only making calls or sending text messages,

but also cover a variety of utilities such as data stor-

age, entertainment and Internet transactions. Since

such devices are likely to be portable personal com-

puters, sensitive personal data is accumulated in them,

which might lead to supplemental security demands.

Additionally, mobile devices tend to become increas-

ingly miniaturized and light, which makes them a lot

easier to lose. A huge amount of personal data could

become exposed to criminals. The most popular au-

thentication technique currently used in mobiles still

relies on the traditional method of using a secret code,

such as a PIN, visual pattern or password (Breitinger

and Nickel, 2010). These techniques are not highly

effective considering the problems of memory and se-

curity (Breitinger and Nickel, 2010). Alternatives us-

ing biometric traits, such as the face, ﬁngerprint or

on-line signature, have been introduced recently on

mobiles, which have helped to mitigate the limitations

of password-based methods (Jain et al., 2004). How-

ever, all of these methods strongly rely on user coop-

eration and might therefore be annoying and obtrusive

in frequent use. Users are forced to pay attention and

perform explicit gestures in order to be authenticated.

Besides, the number of mobile applications is

exploding these days and these various applications

might require different levels of security. Indeed, a

trade-off between usability and security needs to be

taken into consideration. For instance, retrieving the

user’s daily schedule does not require the same level

of security as making an Internet banking transaction.

Applying the same veriﬁcation scheme to all appli-

cations requiring different levels of security would

be somewhat cumbersome. Thus, it is necessary to

provide miscellaneous authentication mechanisms on

the mobile adapting to different security level require-

ments to optimize the user-device interaction. Ac-

Hoang T., Choi D. and Nguyen T..

On the Instability of Sensor Orientation in Gait Veriﬁcation on Mobile Phone.

DOI: 10.5220/0005572001480159

In Proceedings of the 12th International Conference on Security and Cryptography (SECRYPT-2015), pages 148-159

ISBN: 978-989-758-117-5

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

cordingly, an implicit authentication technique needs

to be investigated, which aims to enhance the user ex-

perience and ameliorate mobile security. Human gait

has been studied for a long time and shown to be as an

effective behavioral biometric trait (Jain et al., 2004;

Fish and Nielsen, 1993; Whitle, 2003). Identiﬁcation

using gait signals captured by wearable sensors has

been introduced recently and has achieved positive re-

sults (Ailisto, 2005; Gafurov and Snekkenes, 2009).

Veriﬁcation on mobiles leveraging gait characteristic

of individuals has signiﬁcant advantages in terms of

user friendliness and security, in comparison to other

biometric modalities (Mjaaland et al., 2011; Derawi

and Bours, 2013). Speciﬁcally, gait signals can be

implicitly captured while the user is walking without

his or her intervention. From the security perspective,

it is difﬁcult to counterfeit authentic gait patterns even

if the impostor could record the walking style of the

genuine user (Mjaaland et al., 2011). Conversely, a

copy of a ﬁngerprint or face could be easily obtained

and the system security fully depends on the resis-

tance of the sensor. However, in most existing gait

recognition systems using wearable sensors, the ac-

quiring sensors are likely to be ﬁxed in a speciﬁc ori-

entation and position, such as the waist, ankle or hip,

to ensure that the shape of the acquired gait signals is

similar (Derawi and Bours, 2013; Ailisto, 2005; Ga-

furov and Snekkenes, 2009; Derawi et al., 2010b; Ga-

furov et al., 2010). It can be seen that these positions

might be inappropriate, especially in the mobile con-

text. Moreover, ﬁxing the orientation of the device

seems impossible in practice.

In this paper, we propose a novel gait recogni-

tion scheme which can be used for user veriﬁcation

or identiﬁcation on mobile device that can adapt to

the actual usage in reality. We pay attention to the

context that the mobile is placed in the front pocket,

which is the most appropriate location for the device

in daily use (Breitinger and Nickel, 2010). This study

mainly focuses on addressing the instability problem

of sensor’s orientation that frequently arises when the

device is ﬂexibly attached with its owner in practice.

Furthermore, gait is likely to be considered as a be-

havioral biometric which is not as robust as other

physiological traits since it is affected by many physi-

cal and environmental conditions, such as the cloth-

ing, footwear, ground material, mood, health, age,

weight, etc. Therefore, applying pattern matching,

as in recent studies (Derawi et al., 2010b; Derawi

et al., 2010a; Derawi and Bours, 2013; Gafurov and

Snekkenes, 2009; Gafurov et al., 2010; Rong et al.,

2007), to deal with all these circumstances could be

inefﬁcient. What is more, since the mobile is gen-

erally carried and accessed by its owner, gait signals

can be captured frequently and continuously. We pre-

fer to leverage machine learning techniques to adapt

to the variation of the gait characteristics over time.

Any change in the gait patterns can be implicitly la-

beled and notiﬁed to the system to update the outdated

model when the system frequently fails to verify the

user.

In summary, our main contributions are:

– Addressing the instability of sensor’s orientation

when gait signal of individual is captured. A sim-

ple but effective solution for this issue taking ad-

vantage of the available sensors in mobile devices

is presented (Section 3).

– Proposing a gait recognition model using statis-

tical analysis and supervised machine learning

(Section 4). The results achieved in our exper-

iment show that the proposed system has lower

error rates, in comparison to other state-of-the-art

methods (Section 5).

2 RELATED WORKS

Human gait data are considered to represent the par-

ticular style and manner in which human feet move

and, hence, contain information of identiﬁcation. On

a more detailed level, the mechanism of human gait

involves synchronization between the skeletal, neu-

rological and muscular systems of the human body

(Fish and Nielsen, 1993). In 2005, H. Ailisto et al.

were the ﬁrst to propose gait veriﬁcation using wear-

able sensors (Ailisto, 2005) and this area was further

expanded by Gafurov et al. (Gafurov and Snekkenes,

2009). In general, sensors are attached to a particular

position such as the ankle (Gafurov and Snekkenes,

2009; Gafurov et al., 2010; Li et al., 2011; Terada

et al., 2011), hip (Gafurov and Snekkenes, 2009; De-

rawi et al., 2010b; Sprager and Zazula, 2009), waist

(Ailisto, 2005; Ngo et al., 2014), arm (Gafurov and

Snekkenes, 2009), or multiple positions (Pan et al.,

2009; Mondal et al., 2012) on the body to record lo-

comotion signals. The acquiring sensors can be gy-

roscopes or rotation sensors, but an accelerometer is

most commonly used to capture gait signals. The

most popular approach in this ﬁeld is based on pattern

matching, in which the gait signals are captured, pre-

processed and then split into separate patterns. Vari-

ous distance metrics such as the Dynamic Time Warp-

ing (DTW) (Derawi et al., 2010b; Gafurov et al.,

2010; Rong et al., 2007; Derawi et al., 2010a), Eu-

clidean distance (Terada et al., 2011), auto-correlation

(Ailisto, 2005), and nearest neighbors (Pan et al.,

2009) are used to calculate similarity scores between

the given patterns and the stored templates. The sec-

ond approach is based on machine learning. Fea-

ture vectors are extracted and supervised learning is

adopted to construct general gait veriﬁcation or iden-

tiﬁcation models (Lu et al., 2014; Mondal et al., 2012;

Hoang et al., 2013; Frank et al., 2010)

Although wearable sensors have been imple-

mented with a variety of success rates, they have some

limitations. For example, those sensors are relatively

expensive and cumbersome, due to their size and

weight. The sensor interface is still under develop-

ment. Recently, the improvement of micro electrome-

chanical (MEM) technology has helped to miniatur-

ize such sensors, thus allowing them to be integrated

in mobile devices. Gait identiﬁcation has thus been

implemented on mobile devices (Derawi and Bours,

2013; Lu et al., 2014) for the past few years. In com-

parison to wearable sensors, mobile sensors are de-

signed to be cheaper, simpler and, as a result, their

quality is not guaranteed. For instance, since the sam-

pling rate is low and unstable, the noise level is rather

high. Derawi et al. (Derawi et al., 2010b) demon-

strated these deﬁciencies by re-implementing Holien

et al.’s work (Holien, 2008). The authors achieved an

EER of 20.1%, in comparison to the original EER of

12.9%.

3 THE INSTABILITY OF SENSOR

ORIENTATION

Figure 1: (a) Mobile coordinate system, (b) misplacement

error, (c) disorientation error and (d) disorientation errors

and misplacement errors.

3.1 Problem Statement

Figures 1b–d illustrate the instability of the mobile

in terms of its orientation and position when it is put

freely in the pocket. Because walking is a slow ac-

tivity with a moderate ﬂuctuation, any strong acceler-

ation is likely to last no longer than a few tenths of

a second. Consequently, the impact of different posi-

tions in the pocket is not signiﬁcant and is considered

as noise. This can be mitigated by applying an effec-

tive noise ﬁltering algorithm which will be described

in Section 4.1.2.

Meanwhile, the instability of the mobile’s orien-

tation (namely the disorientation for short) signiﬁ-

cantly affects the quality of the acquired gait sig-

nals. Due to the design of the mobile accelerome-

ter, wherein the gait signals are captured in 3 separate

dimensions, the shape of the acquired signals fully

depends on the relative orientation between the mo-

bile and its carrier. So, the instability of the mobile

orientation would make the gait signals in each sep-

arate dimension dissimilar. This obstacle could ruin

the effectiveness of gait veriﬁcation or identiﬁcation

systems. For instance, the accuracy rate of pattern

matching approaches can be reduced when dealing

with dissimilar gait signals. This circumstance will

be illustrated in Section 5.5. Furthermore, based on

our observations, gait cycle-based segmentation can

be easily performed on the gait signal in the dimen-

sion which represents the vertical walking direction

(viz. the Y −dimension as in Figure 1a). Due to the

disorientation problem, it is difﬁcult to determine the

correct dimension which reﬂects the vertical walk-

ing direction. Errors in the segmentation phase might

propagate to subsequent processing phases, so that the

effectiveness of the system can be compromised. Fi-

nally, extracting reliable features from dissimilar gait

signals could be a problematic issue.

Generally, the main objective of resolving the dis-

orientation problem is to maintain the accuracy rate

of the mobile gait veriﬁcation or identiﬁcation sys-

tems under practical conditions. A small part of this

problem was solved in (Hoang et al., 2013). How-

ever, there are unrealistic assumptions and constraints

which could make the authors’ proposed method dif-

ﬁcult to apply in practice. We present a more ﬂexible

solution to this problem in the following section.

3.2 Proposed Solution

A simple but effective strategy to handle the disorien-

tation is making gait signals always be represented in

a ﬁxed coordinate system which is insensitive to the

device’s orientation. In other words, acceleration vec-

tors representing gait signals should be transformed

from the instable mobile coordinate system to a sta-

ble one. Based on the availability of sensors in the

mobile, the Earth coordinate is likely to be consid-

ered as the effective ﬁxed system to represent the col-

lected acceleration samples. To do that, it is manda-

tory to collect various kinds of sensor data during the

gait sensing period. The following section describes

all necessary sensors need to be activated to collect

enough data used in this study.

3.2.1 Data Acquisition

Obviously, the ﬁrst sensor needs to be activated to

capture gait signal is the mobile accelerometer. The

accelerometer senses forces acting on the mobile

in the three orthogonal axes of X,Y, Z (Figure 1a).

A sequence of acceleration samples output by the

accelerometer during walking is recognized as the

gait signal. Each sample is a 3-dimensional vec-

tor, wherein each component is a combination of the

forces of gravity and user motion acting on each di-

mension.

a = (a

(X)

, a

(Y )

, a

(Z)

), (1)

where a

(D)

is the acceleration value sensed on the

D−axis of the mobile.

Due to the characteristics of the accelerometer,

the raw acceleration samples always comprise grav-

itational acceleration components. In order to obtain

samples which only involve pure gait signals of indi-

viduals, we eliminate the impact of gravity by addi-

tionally activating a virtual sensor of gravity to deter-

mine the gravitational acceleration components on the

3 axes of the mobile during the gait capture process.

The output of the gravity sensor is a 3-component vec-

tor

g = (g

(X)

, g

(Y )

, g

(Z)

), (2)

where g

(D)

is the gravitational acceleration on the

D−axis of the mobile.

Furthermore to resolve the disorientation problem,

we activate a synthetic sensor of orientation, along

with the two sensors above to monitor the orientation

states of the mobile. As in the case of the accelerom-

eter and gravity sensor, the output of the orientation

sensor is a 3-component vector

o = (α, β , γ), (3)

where α, β , γ represent the degrees of rotation around

the Z−, X −,Y − axes of the mobile respectively.

Note that both orientation sensor and gravity sen-

sor are all virtual sensors whose outputs are nor-

mally synthesized from two physical sensors: the ac-

celerometer and the geomagnetic ﬁeld sensor. These

sensors are getting more and more popular, appear-

ing in most modern smartphones so that all mandatory

sensor data needed in this study can be easily obtained

in practice.

3.2.2 Gait Signal Transformation

Let us assume that after a gait sensing period, we ob-

tain n vectors of acceleration a

, orientation o

and

gravity g

A =



. . . a



∈ R

n×3

G =



. . . g



∈ R

n×3

O =



. . . o















∈ R

n×3

(4)

First, the inﬂuence of gravity on the acquired ac-

celeration samples is eliminated to obtain the pure

gait signal.

A ← A − G. (5)

For each rotation vector o

in O, we calculate a

rotation matrix R

which will be used to transform the

acceleration vector in the mobile coordinate system to

the Earth coordinate system.





cosα

cosγ

− sinα

sinβ

sinγ

sinα

cosβ

cosα

sinγ

+ sinα

sinβ

cosγ

−sin α

cosγ

− cosα

sinβ

sinγ

cosγ

cosβ

−sin γ

sinγ

+ cosα

sinβ

cosγ

−cos β

sinγ

−sin β

cosβ

cosγ





(6)

Finally, we transform the gravity-free acceleration

vector representing in the mobile coordinate system to

the new ﬁxed system by multiplying the vector with

the corresponding rotation matrix.

← a

. (7)

The gait signal after transformation is denoted as

A =



















(X)

(Y )

(Z)

(X)

(Y )

(Z)

(X)

(Y )

(Z)









(X)

(Y )

(Z)



. (8)

The acceleration vectors after transformation are

presented in the Earth coordinate system, wherein

the new Z−dimension represents the vertical direc-

tion which is perpendicular to the ground, whereas the

new X− and Y − dimensions represent the horizontal

plane which is parallel to the ground. These trans-

formed X − and Y −dimensions always point towards

the East and the magnetic North Pole respectively re-

gardless of the walking direction. However, due to the

fact that the user can walk in any direction in the hor-

izontal plane, gait signals in the transformed X − and

Y − dimensions which are captured from a session can

be dissimilar to those captured from other sessions re-

spectively. Therefore, instead of using the signals in

each separate dimension of X and Y , we utilize the

combined signal of X −Y

(XY )

= (a

(XY )

, . . . , a

(XY )

, . . . , a

(XY )

), (9)

where a

(XY )

(X)

)

+ (a

(Y )

)

In other words, the gait signals will be ﬁnally rep-

resented in the 2 dimensions of the Earth, wherein the

transformed Z− and XY − axes represent the verti-

cal and horizontal directions of walking, respectively.

Moreover, the magnitude of the gait signal is addi-

tionally utilized as an additional dimension for gait

representation.

(M)

= (a

(M)

, . . . , a

(M)

, . . . , a

(M)

), (10)

where a

(M)

(X)

)

+ (a

(Y )

)

+ (a

(Z)

)

In summary, the gait signal after transformation

will be presented in 3 dimensions as described above.

A =



(Z)

(XY )

(M)









(Z)

(XY )

(M)

(Z)

(XY )

(M)

(Z)

(XY )

(M)







. (11)

Since each acceleration sample is always trans-

formed into the Earth coordinate system according to

the current orientation of the mobile determined as

soon as the acceleration value is returned, it is more

robust than the solution proposed in (Hoang et al.,

2013), in that all of the signals are likely to be trans-

formed according to the initial orientation of the mo-

bile, which is predetermined before the user starts to

walk.

4 GAIT RECOGNITION MODEL

CONSTRUCTION

In this section, we propose a novel gait veriﬁca-

tion system using statistical analysis and a super-

vised learning, working effectively on orientation-

independent gait signals obtained by using the method

presented in the previous section. Our system follows

the traditional pattern recognition process consisting

of mandatory steps such as data preprocessing, seg-

mentation, feature extraction and classiﬁcation.

4.1 Data Preprocessing

4.1.1 Linear Interpolation

As the mobile sensor is a power saving device which

is simpler than standalone sensors, the sampling rate

is not always stable. The time interval between two

consecutive returned samples is not identical. First,

we apply linear interpolation to the acquired acceler-

ation samples to achieve gait signals at a ﬁxed sam-

pling rate.

Moreover, due to the design of the mobile oper-

ating system (e.g., Android OS), the triplet of accel-

eration sample, orientation sample and gravity sam-

ple is not yielded simultaneously. Meanwhile in the

proposed solution to handle the disorientation issue,

it is required that this triplet need to be yielded con-

currently. Therefore, we additionally apply the same

linear interpolation to the obtained orientation sam-

ples and gravity samples. The timestamp of the inter-

polated acceleration samples is used as the reference

axis to determine the approximate orientation vector

and gravity vector yielded at the same time as the ac-

celeration vector.

4.1.2 Noise Elimination

Gait signals captured by the mobile accelerometer in-

evitably contain much noise. This can be due to the

misplacement error (Figure 1b), the quality of the

sensors or bumps on the ground while walking, the

difference in footwear, etc. We apply a multi-level

wavelet decomposition and reconstruction method to

remove the noise components in the signal. Techni-

cally, the detailed coefﬁcients (obtained by HF ﬁlter

as in Figure 2 ) are set to 0s at all decomposition lev-

els. The signal reconstruction process involves com-

bining the detailed coefﬁcients of zero with the coarse

coefﬁcients from the lowest level until the level 0 is

achieved. Speciﬁcally, in this study, we apply the

Daubechies orthogonal wavelet (Db6) (Mallat, 1989;

Daubechies, 1992) with the decomposition at level 2

to mitigate the noise caused by the acquisition envi-

ronment.

Figure 2: Multi-level wavelet decomposition.

4.2 Gait Pattern Extraction

4.2.1 Gait Cycle based Segmentation

Segmentation is the most important process which

could directly affect the quality of the extracted gait

patterns. It can be easily seen that walking is a cyclic

activity so that the gait signal should be segmented

into gait cycles instead of ﬁxed-length patterns.

Figure 3: Illustration of a gait cycle.

Gait cycle is commonly deﬁned as the time inter-

val between two successive occurrences of one of the

repetitive events when walking (Whitle, 2003). Par-

ticularly, a gait cycle can start with initial contact of

the heel and continue until the same heel contacts the

ground again. We assume that the mobile device is

placed at the same side with the leg which is going to

contact the ground as in the phase “a” or “g” in the

Figure 3, for example the right leg. So, at the time

the heel touches the ground, the association of the

ground reaction force and the inertial force together

will act on the right leg, which makes the acceleration

value of the transformed Z−dimension signal sensed

by the accelerometer strongly change and form nega-

tive peaks (illustrated as star points in the Figure 4b).

They are recognized as the starting points of the gait

cycles. Note that when the event “d” happens (e.g.,

the left heel touches the ground), the accelerometer

also generates negative peaks, similar to the “a” event.

However, since the device is placed at the right leg

which is opposite to the left, the accelerometer only

senses insigniﬁcant forces acting on the right leg in

this case. Therefore, the magnitude of peaks gener-

ated by “d” events (Figure 4b, circle points) is not

high as those generated by “a” or “g”. The objective

of the segmentation step is to divide the signal into

separate gait cycles. So, it is required to determine

peaks which are generated by the event of “a” or “g”

in the Figure 3. First of all, we determine the position

of all of the negative peaks in the Z−dimension gait

signal a

(Z)

of length n. Let

Π = {i

(Z)

−1

> a

(Z)

, a

(Z)

> a

(Z)

, i

∈ 1. . . n} (12)

be the set of index of these peaks with the order pre-

served. Assuming that |Π| is always larger than 1

given a gait signal of a walking session, we ﬁlter the

starting points of the gait cycles in Π based on two

criteria.

The ﬁrst criterion is based on the magnitude of the

peaks. We eliminate the noisy peaks whose values are

higher than a threshold δ determined by the mean and

standard deviation of all of the peaks in Π.

δ = µ

− τσ

, (13)

where

|Π|

∑

i∈Π

(Z)

(|Π| − 1)

∑

i∈Π

(Z)

− µ

(14)

τ is a user-deﬁned parameter.

The second is based on the correct positions of the

gait cycle’s starting points. While the distance be-

tween starting points of the gait cycle is assumed to

ﬂuctuate around a constant range in other studies (De-

rawi et al., 2010b; Derawi et al., 2010a), we observed

that such range does not cover all possible cases since

the walking speed of different individuals varies sig-

niﬁcantly. Instead, we estimate the length of the gait

cycle according to the characteristics of each signal.

To determine the periodicity of the gait signal, we

calculate the autocorrelation coefﬁcients c

(0 ≤ t < n)

of the Z−dimension signal by

N −t

∑

N−t

i=1

(Z)

i+t

(Z)

∑

i=1

(Z)

)

. (15)

The moving average algorithm is then applied to

smooth these coefﬁcients. Let us assume that c

and c

are the 1

and 2

peaks autocorrelation coefﬁcients,

respectively, as depicted by two stars in the Figure 4a.

Then, the length of a gait cycle can be approximated

∆ = j. (16)

According to the two criteria of magnitude and po-

sition, we determine the peaks representing the start-

ing points of the gait cycles. Let Ω be the set of these

peaks with the order of indices preserved. Then, Ω

will be given by

Ω = {i

(Z)

< δ, (∃i

∈ Π, k > j, ∆ − ε ≤ i

− i

≤ ∆ + ε), i

∈ Π},

(17)

where ε > 0 is the user-deﬁned parameter. Assuming

that there are k−1 where k > 1 gait cycles in the given

gait signal, hence, |Ω| = k. We separate the signal into

k − 1 distinct segments, with each S

consisting of a

full gait cycle







(Z)

Ω

(XY )

Ω

(M)

Ω

(Z)

Ω

i+1

(XY )

Ω

i+1

(M)

Ω

i+1







. (18)

4.2.2 Pattern Extraction

We form gait patterns by concatenating the separate

one-gait-cycle segments extracted in the previous sec-

tion. Each gait pattern would contain n

consecutive

segments and 50% of them overlaps with the previous

0 50 100 150 200 250 300

0.8

0.9

Normalized coefficient

Time lagged (

)

(a)

100

150

200

250

300

-10

-5

Acceleration (m/s

)

Sample

Event "a"

Event "d"

(b)

Figure 4: (a) Auto-correlation coefﬁcients , (b) Detected marking points in Z−signal.

Table 1: List of gait features extracted in time and frequency domains.

Time domain features

Mean of the max/min value in each s

(D)

in p

(D)

where D = Z, XY M; average absolute difference; root mean

square; standard deviation; waveform length; 10-bin histogram distribution; average length of s

(D)

in p

(D)

Frequency domain features

Magnitudes of ﬁrst 40 FFT coefﬁcients; ﬁrst 40 DCT coefﬁcients.

one. Let

(Z)

(XY )

(M)

be a segment consisting

of a gait cycle, where s

(Z)

. . . a

(Z)

, s

(XY )

. . . a

(XY )

, s

(M)

. . . a

(M)

. Let

(Z)

. . . a

(Z)

. . . a

(Z)

. . . a

(Z)

. . . a

(Z)

. . . a

(Z)

. . . a

(Z)

(XY )

. . . a

(XY )

. . . a

(XY )

. . . a

(XY )

. . . a

(XY )

. . . a

(XY )

. . . a

(XY )

(M)

. . . a

(M)

. . . a

(M)

. . . a

(M)

. . . a

(M)

. . . a

(M)

. . . a

(M)

Then, a gait pattern P is deﬁned by

P =



(Z)

(XY )

(M)









(Z)

(XY )

(M)

(Z)

(XY )

(M)

(Z)

(XY )

(M)







. (19)

4.3 Gait Model Construction

4.3.1 Feature Extraction

We extract the features on both time and frequency

domains as used in (Hoang et al., 2013) for each gait

pattern P. The list of extracted features is brieﬂy sum-

marized in the Table 1. Note that all of the features in

the time and frequency domains are extracted for the

3 dimensions of the gait pattern (viz. p

(Z)

, p

(XY )

, p

(M)

in (19)), except for the “average length of s

(D)

in p

(D)

”

feature since its value is identical in all 3 dimensions.

All of the extracted features are concatenated to form

the ﬁnal feature vector for a gait pattern.

4.3.2 Feature Vector Dimension Reduction

Since we expect the system to run directly on the

mobile phone with limited computational resources,

it is necessary to reduce the dimension of the ex-

tracted feature vectors to lighten the complexity of

the gait model built by using the machine learning al-

gorithms. Thus, we adopt the Principle Component

Analysis (PCA) to reduce the number of dimensions

while maintaining the discriminability of the feature

vectors.

Let us assume that the number of users is denoted

as N. The number of feature vectors extracted from all

of the gait patterns for each user is M. According to

the feature extraction phase, the length of each feature

vector is n

= 289. The j

( j = 1 .. . M) feature vector

of the user i(i = 1. . . N) is denoted as

(i)

j,1

, . . . , f

(i)

j,k

, . . . , f

(i)

j,n

, (20)

where f

(i)

j,k

is the k

feature component of v

(i)

. The

matrix of feature vectors of all users can be formed as







(1)

(i)

(N)













(1)

1,1

(1)

1,k

(1)

1,n

(i)

j,1

(i)

j,k

(i)

j,n

(N)

M,1

(N)

M,k

(N)

M,n



















∈ R

MN×n

(21)

Then, a covariance matrix of F can be calculated by

Σ =

∑

i=1

−

v)(v

−

∈ R

×n

. (22)

Let

−→

λ = (λ

, . . . , λ

) and u

be eigenvalues

and eigenvectors obtained from the Σ, respectively.

All eigenvalues λ

of Σ are sorted in descending or-

der in which the higher the eigenvalues are, the more

important they are. Assuming that λ

< λ

i−1

, to re-

duce the number of dimensions of the original feature

vector from n

to k, k eigenvectors are taken accord-

ing to the order of the eigenvalues

U =



. . . u



∈ R

×k

. (23)

The dimension-reduced matrix of feature vectors can

be calculated by

= F

U. (24)

4.3.3 Gait Recognition Model for Veriﬁcation

and Identiﬁcation

We adopt two schemes, namely feature vector match-

ing and supervised learning, for both identiﬁcation

and veriﬁcation. In the former scheme, the feature

vectors extracted after using PCA are stored in the

mobile storage, which will be used for user identiﬁ-

cation or veriﬁcation. In the latter scheme, we ap-

ply Support Vector Machine (SVM) with a linear ker-

nel to build a gait model for each user. An open li-

brary tool, libsvm (Chang and Lin, 2011), is used in

this study for SVM-based gait model construction and

evaluation.

5 Experiments

5.1 Dataset Description

We use the dataset which is an extended version of

the one used in (Hoang et al., 2013) for experimental

evaluation in this study. We would like to brieﬂy de-

scribe the original and extensions of this dataset and

refer the readers to the original work of the authors

for more details. The dataset consists of gait signals

of 38 subjects captured by using a Google Nexus One

mobile phone. The device is put freely inside the front

trouser pocket and the sampling rate of integrated sen-

sors is set to 27Hz. Besides data described in the

original work, the authors further provide other sen-

sor data which are collected along with acceleration

data during gait sensing period in the extended ver-

sion. List of particular sensors activated in this phase

is summarized in the Table 2.

5.2 Experimental Conﬁguration

Since the sampling rate of the sensor is low (27 Hz),

making the number of samples in a one-gait-cycle

segment small, we form each gait pattern extracted

in Section 4.2.2 by concatenating n

= 4 consecutive

segments, in order to feasibly extract enough features

in the time and frequency domains. In total, around

10226 gait patterns are extracted from the dataset.

Moreover, the length of the feature vectors after ap-

plying PCA is selected to be equal to n

such that the

ﬁrst n

eigenvectors capture at least 99.5% of the total

variance. According to the dataset used in this study,

is equal to 42.

We re-implement several state-of-the-art gait

recognition systems on the dataset used in this experi-

ment ((Rong et al., 2007; Gafurov et al., 2010; Derawi

et al., 2010a)) in order to not only evaluate the effec-

tiveness of the solution proposed to handle the disori-

entation problem, but also compare with our proposed

recognition schemes. The effectiveness of gait recog-

nition systems is evaluated under two aspects: identi-

ﬁcation and veriﬁcation capabilities. Note that in the

comparison of the veriﬁcation and identiﬁcation ca-

pabilities among the studies, the disorientation prob-

lem is not taken into account so that all of the works

will be evaluated on the orientation-independent gait

signals (referred to as the transformed dataset). Fur-

thermore, as Rong et al. used the gait signals of the

X− and Y − dimensions which are not available in

the transformed dataset, we replace them with the gait

signals of the XY − and M− dimensions to make sure

that the number of dimensions is consistent to that in

the original study. In Gafurov et al.’s method, the au-

thors experimented on the gait signals of different di-

Table 2: List of physical and virtual sensors activated during

the gait capture process.

Sensor Name Model name Sampling rate

Magnetic ﬁeld sensor AK 8973 25 Hz

Accelerometer BMA 150 25 Hz

Orientation sensor Virtual 25 Hz

Gravity sensor Virtual 25 Hz

Linear acceleration sensor Virtual 25 Hz

Rotation vector sensor Virtual 25 Hz

Table 3: The conﬁguration differences in between the original study and this experiment.

Method

Original setup This experiment

Axes # Subject Position SR (%) Axes # Subject Position SR

Rong et al. X,Y, Z 38 Ankle 250 Z, XY, M 38 Front pocket 27

Gafurov et al. Z 30 Ankle 100 Z 38 Front pocket 27

Derawi et al. M 60 Hip 100 M 38 Front pocket 27

mensions and achieved various results. Based on the

availability of dimensions in the transformed dataset,

we select the gait signal of the Z−dimension (referred

to as the up-down direction in the original) as the stan-

dard for evaluation and comparison. Table 3 shows

the difference in the conﬁguration settings in between

the original studies and this experiment.

5.3 Veriﬁcation Results

We utilize Receiver Operating Characteristic (ROC)

curves to illustrate the performance of the proposed

system in the aspect of veriﬁcation. Firstly, we ex-

periment with different portions of the training data

and testing data, ranging from k = 5% to 50%, in or-

der to determine the inﬂuence of the number of train-

ing data on the effectiveness of the proposed schemes.

Note that we apply cross-veriﬁcation to overall eval-

uate the performance of the proposed method. Partic-

ipants will be considered as the genuine user in turn.

Speciﬁcally for each user i, in the PCA approach, we

store randomly k gait patterns of the user i as the train-

ing data. The remaining patterns of the user i will be

utilized for testing the false rejection rate (FRR), and

the patterns of all other users j( j 6= i) will be used

for testing false acceptance rate (FAR). Similarly in

the PCA+SVM approach, k genuine gait patterns of

the user i and k patterns of each other users will be

used to construct the gait model for the user i, while

remaining data will be used for evaluating the error

rates of the constructed model.

Figure 5 depicts the error rates of the proposed

method using the PCA and PCA+SVM schemes with

different proportions of training data and testing data.

As expected, a higher proportion of the training data

yield a lower error rate. Moreover, we can see that

applying a supervised learning (PCA+SVM) tech-

nique can help to enhance the accuracy of the system.

The overall error rate achieved using the PCA+SVM

scheme is lower than that when only using the PCA

scheme. Next, we compare the proposed system with

those of other studies which are re-implemented and

evaluated according to the new conﬁguration settings.

The veriﬁcation performance of all of these studies is

investigated on two testing scenarios: Firstly, we con-

sider each walking session as a testing trial, which is

commonly used in comparing studies. Unlike in these

studies, we apply majority voting to our schemes to

validate each walking session. That means the user

is veriﬁed if a larger portion of the gait patterns ex-

tracted in the session is recognized as being authen-

tic. Figure 6a depicts the error rates of the proposed

methods and other studies in this scenario.

From our viewpoint, session-based veriﬁcation

might require a lot of time and efforts from the user

since he/she has to continuously walk for a long dis-

tance, in order to collect enough data to be veriﬁed.

The veriﬁcation process can be performed faster and

more constantly if the system can immediately verify

the user only using the gait pattern instead of hav-

ing to wait until the walking session ﬁnishes. There-

fore, we additionally investigate the performance of

the methods in all of the studies when the separate

gait patterns are treated as independent testing trials.

As depicted in Figure 6b, we can see that the error

rates of all of the approaches are higher than those

in the session-based scenario. Especially in Rong et

al.’s method, the error rate is signiﬁcantly increased,

since the method of gait pattern extraction employed

strongly relies on the whole walking session data. The

error rate of our method using the PCA+SVM scheme

in this scenario is approximately 5.35%, which can

help to reduce the time and effort needed to perform

the veriﬁcation task. Table 4 summarizes the EERs

achieved in all of the studies according to two scenar-

ios. It can be seen that in the session-based scenario,

the achieved EERs with the methods proposed in the

other studies after evaluating them in the transformed

dataset are similar to original values. This reﬂects that

handling the disorientation problem is mandatory in

order to maintain the effectiveness of gait recognition

systems because this problem might result in a signif-

icant increase of the error rates of the systems. This

impact will be clearly shown in the Section 5.5.

5.4 Identiﬁcation Results

We also investigate the identiﬁcation capability of the

proposed method and other studies according to the

two evaluation scenarios described above. The same

1-nearest neighbor algorithm is applied to all meth-

ods, except for the PCA+SVM scheme in order to

measure the performance between studies. The best

accuracy rate belongs to the proposed PCA+SVM

0 0.1 0.2 0.3 0.4 0.5

0.1

0.2

0.3

0.4

0.5

False Acceptance Rate

False Rejection Rate

ROC curve

10%

20%

40%

50%

(a) PCA

0.1

0.2

0.3

0.4

0.5

0.1

0.2

0.3

0.4

0.5

False Acceptance Rate

False Rejection Rate

ROC curve

10%

20%

40%

50%

(b) PCA+SVM

Figure 5: ROC curves of the proposed system using two veriﬁcation schemes according to different portions of training data.

0.1

0.2

0.3

0.4

0.1

0.2

0.3

0.4

False Acceptance Rate

False Rejection Rate

ROC curve

Gafurov et al.

Rong et al.

Deraw i et al.

This study (PCA)

This study (PCA+SVM)

(a) Session-based veriﬁcation

0.1

0.2

0.3

0.4

0.8

0.1

0.2

0.3

0.4

0.8

False Acceptance Rate

False Rejection Rate

ROC curve

Gafurov et al.

Rong et al.

Deraw i et al.

This study (PCA)

This study (PCA+SVM)

(b) Pattern-based veriﬁcation

Figure 6: The ROC curves of the proposed method and other studies which are re-implemented and evaluated according to

the conﬁguration in Table 3.

scheme, with an amount of approximately 99.14%

being achieved under session-based identiﬁcation as-

pect. Table 5 shows the identiﬁcation performance of

the proposed method and comparing studies. Similar

to the veriﬁcation results, the accuracy rate of pattern-

based identiﬁcation is normally lower than that of

session-based identiﬁcation. Especially in Rong et

al.’s method, the accuracy of the system strongly de-

creases an amount of approximately 30%.

5.5 The Impacts of Disorientation Error

Finally, we illustrate the impact of disorientation er-

rors on the accuracy of the gait veriﬁcation systems.

As already mentioned, the instability of sensor ori-

entation would cause the gait signals acquired in the

Table 4: The error rates of session-based and pattern-based gait veriﬁcation methods.

Method

Session-based Pattern-based

EER(%)

(original)

EER (%)

FRR (%)

(at FAR = 1%)

EER (%)

FRR (%)

(at FAR = 1%)

Rong et al. 5.6 5.28 16.47 26.67 84.27

Gafurov et al. 2.2 − 23.6 8.07 28.43 14.11 52.37

Derawi et al. 5.7 4.59 10.71 10.49 31.86

Proposed method (PCA) – 3.83 10.75 11.23 35.03

Proposed method (PCA+SVM) – 2.45 3.75 5.35 14.38

0.1

0.2

0.3

0.4

0.6

0.1

0.2

0.3

0.4

0.6

False Acceptance Rate

False Rejection Rate

{X,Y,Z}

original

{M}

original

{Z,XY,M}

transformed

(a) Rong et al.

0 0.1 0.2 0.3 0.4 0.6

0.1

0.2

0.3

0.4

0.6

False Acceptance Rate

False Rejection Rate

{Z}

original

{M}

original

{Z}

transformed

{Z,XY,M}

transformed

(b) Gafurov et al.

0.1

0.2

0.3

0.4

0.6

0.1

0.2

0.3

0.4

0.6

False Acceptance Rate

False Rejection Rate

{M}

original

{M}

transformed

{Z,XY,M}

transformed

0.1

0.2

0.3

0.4

0.6

0.1

0.2

0.3

0.4

0.6

False Acceptance Rate

False Rejection Rate

{M}

original

(PCA)

{M}

original

(PCA+SVM)

{Z,XY,M}

transformed

(PCA)

{Z,XY,M}

transformed

(PCA+SVM)

(d) The proposed method

Figure 7: The impacts of the disorientation error on the error rates of the gait veriﬁcation systems.

Table 5: The error rates of session-based and pattern-based

gait identiﬁcation methods.

Method

Accuracy rate (%)

Session-based Pattern-based

Rong et al. (+kNN) 93.12 64.82

Gafurov et al. (+kNN) 87.68 76.55

Derawi et al. (+kNN) 93.41 88.09

Proposed method (PCA+kNN) 96.56 85.48

Proposed method (PCA+SVM) 99.14 94.93

3 separate dimensions to be dissimilar. As can be

seen in Figure 7a (the triangle line), since the authors

store the gait patterns of the separate dimensions, in-

cluding the X-Template, Y-Template and Z-Template,

as the reference set for individual matching, the er-

ror rate is signiﬁcantly increased, because of the dis-

similarity issues. This is similar to Gafurov et al.’s

work (Figure 7b). Looking at both Figures 7a, 7b, it

can be seen that protecting the similarity of the gait

signals from the disorientation problem can help to

maintain the accuracy rate of the system. Based on

our observations, the magnitude of the gait signal is

orientation-independent, so it can be used to construct

the gait veriﬁcation system in spite of the disorienta-

tion issues. This signal was used in the original study

of Derawi et al. and achieved positive results (Fig-

ure 7c). Therefore, we also modiﬁed the methods

of Rong et al. and Gafurov et al. by only using the

magnitude of the signal and found that the error rates

could be enhanced. However, from our perspective,

we are strongly convinced that the gait can be more

distinguishable if the gait signal can be expressed

in higher dimensions. Consequently, additional ex-

periments are conducted according to the hypothesis,

wherein we employ the gait signals of all dimensions,

which can be obtained after overcoming the disorien-

tation problem. As expected, the error rates achieved

with the methods of all of the studies are likely to be

more decreased when the gait signals in the dimen-

sions of Z, XY, M are all used (Figure 7). Therefore,

we believe that overcoming the disorientation prob-

lem, in order to maintain the number of dimensions

of the acquired gait signals, is mandatory to optimize

the performance of gait veriﬁcation and identiﬁcation

systems.

6 CONCLUSIONS

In this paper, we addressed the sensor disorientation

problem in gait veriﬁcation or identiﬁcation systems

which can frequently arise in reality, especially in

the mobile context. A simple but effective solution

taking advantages of available sensors in mobile de-

vice was proposed. A gait recognition model leverag-

ing statistical analysis and supervised machine learn-

ing which could be used to verify or identify mo-

bile user was also presented. The results achieved

are highly promising, especially with regard to iden-

tiﬁcation. They reﬂect the good potential of deploy-

ing a gait-based authentication to ameliorate the se-

curity on portable devices. Note that our proposed

method does not aim to completely replace the exist-

ing explicit authentication schemes on mobiles, since

at this moment it is infeasible to achieve a perfect se-

curity level (e.g., the zero-FAR is always achieved) of

any behavioral biometric-based veriﬁcation systems.

However, the proposed method can be used as an ad-

ditional authentication scheme, especially for applica-

tions which do not require excessively strict security

levels, to enhance the usability of the device. In a fu-

ture work, we would like to investigate on developing

a unique gait recognition model working effectively

regardless of the relative position of the mobile to its

owner. A protection scheme used to secure gait tem-

plate/ models stored directly in the device will also be

our main further work.

ACKNOWLEDGEMENTS

This research was supported by Basic Science Re-

search Program through the National Research Foun-

dation of Korea (NRF) funded by the Ministry of Edu-

cation (2012R1A1A2007014). The research was also

supported by 2012-18-02TD VNU–HCMC Project.

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