Research Article Gait Signal Analysis with Similarity...

Research ArticleGait Signal Analysis with Similarity Measure

Sanghyuk Lee1 and Seungsoo Shin2

1 Department of Electrical and Electronic Engineering Xirsquoan Jiaotong-Liverpool University Suzhou 215123 China2Department of Information Security Tongmyong University Sinseonno Nam-gu Busan 608-711 Republic of Korea

Correspondence should be addressed to Seungsoo Shin shinsstuackr

Received 25 April 2014 Accepted 10 June 2014 Published 7 July 2014

Academic Editor T O Ting

Copyright copy 2014 S Lee and S Shin This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Human gait decision was carried out with the help of similarity measure design Gait signal was selected through hardwareimplementation including all in one sensor control unit and notebook with connector Each gait signal was considered as highdimensional dataTherefore high dimensional data analysis was considered via heuristic technique such as the similarity measureEach human pattern such as walking sitting standing and stepping up was obtained through experiment By the results of theanalysis we also identified the overlapped and nonoverlapped data relation and similaritymeasure analysis was also illustrated andcomparison with conventional similarity measure was also carried out Hence nonoverlapped data similarity analysis provided theclue to solve the similarity of high dimensional data Considered high dimensional data analysis was designed with considerationof neighborhood information Proposed similarity measure was applied to identify the behavior patterns of different persons anddifferent behaviours of the same person Obtained analysis can be extended to organize health monitoring system for speciallyelderly persons

1 Introduction

Analysis on the human gait signal has been studied steadilyby numerous researchers [1ndash3]The research on the gait signalapplies to the field of healthcare development security sys-tem and another related area Researchmethodology is basedon how to classify the signal and develop pattern recognitionalgorithm for the comparable data setsThis algorithmappliesthe processing of the different signals of the same personand same action signals from multiple persons Developingmethodology for gait discrimination is challenge Howeverhuman gait signal has high dimensional characteristics henceanalyzing and designing explicit classifying formula is needed[3]

Generally human gait signals consist of walking sittingstanding stepping up and down and other usual behaviorSuch a usual behavior would be done in house life then itis quite easy for us to identify when we watch them in realsituation In order to develop a more massive monitoringsystem and healthcare system to analyze and identify behav-ior signal of each person decision and classifying system for

the gait signal is requiredMore specifically decision whetherheshe is doing in normal activities or not can be applied tothe design of health care systemTherefore obtained researchoutput can be applied to the identification healthcare andother related fields Additionally more detail checking resulteven for the healthy people such as athletes can provideuseful information whether heshe has suffered from otherproblems compared to the previous behavior

To discriminate between different patterns rationalmeasure obtained from a statistical approach or heuristicapproach is needed By the point of statistical method signalautocorrelation and cross correlation knowledge are usefulbecause such formula provide us how much the signalsare related with each other by the numeric value Also itis rather convenient to calculate due to the conventionalsoftware such as Matlab toolbox However it is not easyfor high dimensional data to construct high dimensionalcorrelationcovariance matrices For heuristic approach itneeds preliminary processing for the signal such as dataredefinition and measure design based on the human think-ing Even the realization of measure based on heuristic

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 136018 8 pageshttpdxdoiorg1011552014136018

2 The Scientific World Journal

idea is considered ordinary measure for discrimination hasto be considered such as distance Fortunately similaritymeasure design for the vague data has become a moreinteresting research topic hence numerous researchers havebeen focused on the similarity measure entropy designproblem for fuzzy set and intuitionistic fuzzy set [4ndash8]

Similarity measure [9ndash12] provides useful knowledge tothe clustering and pattern recognition for data sets [13]However most of the conventional results were not includedin high dimensional data Human gait signal representshigh dimensional data characteristics So similarity measuredesign problem for high dimensional data are also neededto deal with the human gait signal Similarity measureresearch has rather long history square error clusteringalgorithm has been used from the late 1960s [14] And itwas modified to create the cluster program [15] Naturallysimilarity measure topic has been moved to many areassuch as statistics [16] machine learning [17 18] patternrecognition [19] and image processing Extended researchon high-dimensional data can be applied to the securitybusiness including fingerprint and iris identification imageprocessing enhancement and even big data applicationrecently

Then distance between vectors can be organized bynorms such as 1-norm Euclidean-norm and so forth Sim-ilarity measure is also designed explicitly with the dis-tance norm Similarity measure design problem for high-dimension needs more considerate approach Convention-ally the similarity measure has been designed based onthe distance measure between two considered data thatis distance measure was considered information distancebetween two membership functions In the similarity mea-sure design with distance measure measure structure shouldbe related to the same support of the universe of discourse[14 15] Additionally similarity measure consideration onoverlapped or nonoverlapped data is needed because manycases of high dimensional data are represented nonover-lapped data structure With conventional similarity measurenonoverlapped data analysis is not possible Hence similaritymeasure design for nonoverlapped data should be followedIn order to design similarity measure on nonoverlappeddata neighbor data information was considered Data hasto be affected from the adjacent information so similaritymeasure on nonoverlapped data was designed Inside ofliterature artificial data was given to compare with con-ventional similarity measure calculation result was alsoillustrated

In the following section preliminary results on the simi-larity measure on overlapped and nonoverlapped data wereintroduced Proposed similarity measure was proved andapplied to overlapped and nonoverlapped artificial data InSection 3 gait signal acquisition system was considered withsensor and data acquisition Gait signal which was also illus-trated with different behaviors High dimensional similaritymeasure was proposed and proved in Section 4 Similaritymeasure design for high dimensional data was also discussedby way of norm structure Similarity calculation results fordifferent behavior and individuals were also shown Finallyconclusions are followed in Section 5

2 Similarity Measure Based Distance Property

In order to design similarity measure explicitly usual mea-sure such as Hamming distance was commonly used asdistance measure between sets 119860 and 119861 as follows

119889 (119860 119861) =1

119899

119899

sum

119894=1

1003816100381610038161003816120583119860 (119909119894) minus 120583119861 (119909119894)1003816100381610038161003816 (1)

where 119883 = 1199091 1199092 119909

119899 120583119860(119909119894) and 120583

119861(119909119894) are fuzzy

membership function of fuzzy sets 119860 and 119861 at 119909119894 and |119896|

was the absolute value of 119896 The membership function of119860 isin 119865(119883) is represented by 119860 = (119909 120583

119860(119909)) | 119909 isin 119883 0 le

120583119860(119909) le 1 119883 is total set and 119865(119883) is the class of all fuzzy

sets of 119883 Similarity measure definition was defined with thehelp of distance measure [14] There are numerous similaritymeasures satisfying the following definition

Definition 1 (see [14]) A real function 119904 1198652 rarr 119877+ is called a

similarity measure if 119904 has the following properties

(S1) 119904(119860 119861) = 119904(119861 119860) 119860 119861 isin 119865(119883)(S2) 119904(119863119863119862) = 0 119863 isin 119875(119883)(S3) 119904(119862 119862) = max

119860119861isin119865119904(119860 119861) 119862 isin 119865(119883)

(S4) 119860 119861 119862 isin 119865(119883) if 119860 sub 119861 sub 119862 then 119904(119860 119861) ge 119904(119860 119862)and 119904(119861 119862) ge 119904(119860 119862)

where 119877+ = [0infin) 119875(119883) is the class of ordinary sets of119883 and 119863119862 is the complement set of 119863 By this definitionnumerous similarity measures could be derived In thefollowing theorem similarity measures based on distancemeasure is illustrated

Theorem 2 For any set 119860 119861 isin 119865(119883) if 119889 satisfies Hammingdistance measure then

119904 (119860 119861) = 119889 ((119860 cap 119861) [0]119883) + 119889 ((119860 cup 119861) [1]

119883) (2)

is the similarity measure between sets 119860 and 119861

Proof Commutativity of (S1) is clear from (9) itself that is119904(119860 119861) = 119904(119861 119860)

For (S2)

119904 (119863119863119862

) = 119889 ((119863 cap 119863119862

) [0]119883) + 119889 ((119863 cup 119863

119862

) [1]119883)

= 119889 ([0]119883 [0]119883) + 119889 ([1]

119883 [1]119883) = 0

(3)

is obtained because of (119863 cap 119863119862) = [0]119883and (119863 cup 119863119862) =

[1]119883 where [0]

119883and [1]

119883denote zero and one over thewhole

universe of discourse of119883 Hence (S2) was satisfied(S3) is also easy to prove as follows

119904 (119862 119862) = 119889 ((119862 cap 119862) [0]119883) + 119889 ((119862 cup 119862) [1]

119883)

= 119889 (119862 [0]119883) + 119889 (119862 [1]

119883) = 1

(4)

It is natural that 119904(119862 119862) satisfied maximal value Finally

119889 ((119860 cap 119861) [0]119883) = 119889 ((119860 cap 119862) [0]

119883)

119889 ((119860 cup 119862) [1]119883) lt 119889 ((119860 cup 119861) [1]

119883)

(5)

The Scientific World Journal 3M

embe

rshi

p va

lue

Universe of discourse X

1

0x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12

Figure 1 Overlapped data distribution

guarantees 119904(119860 119862) lt 119904(119860 119861) and

119889 ((119861 cap 119862) [0]119883) = 119889 ((119860 cap 119862) [0]

119883)

119889 ((119860 cup 119862) [1]119883) lt 119889 ((119861 cup 119862) [1]

119883)

(6)

also guarantees 119904(119860 119862) lt 119904(119860 119861) therefore triangularequality is obvious by the definition and hence (S4) is alsosatisfied

Besides Theorem 2 numerous similarity measuresare possible Another similarity measure is illustrated inTheorem 3 and its proof is also found in the previous result[15 16]


119904 (119860 119861) = 1 minus 119889 ((119860 cap 119861) (119860 cup 119861)) (7)

119904 (119860 119861) = 1 minus 119889 (119860 119860 cap 119861) minus 119889 (119861 119860 cap 119861) (8)

119904 (119860 119861) = 2 minus 119889 ((119860 cap 119861) [1]119883) minus 119889 ((119860 cup 119861) [0]

119883) (9)

are the similarity measure between sets 119860 and 119861

Proof Proofs are easy to be derived and it was found inprevious results [15 16]

Besides similarity measures of (7) to (9) other similaritymeasures are also illustrated in previous results [15ndash17] Withsimilarity measure in Theorems 2 and 3 it is only possi-ble to compute the similarity measure for overlapped data(Figure 1) Following data distributions of diamonds (⧫) andcircles (e) illustrates nonoverlapped data it is appropriateto design similarity measure for data in Figure 2 Considerthe nonoverlapped data distribution of diamonds (⧫) andcircles (e) the similaritymeasure of (7) to (9) cannot providethe appropriate solution for the nonoverlapped distributionTwo data pairs that constitute different distributions areconsidered in Figure 2 Twelve data with six diamonds (⧫)and six circles (e) are illustrated with different combinationin Figures 2(a) and 2(b) Similarity degree between circles anddiamonds must be different between Figures 2(a) and 2(b)because of different distribution For example (7) represents

119904 (119860 119861) = 1 minus 119889 ((119860 cap 119861) (119860 cup 119861)) (10)

From (7) 119889((119860 cap 119861) (119860 cup 119861)) provides distance between(119860 cap 119861) and (119860 cup 119861) By the following definitions

119860 cap 119861 = min (119860 119861) 119860 cup 119861 = max (119860 119861) (11)

Nonoverlapped data satisfies119860cap119861 = min(119860 119861) = 0 and119860 cup119861 is defined as119860 or119861 Hence 119904(119860 119861) = 1minus(1119873)summax(119860 119861)shows similaritymeasure where119873 is the total number of datasets 119860 and 119861 From this property

119904 (119860 119861) = 1 minus1

119873summax (119860 119861)

= 1 minus1

12sum (05 + 08 + 06 + 04 + 05 + 06 + 07

+04 + 05 + 1 + 08 + 06) = 038

(12)

and the same result is obtained for Figures 2(a) and 2(b)Hence similarity measures (2) to (9) are not proper forthe nonoverlapped data distribution Two different data inFigure 2(a) are less discriminate than Figure 2(b) It meansthat similarity measure of Figure 2(a) has a higher valuethan Figure 2(b) Similar results are also obtained by thecalculation of similarity measures (8) and (9)

Hence it is required to design similarity measure fornonoverlapping data distribution Consider the followingsimilarity measure for nonoverlapped data such as Figures2(a) and 2(b)

Theorem 4 For singletons or discrete data 119886 119887 isin 119875(119883) if119889satisfied Hamming distance measure then

119904 (119886 119887) = 1 minus1003816100381610038161003816119904119886 minus 119904119887

1003816100381610038161003816 (13)

is a similarity measure between singletons 119886 and 119887 In (13)119904119886and 119904

119887satisfy 119889((119886 cap R) [1]

119883) and 119889((119887 cap R) [1]

119883)

respectivelyWhereR is whole data distribution including 119886 and119887

Proof (S1) and (S2) are clear (S3) is also clear from definitionas follows

119904 (119862 119862) = 1 minus1003816100381610038161003816119904119862 minus 119904119862

1003816100381610038161003816

= 1 minus1003816100381610038161003816119889 ((119862 cap R) [1]119883) minus 119889 ((119862 cap R) [1]119883)

1003816100381610038161003816 = 1

(14)

Finally (S4) 119860 119861 119862 isin 119865(119883) if 119860 lt 119861 lt 119862 then

119904 (119860 119861) = 1 minus1003816100381610038161003816119889 ((119860 cap R) [1]119883) minus 119889 ((119861 cap R) [1]119883)

1003816100381610038161003816

ge 1 minus1003816100381610038161003816119889 ((119860 cap R) [1]119883) minus 119889 ((119862 cap R) [1]119883)

1003816100381610038161003816

= 119904 (119860 119862)

(15)

because 119889((119861 cap R) [1]119883) gt 119889((119862 cap R) [1]

119883) is satisfied

Similarly 119904(119861 119862) ge 119904(119860 119862) is also satisfied

Similarity measure (13) is also designed with the dis-tance measure such as Hamming distance As noted beforeconventional measures were not proper for nonoverlapping


a = 05

b = 08

c = 06

e = 05

f = 06

d = 04

g = 07

h = 04

i = 05

j = 10

k = 08

l = 06

Mem

bers

hip

valu

e


1

0

(a)

a = 05

b = 08

c = 06

e = 05d = 04

h = 04

i = 05

j = 10

k = 08

l = 06

Mem

bers

hip

valu

e


1

0

f = 06g = 07

(b)

Figure 2 (a) Data distribution between circle and diamond (b) Data distribution between circle and diamond

continuous data distributions this property is verified by thesimilarity measure calculation of Figures 2(a) and 2(b)

Next calculate the similarity measure between circle anddiamond with (13)

For Figure 2(a)

119904 (⧫e) = 1 minus 1003816100381610038161003816119889 ((⧫ cap R) [1]119883) minus 119889 ((e cap R) [1]119883)1003816100381610038161003816

= 1 minus 1 times (6 |((1 minus 05) + (1 minus 08) + (1 minus 06)

+ (1 minus 05) + (1 minus 04) + (1 minus 1))

minus ((1 minus 04) + (1 minus 06) + (1 minus 07)

+ (1 minus 05)+(1 minus 08)+(1 minus 06))|)minus1

= 1 minus1

6 |23 minus 24|= 0983

(16)

is satisfiedFor the calculation of Figure 2(b)





+ (1 minus 1) + (1 minus 08) + (1 minus 06))|)minus1

= 1 minus1

6 |28 minus 18|= 0833

(17)

Calculation result shows that the proposed similarity mea-sure is possible to evaluate the degree of similarity fornonoverlapped distributions By comparison with Figure 2distribution between diamond and circle in Figure 2(a) showsmore similar

3 Human Behavior SignalAnalysis and Experiments

Gait signals are collected with experiment unit acquisitionsystem (Figure 3) system is composedwith all in one sensor in

Figure 3 Data acquisition experiment

which accelerator magnetic andGyro sensor mobile stationand connector are integrated Signal acquisition experimentwas done as shown in the following figures

Gait patterns are composed of walking step up andstep down for 20 persons For each behavior signals aremeasured with all in one sensor which integrated withthree sensors (accelerator magnetic and Gyro sensors)each sensor represents three dimension direct signals Foursensors are attached to waist two legs and head Example ofobtained gait signals is illustrated in the following Figure 4Among numerous cases walking and stair up signals areillustrated with acceleration sensor in Figures 4(a) and 4(b)magnetic sensor in Figures 4(c) and 4(d) and Gyro sensor inFigures 4(e) and 4(f) respectively Full signal was illustratedin Figure 4(f) for stair up with Gyro sensor we can notice12 signals for 119909-119910-119911 direction and it shows almost the samepattern for similar gait Hence 119909-119911 direction signals areconsidered in each figure Due to the fact that signal patternsare almost the same and numerous quantity we collecttwo directional signals From the top the first two signalsrepresent 119911-119909 signals at head and next ones are waist andleft and right leg signals respectively We also carried outpreprocessing to make synchronize signals and obtained gaitsignals that are illustrated in Figure 4

The Scientific World Journal 5

0

0

2 4 6 8 10 12 14 16 18 20minus4000

minus3500

minus3000

minus2500

minus2000

minus1500

minus1000

minus500

500

z-headz-waistz-leftz-right

x-headx-waistx-leftx-right

Acce

lero

met

er (m

g)

Imu4 walk

(a) Walking with acceleration sensor

0 2 4 6 8 10 12 14 16 18 20

0

minus4000

minus3500

minus3000

minus2500

minus2000

minus1500

minus1000

minus500

500

1000



Imu4 step

Acce

lero

met

er (m

g)

(b) Stair up with acceleration sensor

0 2 4 6 8 10 12 14 16 18 20minus1000

minus800

minus600

minus400

minus200

0

200

400

Mag

netic

(mG

a)



Imu4 walk

(c) Walking with magnetic sensor

0 2 4 6 8 10 12 14 16 18 20



minus1200

minus1000

minus800

minus600

minus400

minus200

0

200M

agne

tic (m

Ga)

Imu4 step

(d) Stair up with magnetic sensor

0 2 4 6 8 10 12 14 16 18 20



minus1000

minus800

minus600

minus400

minus200

0

200

Rate

Gyr

o (d

egs

)

Imu4 walk

(e) Walking with Gyro sensor

0 2 4 6 8 10 12 14 16 18 20



Imu4 walk

minus1000

minus800

minus600

minus400

minus200

0

200

y-heady-waisty-lefty-right

Rate

Gyr

o (d

egs

)

(f) Stair up with Gyro sensor

Figure 4 Gait signal with all in one sensor


We get the signals from the control unit and the signalis processed in a note book Signal characteristics wereconsidered peak value and magnitude distance between eachgait signal Next by the application of the similarity measurewe get the calculation of each action such as walking step upand so on

4 Numerical Decision Calculation

41 High Dimensional Analysis Research on big data analysishas been emphasized by research outcomes recently [7 8 1319] Big data examples are illustrated as follows

(i) Biomedical data such as DNA sequence or Electroen-cephalography (EEG) data It contains not only highdimension but also large number of channel data

(ii) Recommendation systems and target marketing areimportant applications in the e-commerce area Setsof customersclientsrsquo information analysis help topredict their action to purchase based on customersrsquointerest It also includes a huge amount of data andhigh dimensional structure

(iii) Industry application such as EV station schedulingproblem needs geometrical information city sizepopulation traffic flow and others Hence number ofstation and station size constitute huge data and highdimension

Data might be expressed as high dimensional structure suchas

119863119894= (1198891198941 1198891198942 1198891198943 119889

119894119895)

where 119894 = 1 119899 119895 = 1 119898(18)

where 119899 and 119898 denote the number of data and dimensionrespectively

Direct data comparison is applicable to overlapped datawith norm definition including Euclidean norm such as

d1(119863119894 119863119895) =

119898

sum

119896=1

10038161003816100381610038161003816119889119894119896minus 119889119895119896

10038161003816100381610038161003816 L

1norm

d2(119863119894 119863119895) = radic

119898

sum

119896=1

(119889119894119896minus 119889119895119896)2

Euclidean-norm

d119901(119863119894 119863119895) = (

119898

sum

119896=1

10038161003816100381610038161003816119889119894119896minus 119889119895119896

10038161003816100381610038161003816

119901

)

1119901

L119901norm

(19)

Information distributions show various configurations andhence it needs consider various types of distance measureto complete discriminative measure Furthermore analysis ofsimilarity and relation between different information shouldbe considered carefully when it represents high-dimensionaldata Specifically 119898 dimension represents the independentnumber of characteristics or attributes

Table 1 Similarity measure comparison between patterns

Similarity measure Values119904 (119882119894 119878119880119894) 0344

119904 (119882119894 119878119863119894) 0278

119904 (119878119880119894 119878119863119894) 0550

Table 2 Average similarity measure between individuals

Similarity measure Values119904 (119875119882

119894 119875119882119895) 0624

119904 (119875119878119863119894 119875119878119863

119895) 0643

119904 (119875119878119880119894 119875119878119880

119895) 0712

42 Illustrative Example Hence analysis and comparisonwith each attribute provide explicit importance of each dataSimilarity measure provides analysis between patterns suchas

119904 (119863119894 119863119895) forall119894 119895 = 1 119899 (20)

And comparison with different patterns for the same personis carrying out between walking step up or step downGait signal related with hisher movement was gathered toanalyze their different patterns and different persons Eachsignal constitutes walking stair up and stair down with 20personsrsquo gaits were gathered Hence personal informationcan be represented by multidimensional information such as

119875119894= (119882119894 119878119880119894 119878119863119894) where 119894 = 1 20 (21)

And among 20 personal data 3 different behaviors werealso expressed Considering the data it is obvious that datais overlapped Hence it is clear that similarity measures of(2) and (7)ndash(9) provide similarity calculation for overlappeddata

Similaritymeasure between person to person is expressedas

119904 (119875119894 119875119895) = 1 minus 119889 ((119875

119894cap 119875119895) (119875119894cup 119875119895)) (22)

Also different action from the same person as follows

119904 (119882119894 119878119880119894) = 1 minus 119889 ((119882

119894cap 119878119880119894) (119882119894cup 119878119880119894)) (23)

Normalized similarity calculation results are illustrated inTable 1

Results illustrate that the stair up and down shows highersimilarity than the others However even similarity calcula-tion result is higher than others it is not much close to oneit just satisfies 055 Due to different directions stair updownshould have basic limit to close maximum similarity

Table 2 shows the average similarity between differentindividuals Results show that the stair up is the closest evenwith a different gait Naturally walking pattern represents theleast similar In Table 3 walking similarity between different


Table 3 Similarity measure comparison between individuals (walking)

Similaritymeasure 1 2 3 4 5 6 7 sdot sdot sdot 18 19 20

1 1 0511 0621 0420 0462 0581 0617 0581 0470 06232 0511 1 0592 0590 0490 0632 0543 0603 0619 05773 0621 0592 1 0510 0611 0640 0599 0710 0566 05824 0420 0590 0510 1 0701 0653 0589 sdot sdot sdot 0612 0629 05855 0462 0490 0611 0701 1 0599 0603 0489 0581 06206 0581 0632 0640 0653 0599 1 0576 0499 0545 06297 0617 0543 0599 0589 0603 0576 1 0710 0627 0634

0590 0611 0589

0429 0570 0630

0559 0628 054918 0581 0603 0710 0612 0489 0499 0710 0590 0429 0559 1 0345 062619 0470 0619 0566 0629 0581 0545 0627 0611 0570 0628 0345 1 055620 0623 0577 0582 0585 0620 0629 0634 0589 0630 0549 0626 0556 1

individuals is illustrated symmetric results of 20 persons arelisted in Table 3

Similar results for stair up and down are obtained

5 Conclusions

Gait signal identification was carried out through similaritymeasure design Gait signal was obtained via data acquisitionsystem including mobile station all in one sensor attachedto the head waist and two legs In order to discriminate thegait signal with respect to different behaviors and individualssimilaritymeasure designwas considered Similaritymeasurewas considered with the distance measure For data dis-tribution overlapped and nonoverlapped distribution wereconsidered and similarity measure was applied to calculatethe similarity However the conventional similarity measurewas shown that it was not available to calculate the similarityon non-overlapped data To overcome such a drawback thesimilarity measure was considered with data informationof neighbor Closeness between neighbor data provides ameasure of similarity among data sets hence the similaritymeasure was calculated Calculation proposed two differentartificial data and the proposed similarity measure wasuseful to identify nonoverlapped data distribution It ismeaningful that similarity measure design can be extendedto high dimensional data processing because gait signal wasconsidered as a high dimensional data With data acquisi-tion system 20 person gait signals were collected throughexperiments Different gaits walking stair up and stair downsignals were obtained and similarity measure was appliedBy calculation similarity between stair up and stair downshowed higher similarity than others Individual similarityfor a different gait signal was also obtained

Gait signal analysis can be used for behavior decisionsystem development it is also naturally extended to healthcare system especially to elderly people Additionally it isalso useful for athlete to provide useful information if heshe

is suffering from different actions compared to previousbehavior

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

Thisworkwas supported in part by aGrant from theResearchDevelopment Fund of XJTLU (RDF 11-02-03)

References

[1] D H Fisher ldquoKnowledge acquisition via incremental concep-tual clusteringrdquoMachine Learning vol 2 no 2 pp 139ndash172 1987

[2] A K Jain and R C Dubes Algorithms for Clustering DataPrentice Hall 1988

[3] F Murtagh ldquoA survey of recent advances in hierarchicalclustering algorithmsrdquoComputer Journal vol 26 no 4 pp 354ndash359 1983

[4] R S Michalski and R E Stepp ldquoLearning from observationconceptual clusteringrdquo inMachine Learning An Artificial Intel-ligence Approach pp 331ndash363 Springer Berlin Germany 1983

[5] H P Friedman and J Rubin ldquoOn some invariant criteria forgrouping datardquo Journal of the American Statistical Associationvol 62 no 320 pp 1159ndash1178 1967

[6] K Fukunaga Introduction to Statistical Pattern RecognitionAcademic Press New York NY USA 1990

[7] ldquoAdvancing Discovery in Science and Engineering ComputingCommunity Consortiumrdquo Spring 2011

[8] Advancing Personalized Education Computing CommunityConsortium 2011

[9] S Lee and T O Ting ldquoThe evaluation of data uncertainty andentropy analysis for multiple eventsrdquo in Advances in SwarmIntelligence pp 175ndash182 Springer New York NY USA 2012


[10] S Park S Lee S Lee andTO Ting ldquoDesign similaritymeasureand application to fault detection of lateral directional modeflight systemrdquo in Advances in Swarm Intelligence vol 7332 ofLecture Notes in Computer Science pp 183ndash191 Springer NewYork NY USA 2012

[11] S Lee and T O Ting ldquoUncertainty evaluation via fuzzy entropyformultiple factsrdquo International Journal of Electronic Commercevol 4 no 2 pp 345ndash354 2013

[12] S Lee W He and T O Ting ldquoStudy on similarity measurefor overlapped and non-overlapped datardquo in Proceedings of theInternational Conference on Information Science and Technology(ICIST 13) pp 48ndash53 March 2013

[13] ldquoSmart Health and Wellbeingrdquo Computing Community Con-sortium 2011

[14] X C Liu ldquoEntropy distance measure and similarity measure offuzzy sets and their relationsrdquo Fuzzy Sets and Systems vol 52no 3 pp 305ndash318 1992

[15] S Lee W Pedrycz and G Sohn ldquoDesign of similarity anddissimilarity measures for fuzzy sets on the basis of distancemeasurerdquo International Journal of Fuzzy Systems vol 11 no 2pp 67ndash72 2009

[16] S Lee K H Ryu andG Sohn ldquoStudy on entropy and similaritymeasure for fuzzy setrdquo IEICE Transactions on Information andSystems vol 92 no 9 pp 1783ndash1786 2009

[17] S H Lee S J Kim and N Y Jang ldquoDesign of fuzzyentropy for non convex membership functionrdquo in AdvancedIntelligent Computing Theories and Applications With Aspectsof Contemporary Intelligent Computing Techniques vol 15 ofCommunications in Computer and Information Science pp 55ndash60 2008

[18] Y Cheng and G Church ldquoBiclustering of expression datardquo inProceedings of the 8th International Conference on IntelligentSystem for Molecular Biology 2000

[19] D M West Big Data for Education Data Mining Data Ana-lytics and Web Dashboards Governance Studies at BrookingsWashington DC USA 2012

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Distributed Sensor Networks


Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014


ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014


Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications


Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia


Biomedical Imaging


ArtificialNeural Systems

Advances in


RoboticsJournal of



Computational Intelligence and Neuroscience

Industrial EngineeringJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in



idea is considered ordinary measure for discrimination hasto be considered such as distance Fortunately similaritymeasure design for the vague data has become a moreinteresting research topic hence numerous researchers havebeen focused on the similarity measure entropy designproblem for fuzzy set and intuitionistic fuzzy set [4ndash8]

Similarity measure [9ndash12] provides useful knowledge tothe clustering and pattern recognition for data sets [13]However most of the conventional results were not includedin high dimensional data Human gait signal representshigh dimensional data characteristics So similarity measuredesign problem for high dimensional data are also neededto deal with the human gait signal Similarity measureresearch has rather long history square error clusteringalgorithm has been used from the late 1960s [14] And itwas modified to create the cluster program [15] Naturallysimilarity measure topic has been moved to many areassuch as statistics [16] machine learning [17 18] patternrecognition [19] and image processing Extended researchon high-dimensional data can be applied to the securitybusiness including fingerprint and iris identification imageprocessing enhancement and even big data applicationrecently

Then distance between vectors can be organized bynorms such as 1-norm Euclidean-norm and so forth Sim-ilarity measure is also designed explicitly with the dis-tance norm Similarity measure design problem for high-dimension needs more considerate approach Convention-ally the similarity measure has been designed based onthe distance measure between two considered data thatis distance measure was considered information distancebetween two membership functions In the similarity mea-sure design with distance measure measure structure shouldbe related to the same support of the universe of discourse[14 15] Additionally similarity measure consideration onoverlapped or nonoverlapped data is needed because manycases of high dimensional data are represented nonover-lapped data structure With conventional similarity measurenonoverlapped data analysis is not possible Hence similaritymeasure design for nonoverlapped data should be followedIn order to design similarity measure on nonoverlappeddata neighbor data information was considered Data hasto be affected from the adjacent information so similaritymeasure on nonoverlapped data was designed Inside ofliterature artificial data was given to compare with con-ventional similarity measure calculation result was alsoillustrated

In the following section preliminary results on the simi-larity measure on overlapped and nonoverlapped data wereintroduced Proposed similarity measure was proved andapplied to overlapped and nonoverlapped artificial data InSection 3 gait signal acquisition system was considered withsensor and data acquisition Gait signal which was also illus-trated with different behaviors High dimensional similaritymeasure was proposed and proved in Section 4 Similaritymeasure design for high dimensional data was also discussedby way of norm structure Similarity calculation results fordifferent behavior and individuals were also shown Finallyconclusions are followed in Section 5

2 Similarity Measure Based Distance Property

In order to design similarity measure explicitly usual mea-sure such as Hamming distance was commonly used asdistance measure between sets 119860 and 119861 as follows

119889 (119860 119861) =1

119899

119899

sum

119894=1

1003816100381610038161003816120583119860 (119909119894) minus 120583119861 (119909119894)1003816100381610038161003816 (1)

where 119883 = 1199091 1199092 119909

119899 120583119860(119909119894) and 120583

119861(119909119894) are fuzzy

membership function of fuzzy sets 119860 and 119861 at 119909119894 and |119896|

was the absolute value of 119896 The membership function of119860 isin 119865(119883) is represented by 119860 = (119909 120583

119860(119909)) | 119909 isin 119883 0 le

120583119860(119909) le 1 119883 is total set and 119865(119883) is the class of all fuzzy

sets of 119883 Similarity measure definition was defined with thehelp of distance measure [14] There are numerous similaritymeasures satisfying the following definition

Definition 1 (see [14]) A real function 119904 1198652 rarr 119877+ is called a

similarity measure if 119904 has the following properties

(S1) 119904(119860 119861) = 119904(119861 119860) 119860 119861 isin 119865(119883)(S2) 119904(119863119863119862) = 0 119863 isin 119875(119883)(S3) 119904(119862 119862) = max

119860119861isin119865119904(119860 119861) 119862 isin 119865(119883)

(S4) 119860 119861 119862 isin 119865(119883) if 119860 sub 119861 sub 119862 then 119904(119860 119861) ge 119904(119860 119862)and 119904(119861 119862) ge 119904(119860 119862)

where 119877+ = [0infin) 119875(119883) is the class of ordinary sets of119883 and 119863119862 is the complement set of 119863 By this definitionnumerous similarity measures could be derived In thefollowing theorem similarity measures based on distancemeasure is illustrated


119904 (119860 119861) = 119889 ((119860 cap 119861) [0]119883) + 119889 ((119860 cup 119861) [1]

119883) (2)

is the similarity measure between sets 119860 and 119861

Proof Commutativity of (S1) is clear from (9) itself that is119904(119860 119861) = 119904(119861 119860)

For (S2)

119904 (119863119863119862

) = 119889 ((119863 cap 119863119862

) [0]119883) + 119889 ((119863 cup 119863

119862

) [1]119883)

= 119889 ([0]119883 [0]119883) + 119889 ([1]

119883 [1]119883) = 0

(3)

is obtained because of (119863 cap 119863119862) = [0]119883and (119863 cup 119863119862) =

[1]119883 where [0]

119883and [1]

119883denote zero and one over thewhole

universe of discourse of119883 Hence (S2) was satisfied(S3) is also easy to prove as follows

119904 (119862 119862) = 119889 ((119862 cap 119862) [0]119883) + 119889 ((119862 cup 119862) [1]

119883)

= 119889 (119862 [0]119883) + 119889 (119862 [1]

119883) = 1

(4)

It is natural that 119904(119862 119862) satisfied maximal value Finally

119889 ((119860 cap 119861) [0]119883) = 119889 ((119860 cap 119862) [0]

119883)

119889 ((119860 cup 119862) [1]119883) lt 119889 ((119860 cup 119861) [1]

119883)

(5)


embe

rshi

p va

lue


1

0x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12



119889 ((119861 cap 119862) [0]119883) = 119889 ((119860 cap 119862) [0]

119883)

119889 ((119860 cup 119862) [1]119883) lt 119889 ((119861 cup 119862) [1]

119883)

(6)




119904 (119860 119861) = 1 minus 119889 ((119860 cap 119861) (119860 cup 119861)) (7)



119883) (9)




119904 (119860 119861) = 1 minus 119889 ((119860 cap 119861) (119860 cup 119861)) (10)


119860 cap 119861 = min (119860 119861) 119860 cup 119861 = max (119860 119861) (11)


119904 (119860 119861) = 1 minus1

119873summax (119860 119861)

= 1 minus1

12sum (05 + 08 + 06 + 04 + 05 + 06 + 07

+04 + 05 + 1 + 08 + 06) = 038

(12)




119904 (119886 119887) = 1 minus1003816100381610038161003816119904119886 minus 119904119887

1003816100381610038161003816 (13)


119887satisfy 119889((119886 cap R) [1]

119883) and 119889((119887 cap R) [1]

119883)



119904 (119862 119862) = 1 minus1003816100381610038161003816119904119862 minus 119904119862

1003816100381610038161003816


1003816100381610038161003816 = 1

(14)



1003816100381610038161003816


1003816100381610038161003816

= 119904 (119860 119862)

(15)






a = 05

b = 08

c = 06

e = 05

f = 06

d = 04

g = 07

h = 04

i = 05

j = 10

k = 08

l = 06

Mem

bers

hip

valu

e


1

0

(a)

a = 05

b = 08

c = 06

e = 05d = 04

h = 04

i = 05

j = 10

k = 08

l = 06

Mem

bers

hip

valu

e


1

0

f = 06g = 07

(b)




For Figure 2(a)






= 1 minus1

6 |23 minus 24|= 0983

(16)







= 1 minus1

6 |28 minus 18|= 0833

(17)








0

0

2 4 6 8 10 12 14 16 18 20minus4000

minus3500

minus3000

minus2500

minus2000

minus1500

minus1000

minus500

500



Acce

lero

met

er (m

g)

Imu4 walk


0 2 4 6 8 10 12 14 16 18 20

0

minus4000

minus3500

minus3000

minus2500

minus2000

minus1500

minus1000

minus500

500

1000



Imu4 step

Acce

lero

met

er (m

g)


0 2 4 6 8 10 12 14 16 18 20minus1000

minus800

minus600

minus400

minus200

0

200

400

Mag

netic

(mG

a)



Imu4 walk


0 2 4 6 8 10 12 14 16 18 20



minus1200

minus1000

minus800

minus600

minus400

minus200

0

200M

agne

tic (m

Ga)

Imu4 step


0 2 4 6 8 10 12 14 16 18 20



minus1000

minus800

minus600

minus400

minus200

0

200

Rate

Gyr

o (d

egs

)

Imu4 walk


0 2 4 6 8 10 12 14 16 18 20



Imu4 walk

minus1000

minus800

minus600

minus400

minus200

0

200


Rate

Gyr

o (d

egs

)











119863119894= (1198891198941 1198891198942 1198891198943 119889

119894119895)

where 119894 = 1 119899 119895 = 1 119898(18)



d1(119863119894 119863119895) =

119898

sum

119896=1

10038161003816100381610038161003816119889119894119896minus 119889119895119896

10038161003816100381610038161003816 L

1norm

d2(119863119894 119863119895) = radic

119898

sum

119896=1

(119889119894119896minus 119889119895119896)2

Euclidean-norm

d119901(119863119894 119863119895) = (

119898

sum

119896=1

10038161003816100381610038161003816119889119894119896minus 119889119895119896

10038161003816100381610038161003816

119901

)

1119901

L119901norm

(19)




119904 (119882119894 119878119863119894) 0278

119904 (119878119880119894 119878119863119894) 0550



119894 119875119882119895) 0624

119904 (119875119878119863119894 119875119878119863

119895) 0643

119904 (119875119878119880119894 119875119878119880

119895) 0712


119904 (119863119894 119863119895) forall119894 119895 = 1 119899 (20)


119875119894= (119882119894 119878119880119894 119878119863119894) where 119894 = 1 20 (21)



119904 (119875119894 119875119895) = 1 minus 119889 ((119875

119894cap 119875119895) (119875119894cup 119875119895)) (22)


119904 (119882119894 119878119880119894) = 1 minus 119889 ((119882

119894cap 119878119880119894) (119882119894cup 119878119880119894)) (23)







1 1 0511 0621 0420 0462 0581 0617 0581 0470 06232 0511 1 0592 0590 0490 0632 0543 0603 0619 05773 0621 0592 1 0510 0611 0640 0599 0710 0566 05824 0420 0590 0510 1 0701 0653 0589 sdot sdot sdot 0612 0629 05855 0462 0490 0611 0701 1 0599 0603 0489 0581 06206 0581 0632 0640 0653 0599 1 0576 0499 0545 06297 0617 0543 0599 0589 0603 0576 1 0710 0627 0634

0590 0611 0589

0429 0570 0630

0559 0628 054918 0581 0603 0710 0612 0489 0499 0710 0590 0429 0559 1 0345 062619 0470 0619 0566 0629 0581 0545 0627 0611 0570 0628 0345 1 055620 0623 0577 0582 0585 0620 0629 0634 0589 0630 0549 0626 0556 1



5 Conclusions






Acknowledgment


References




























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




embe

rshi

p va

lue


1

0x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12



119889 ((119861 cap 119862) [0]119883) = 119889 ((119860 cap 119862) [0]

119883)

119889 ((119860 cup 119862) [1]119883) lt 119889 ((119861 cup 119862) [1]

119883)

(6)




119904 (119860 119861) = 1 minus 119889 ((119860 cap 119861) (119860 cup 119861)) (7)



119883) (9)




119904 (119860 119861) = 1 minus 119889 ((119860 cap 119861) (119860 cup 119861)) (10)


119860 cap 119861 = min (119860 119861) 119860 cup 119861 = max (119860 119861) (11)


119904 (119860 119861) = 1 minus1

119873summax (119860 119861)

= 1 minus1

12sum (05 + 08 + 06 + 04 + 05 + 06 + 07

+04 + 05 + 1 + 08 + 06) = 038

(12)




119904 (119886 119887) = 1 minus1003816100381610038161003816119904119886 minus 119904119887

1003816100381610038161003816 (13)


119887satisfy 119889((119886 cap R) [1]

119883) and 119889((119887 cap R) [1]

119883)



119904 (119862 119862) = 1 minus1003816100381610038161003816119904119862 minus 119904119862

1003816100381610038161003816


1003816100381610038161003816 = 1

(14)



1003816100381610038161003816


1003816100381610038161003816

= 119904 (119860 119862)

(15)






a = 05

b = 08

c = 06

e = 05

f = 06

d = 04

g = 07

h = 04

i = 05

j = 10

k = 08

l = 06

Mem

bers

hip

valu

e


1

0

(a)

a = 05

b = 08

c = 06

e = 05d = 04

h = 04

i = 05

j = 10

k = 08

l = 06

Mem

bers

hip

valu

e


1

0

f = 06g = 07

(b)




For Figure 2(a)






= 1 minus1

6 |23 minus 24|= 0983

(16)







= 1 minus1

6 |28 minus 18|= 0833

(17)








0

0

2 4 6 8 10 12 14 16 18 20minus4000

minus3500

minus3000

minus2500

minus2000

minus1500

minus1000

minus500

500



Acce

lero

met

er (m

g)

Imu4 walk


0 2 4 6 8 10 12 14 16 18 20

0

minus4000

minus3500

minus3000

minus2500

minus2000

minus1500

minus1000

minus500

500

1000



Imu4 step

Acce

lero

met

er (m

g)


0 2 4 6 8 10 12 14 16 18 20minus1000

minus800

minus600

minus400

minus200

0

200

400

Mag

netic

(mG

a)



Imu4 walk


0 2 4 6 8 10 12 14 16 18 20



minus1200

minus1000

minus800

minus600

minus400

minus200

0

200M

agne

tic (m

Ga)

Imu4 step


0 2 4 6 8 10 12 14 16 18 20



minus1000

minus800

minus600

minus400

minus200

0

200

Rate

Gyr

o (d

egs

)

Imu4 walk


0 2 4 6 8 10 12 14 16 18 20



Imu4 walk

minus1000

minus800

minus600

minus400

minus200

0

200


Rate

Gyr

o (d

egs

)











119863119894= (1198891198941 1198891198942 1198891198943 119889

119894119895)

where 119894 = 1 119899 119895 = 1 119898(18)



d1(119863119894 119863119895) =

119898

sum

119896=1

10038161003816100381610038161003816119889119894119896minus 119889119895119896

10038161003816100381610038161003816 L

1norm

d2(119863119894 119863119895) = radic

119898

sum

119896=1

(119889119894119896minus 119889119895119896)2

Euclidean-norm

d119901(119863119894 119863119895) = (

119898

sum

119896=1

10038161003816100381610038161003816119889119894119896minus 119889119895119896

10038161003816100381610038161003816

119901

)

1119901

L119901norm

(19)




119904 (119882119894 119878119863119894) 0278

119904 (119878119880119894 119878119863119894) 0550



119894 119875119882119895) 0624

119904 (119875119878119863119894 119875119878119863

119895) 0643

119904 (119875119878119880119894 119875119878119880

119895) 0712


119904 (119863119894 119863119895) forall119894 119895 = 1 119899 (20)


119875119894= (119882119894 119878119880119894 119878119863119894) where 119894 = 1 20 (21)



119904 (119875119894 119875119895) = 1 minus 119889 ((119875

119894cap 119875119895) (119875119894cup 119875119895)) (22)


119904 (119882119894 119878119880119894) = 1 minus 119889 ((119882

119894cap 119878119880119894) (119882119894cup 119878119880119894)) (23)







1 1 0511 0621 0420 0462 0581 0617 0581 0470 06232 0511 1 0592 0590 0490 0632 0543 0603 0619 05773 0621 0592 1 0510 0611 0640 0599 0710 0566 05824 0420 0590 0510 1 0701 0653 0589 sdot sdot sdot 0612 0629 05855 0462 0490 0611 0701 1 0599 0603 0489 0581 06206 0581 0632 0640 0653 0599 1 0576 0499 0545 06297 0617 0543 0599 0589 0603 0576 1 0710 0627 0634

0590 0611 0589

0429 0570 0630

0559 0628 054918 0581 0603 0710 0612 0489 0499 0710 0590 0429 0559 1 0345 062619 0470 0619 0566 0629 0581 0545 0627 0611 0570 0628 0345 1 055620 0623 0577 0582 0585 0620 0629 0634 0589 0630 0549 0626 0556 1



5 Conclusions






Acknowledgment


References




























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




a = 05

b = 08

c = 06

e = 05

f = 06

d = 04

g = 07

h = 04

i = 05

j = 10

k = 08

l = 06

Mem

bers

hip

valu

e


1

0

(a)

a = 05

b = 08

c = 06

e = 05d = 04

h = 04

i = 05

j = 10

k = 08

l = 06

Mem

bers

hip

valu

e


1

0

f = 06g = 07

(b)




For Figure 2(a)






= 1 minus1

6 |23 minus 24|= 0983

(16)







= 1 minus1

6 |28 minus 18|= 0833

(17)








0

0

2 4 6 8 10 12 14 16 18 20minus4000

minus3500

minus3000

minus2500

minus2000

minus1500

minus1000

minus500

500



Acce

lero

met

er (m

g)

Imu4 walk


0 2 4 6 8 10 12 14 16 18 20

0

minus4000

minus3500

minus3000

minus2500

minus2000

minus1500

minus1000

minus500

500

1000



Imu4 step

Acce

lero

met

er (m

g)


0 2 4 6 8 10 12 14 16 18 20minus1000

minus800

minus600

minus400

minus200

0

200

400

Mag

netic

(mG

a)



Imu4 walk


0 2 4 6 8 10 12 14 16 18 20



minus1200

minus1000

minus800

minus600

minus400

minus200

0

200M

agne

tic (m

Ga)

Imu4 step


0 2 4 6 8 10 12 14 16 18 20



minus1000

minus800

minus600

minus400

minus200

0

200

Rate

Gyr

o (d

egs

)

Imu4 walk


0 2 4 6 8 10 12 14 16 18 20



Imu4 walk

minus1000

minus800

minus600

minus400

minus200

0

200


Rate

Gyr

o (d

egs

)











119863119894= (1198891198941 1198891198942 1198891198943 119889

119894119895)

where 119894 = 1 119899 119895 = 1 119898(18)



d1(119863119894 119863119895) =

119898

sum

119896=1

10038161003816100381610038161003816119889119894119896minus 119889119895119896

10038161003816100381610038161003816 L

1norm

d2(119863119894 119863119895) = radic

119898

sum

119896=1

(119889119894119896minus 119889119895119896)2

Euclidean-norm

d119901(119863119894 119863119895) = (

119898

sum

119896=1

10038161003816100381610038161003816119889119894119896minus 119889119895119896

10038161003816100381610038161003816

119901

)

1119901

L119901norm

(19)




119904 (119882119894 119878119863119894) 0278

119904 (119878119880119894 119878119863119894) 0550



119894 119875119882119895) 0624

119904 (119875119878119863119894 119875119878119863

119895) 0643

119904 (119875119878119880119894 119875119878119880

119895) 0712


119904 (119863119894 119863119895) forall119894 119895 = 1 119899 (20)


119875119894= (119882119894 119878119880119894 119878119863119894) where 119894 = 1 20 (21)



119904 (119875119894 119875119895) = 1 minus 119889 ((119875

119894cap 119875119895) (119875119894cup 119875119895)) (22)


119904 (119882119894 119878119880119894) = 1 minus 119889 ((119882

119894cap 119878119880119894) (119882119894cup 119878119880119894)) (23)







1 1 0511 0621 0420 0462 0581 0617 0581 0470 06232 0511 1 0592 0590 0490 0632 0543 0603 0619 05773 0621 0592 1 0510 0611 0640 0599 0710 0566 05824 0420 0590 0510 1 0701 0653 0589 sdot sdot sdot 0612 0629 05855 0462 0490 0611 0701 1 0599 0603 0489 0581 06206 0581 0632 0640 0653 0599 1 0576 0499 0545 06297 0617 0543 0599 0589 0603 0576 1 0710 0627 0634

0590 0611 0589

0429 0570 0630

0559 0628 054918 0581 0603 0710 0612 0489 0499 0710 0590 0429 0559 1 0345 062619 0470 0619 0566 0629 0581 0545 0627 0611 0570 0628 0345 1 055620 0623 0577 0582 0585 0620 0629 0634 0589 0630 0549 0626 0556 1



5 Conclusions






Acknowledgment


References




























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




0

0

2 4 6 8 10 12 14 16 18 20minus4000

minus3500

minus3000

minus2500

minus2000

minus1500

minus1000

minus500

500



Acce

lero

met

er (m

g)

Imu4 walk


0 2 4 6 8 10 12 14 16 18 20

0

minus4000

minus3500

minus3000

minus2500

minus2000

minus1500

minus1000

minus500

500

1000



Imu4 step

Acce

lero

met

er (m

g)


0 2 4 6 8 10 12 14 16 18 20minus1000

minus800

minus600

minus400

minus200

0

200

400

Mag

netic

(mG

a)



Imu4 walk


0 2 4 6 8 10 12 14 16 18 20



minus1200

minus1000

minus800

minus600

minus400

minus200

0

200M

agne

tic (m

Ga)

Imu4 step


0 2 4 6 8 10 12 14 16 18 20



minus1000

minus800

minus600

minus400

minus200

0

200

Rate

Gyr

o (d

egs

)

Imu4 walk


0 2 4 6 8 10 12 14 16 18 20



Imu4 walk

minus1000

minus800

minus600

minus400

minus200

0

200


Rate

Gyr

o (d

egs

)











119863119894= (1198891198941 1198891198942 1198891198943 119889

119894119895)

where 119894 = 1 119899 119895 = 1 119898(18)



d1(119863119894 119863119895) =

119898

sum

119896=1

10038161003816100381610038161003816119889119894119896minus 119889119895119896

10038161003816100381610038161003816 L

1norm

d2(119863119894 119863119895) = radic

119898

sum

119896=1

(119889119894119896minus 119889119895119896)2

Euclidean-norm

d119901(119863119894 119863119895) = (

119898

sum

119896=1

10038161003816100381610038161003816119889119894119896minus 119889119895119896

10038161003816100381610038161003816

119901

)

1119901

L119901norm

(19)




119904 (119882119894 119878119863119894) 0278

119904 (119878119880119894 119878119863119894) 0550



119894 119875119882119895) 0624

119904 (119875119878119863119894 119875119878119863

119895) 0643

119904 (119875119878119880119894 119875119878119880

119895) 0712


119904 (119863119894 119863119895) forall119894 119895 = 1 119899 (20)


119875119894= (119882119894 119878119880119894 119878119863119894) where 119894 = 1 20 (21)



119904 (119875119894 119875119895) = 1 minus 119889 ((119875

119894cap 119875119895) (119875119894cup 119875119895)) (22)


119904 (119882119894 119878119880119894) = 1 minus 119889 ((119882

119894cap 119878119880119894) (119882119894cup 119878119880119894)) (23)







1 1 0511 0621 0420 0462 0581 0617 0581 0470 06232 0511 1 0592 0590 0490 0632 0543 0603 0619 05773 0621 0592 1 0510 0611 0640 0599 0710 0566 05824 0420 0590 0510 1 0701 0653 0589 sdot sdot sdot 0612 0629 05855 0462 0490 0611 0701 1 0599 0603 0489 0581 06206 0581 0632 0640 0653 0599 1 0576 0499 0545 06297 0617 0543 0599 0589 0603 0576 1 0710 0627 0634

0590 0611 0589

0429 0570 0630

0559 0628 054918 0581 0603 0710 0612 0489 0499 0710 0590 0429 0559 1 0345 062619 0470 0619 0566 0629 0581 0545 0627 0611 0570 0628 0345 1 055620 0623 0577 0582 0585 0620 0629 0634 0589 0630 0549 0626 0556 1



5 Conclusions






Acknowledgment


References




























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in











119863119894= (1198891198941 1198891198942 1198891198943 119889

119894119895)

where 119894 = 1 119899 119895 = 1 119898(18)



d1(119863119894 119863119895) =

119898

sum

119896=1

10038161003816100381610038161003816119889119894119896minus 119889119895119896

10038161003816100381610038161003816 L

1norm

d2(119863119894 119863119895) = radic

119898

sum

119896=1

(119889119894119896minus 119889119895119896)2

Euclidean-norm

d119901(119863119894 119863119895) = (

119898

sum

119896=1

10038161003816100381610038161003816119889119894119896minus 119889119895119896

10038161003816100381610038161003816

119901

)

1119901

L119901norm

(19)




119904 (119882119894 119878119863119894) 0278

119904 (119878119880119894 119878119863119894) 0550



119894 119875119882119895) 0624

119904 (119875119878119863119894 119875119878119863

119895) 0643

119904 (119875119878119880119894 119875119878119880

119895) 0712


119904 (119863119894 119863119895) forall119894 119895 = 1 119899 (20)


119875119894= (119882119894 119878119880119894 119878119863119894) where 119894 = 1 20 (21)



119904 (119875119894 119875119895) = 1 minus 119889 ((119875

119894cap 119875119895) (119875119894cup 119875119895)) (22)


119904 (119882119894 119878119880119894) = 1 minus 119889 ((119882

119894cap 119878119880119894) (119882119894cup 119878119880119894)) (23)







1 1 0511 0621 0420 0462 0581 0617 0581 0470 06232 0511 1 0592 0590 0490 0632 0543 0603 0619 05773 0621 0592 1 0510 0611 0640 0599 0710 0566 05824 0420 0590 0510 1 0701 0653 0589 sdot sdot sdot 0612 0629 05855 0462 0490 0611 0701 1 0599 0603 0489 0581 06206 0581 0632 0640 0653 0599 1 0576 0499 0545 06297 0617 0543 0599 0589 0603 0576 1 0710 0627 0634

0590 0611 0589

0429 0570 0630

0559 0628 054918 0581 0603 0710 0612 0489 0499 0710 0590 0429 0559 1 0345 062619 0470 0619 0566 0629 0581 0545 0627 0611 0570 0628 0345 1 055620 0623 0577 0582 0585 0620 0629 0634 0589 0630 0549 0626 0556 1



5 Conclusions






Acknowledgment


References




























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






1 1 0511 0621 0420 0462 0581 0617 0581 0470 06232 0511 1 0592 0590 0490 0632 0543 0603 0619 05773 0621 0592 1 0510 0611 0640 0599 0710 0566 05824 0420 0590 0510 1 0701 0653 0589 sdot sdot sdot 0612 0629 05855 0462 0490 0611 0701 1 0599 0603 0489 0581 06206 0581 0632 0640 0653 0599 1 0576 0499 0545 06297 0617 0543 0599 0589 0603 0576 1 0710 0627 0634

0590 0611 0589

0429 0570 0630

0559 0628 054918 0581 0603 0710 0612 0489 0499 0710 0590 0429 0559 1 0345 062619 0470 0619 0566 0629 0581 0545 0627 0611 0570 0628 0345 1 055620 0623 0577 0582 0585 0620 0629 0634 0589 0630 0549 0626 0556 1



5 Conclusions






Acknowledgment


References




























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





















Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



Research Article Gait Signal Analysis with Similarity...

Documents

Transcript of Research Article Gait Signal Analysis with Similarity...