specialobjectrecognitionbasedonsparserepresentationin...

Research ArticleSpecial Object Recognition Based on Sparse Representation inMultisource Data Fusion Samples

Changjun Zha 12

1College of Advanced Manufacturing Engineering Hefei University Hefei 230601 China2Key Laboratory of Intelligent Computing amp Signal Processing Ministry of Education Anhui University Hefei 230039 China

Correspondence should be addressed to Changjun Zha 11586292qqcom

Received 16 December 2019 Accepted 15 May 2020 Published 28 May 2020

Academic Editor Sebastian Anita

Copyright copy 2020 Changjun Zha is 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

Wireless sensor networks (WSNs) suffer from limited power and large amounts of redundant data is paper describes amultisource data fusion method for WSNs that can be combined with the characteristics of a profile detection system Firstprincipal component analysis is used to extract sample features and eliminate redundant information Feature samples fromdifferent sources are then fused using a method of superposition to reduce the amount of data transmitted by the network Finallya mathematical model is proposed On the basis of this model a novel method of special object recognition based on sparserepresentation is developed for multisource data fusion samples according to the distribution of nonzero coefficients under anovercomplete dictionary e experimental results from numerical simulations show that the proposed recognition method caneffectively identify special objects in the fusion samples and the overall performance is better than that of traditional methods

1 Introduction

In general objects moving across borders or uninhabitedregions could be either humans or animals As there aresignificant differences between human and animal profiles itis feasible to use certain features to recognize and monitorspecial objects (humans) [1ndash3] However previous studiesare largely concerned with the acquisition of object profilesamples and recognition using traditional methods such ask-nearest neighbors (KNN) and support vector machines(SVMs) [4ndash6] ere has been no detailed discussion on thefusion of data or reducing the amount of data transmittedover the network In this paper we discuss these issues indetail based on previous work [7]

e main contribution of this paper is to construct awireless monitoring network with a profile detection systemas a network node To reduce the amount of data transmittedin the network as much as possible the network uses a sinknode to fuse the feature samples sent by each network nodethe fused data are then sent to the terminal for identificationallowing the determination of whether a special object(human) is passing through the monitoring area

is paper describes the fusion of multisource featuresamples through a superposition approach meaning thattraditional recognition methods such as KNN SVM andsparse representation classification (SRC) [8ndash10] cannotaccurately identify whether there is one or more class objectsin the fused sample To solve this problem we propose anovel object recognition method based on sparse repre-sentation Different from classical SRC the method de-scribed in this paper uses the distribution of nonzerocoefficients in the sparse representation to identify specialobjects in the fusion sample e experimental results verifythe effectiveness of this method

2 Related Work

In our previous work we designed the profile detectionsystem shown in Figure 1 In the system the signal sensingunit is composed of photoelectric sensors installed at evenintervals on a vertical fixed bracket with a length of 2mWhen a moving object passes through the sensorrsquos field ofview the profile feature information of the object is capturedby the sensing unit [1 2 7]

HindawiMathematical Problems in EngineeringVolume 2020 Article ID 4138746 8 pageshttpsdoiorg10115520204138746

is paper mainly studies the profile classification ofthree kinds of moving objects humans squatting humansand animals (namely dogs) In practice when objects enterthe sensorrsquos field of view their position speed attitude andother conditions are different To obtain a better recognitioneffect samples of various angles speeds and attitudes en-tering the field of view are collected for training as shown inFigure 2

3 Sample Feature Extraction and Data Fusion

31 Feature Extraction According to Zha et al [7] theprofile detection system of the network monitoring node inthe wireless monitoring network expresses an object profilesample P as an S times L matrix e number of columns of eachsample matrix is different and there is a large amount ofredundant information Sending the sample matrix signaldirectly through the network wastes network resources andis inconvenient for data processing because of the differentdimensions of the matrix formed by P To solve theseproblems we use principal component analysis (PCA)[11ndash13] to pretreat the sample data e specific process is asfollows

(1) Input sample matrix P isin RStimesL(2) Calculate the covariance

CXX E PTminus E PT

1113872 11138731113872 1113873(P minus E(P))1113960 1113961 (1)

(3) Determine eigenvalues and eigenvectors

CXX UΛUT (2)

namely the eigenvaluesΛ λ1 λ2 middot middot middot λL1113858 1113859 and thecorresponding eigenvectors U μ1 μ2 μL1113858 1113859

(4) Construct transformation matrix select the eigen-vectors corresponding to the k(kleL) largest ei-genvalues to construct the transformation matrixnamely

Uk μ1 μ2 μk1113858 1113859 ieUk isin RLtimesk

(3)

(5) Dimension reduction

Pand

UTkP

T (4)

(6) Output matrix vectorization

y vec(PΛ

) isin Rc(c k times S) (5)

After pretreatment the vector y is taken as the featuresample of the object and sent to the sink node for datafusion

32 Multisource Data Fusion Model Suppose that thewireless sensor network (WSN) contains N networkmonitoring nodes and that the jth network node acquires thefeature sample of the object as yj isin Rc(1le jleN) e sinknode receives the feature sample of each network node andperforms data fusion e network topology is shown inFigure 3 To reduce the computational complexity of the datafusion process we adopt the method of superposition toachieve fusion us the fusion sample can be expressed asfollows

r y1 + y2 + middot middot middot + yN 1113944N

j1yj (6)

Considering the signal transmission power channelfading noise interference and other factors associated witheach network node equation (6) can be rewritten as follows

r ρ1

radicmiddot α1 middot y1 +

ρ2

radicmiddot α2 middot y2 + middot middot middot +

ρN

radicmiddot αN middot yN( 1113857 + n

1113944N

j1

ρj

1113968 αjyj + n

(7)

where r isin Rc and the parameters ρj and αj(1le jleN) are thesignal transmission power and channel link gain of the jthnetwork node respectively and n is the additive whiteGaussian noise When the dimension of the feature sampleof each network node is large and the amount of data to betransmitted needs to be further reduced the feature samplecan be projected into a low-dimensional space through theprojection matrix Ψ isin Rdtimesc(dlt c) e signal model isshown in Figure 4 e mathematical model of the fusionsamples can be written as follows

rand

1113944

N

j1

ρj

1113968αjΨyj + n 1113944

N

j1

ρj

1113968αjyand

j + n (8)

Sensors

Figure 1 Profile detection system

2 Mathematical Problems in Engineering

where yand

j Ψyj isin Rd

4 Sparsity Analysis and Construction ofOvercomplete Dictionary

To analyze the sparsity of the fusion samples it is assumedthat r is composed of three different feature samples (ie y1y2 and y3) namely

r y1 + y2 + y3 (9)

Furthermore suppose that xi(1le ile 3) are sparse rep-resentation coefficients of eigenvector yi under the over-complete dictionary Ai en

y1 A1x1

y2 A2x2

y3 A3x3

⎧⎪⎪⎨

⎪⎪⎩(10)

Combined with equation (10) equation (9) can be re-written as follows

Terminal

Intra cluster linkFusion samples linkNetwork node

Sink node

Monitoringarea

Figure 3 Network topology

Pretreatment Projectionmatrix

Datafusion

Reco

gniti

on

Pretreatment

Output

P1

PN Projectionmatrix

y1

yN

y1

yN

Figure 4 Multisource data fusion model

(a) (b) (c) (d) (e) (f )

Figure 2 Profile images of different types of object (a) one person (b) backpacker (c) dog (d) jumping dog (e) squatting human (f ) twopeople

Mathematical Problems in Engineering 3

r 11139443

i1yi 1113944

3

i1Aixi A1A2A31113858 1113859

x1x2x3

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Aaxa

(11)

where Aa [A1A2A3] and xa [xT1 xT

2 xT3 ]T It can be

seen from equation (11) that the fusion sample r can besparsely represented under the dictionary Aa and the sparsecoefficients can be obtained by solving the followingl1-minimization problem [14ndash16]

xanda argminxa

xa

1

st r minus Aaxa

22 le ε

(12)

where the parameter ε is the error tolerance Similarly whenthe fusion sample r is composed of k feature samples it canbe sparsely represented and the overcomplete dictionary isAa [A1A2 Ak]

To represent the fusion sample sparsely we use thetraining samples to construct an overcomplete dictionarydirectly [7 17ndash19] Assuming that there are T classes oftraining samples the number of training samples in eachclass is N1 N2 NT and the ith (1le ileNj) trainingsample in the jth (1le jleT) class is expressed as Pji isin RStimesLi and the specific process of constructing the dictionary is asfollows

(1) Input training samples Pji isin RStimesLi (2) Pretreatment of training samples

All training samples Pji isin RStimesLi are pretreated andthe feature vector φji isin Rc(c S times k) of the pre-treated sample is used as a dictionary atom

(3) Output construct overcomplete dictionaryAa [φ11φ12 φTNT

] isin Rctimesn(clt n) wheren N1 + N2 + middot middot middot + NT

rough the above process we can obtain an over-complete dictionary

5 Special Object Recognition Method

According to the above sparsity analysis when there isone class of feature samples in the fusion sample themain nonzero coefficients in the sparse coefficient vectorobtained by l1-minimization are distributed on thecorresponding class of atoms whereas the coefficients forother classes of atoms are zero or very small If the fusionsample contains multiple classes the main nonzerocoefficients in the sparse coefficient vector are distributedon these classes Based on this feature we propose aspecial object recognition method for multisource datafusion samples e method is illustrated in Figure 5 andthe specific steps are as follows

(1) Input dictionaryAa [A1A2 AT] isin Rctimesn for T

classes and fusion sample r isin Rc(2) Sparse representation

xanda argminxa

xa

1

st r minus Aaxa

22 le ε

(13)

where ε is the error tolerance(3) Calculate coefficient l1-norm of each class

sj δj xand

a1113874 1113875

1 for j 1 T (14)

where δj is the characteristic function that selects thecoefficients associated with the jth class

(4) Multiclass discriminant rule

identity(r) jsj

xand1

ge τ j 1 T

1113868111386811138681113868111386811138681113868111386811138681113868

⎧⎨

⎩

⎫⎬

⎭ (15)

where τ isin [0 1](5) Output based on the results of step 4 check whether

the special object is included

6 Experimental Simulation andResults Analysis

Experiments are conducted based on the profile detectionsystem which uses 16 E3F-R2NK photoelectric sensors toconstruct a signal sensing unit e effective distance of thesensors is 2m In the actual environment the profile de-tection system mainly collects three kinds of object profilesamples for training and testing humans squatting humansand animals (dogs) e numbers of training samples andtest samples are listed in Table 1

It is assumed that each network node can detect at mostone object in a certain period of time In the followingexperiments the fusion samples are composed of humansand dogs and we consider the humans as the special objectsUnder different experimental conditions the proposedmethod can judge whether there is a special object (human)in the fusion sample and considers this a correct recognition

For the convenience of analysis and comparison it isassumed that the signal transmission power of each networknode is the same and the channel link gain remains constantat 1 e performance of the proposed method is comparedwith that of the traditional nearest-neighbor classifier (NN)[20] and the KNN SVM and SRC methods

e experiments are conducted on a Windows 7 PCrunning MATLAB (R2014a) with a 30GHz CPU and 8GBmemory

61 Experiment 1 Verifying the Sparsity of Fusion SamplesIt is assumed that within a certain period of time twonetwork nodes in the monitoring area detect objects passingby among which one node is a single person and one node isa dog After each node extracts the sample feature infor-mation the sink node performs data fusion e sparsity ofthe fused feature sample is analyzed and the distribution ofsparse representation coefficients is shown in Figure 6


As can be seen from Figure 6 the coefficients of thefusion samples are still sparse and distributed on the atomicterms of the two classes of human and animal e fusionsamples do not contain images that include squattinghumans so the coefficients for the linear representation of asquatting human are close to zero

ese experimental results show that the following (1)multisource data fusion samples can be sparsely representedunder the overcomplete dictionary (2) according to thedistribution of the main nonzero coefficients in the coeffi-cient vector the combination of different classes in thefusion sample can be distinguished and the special object(human) can be identified

62 Experiment 2 Relationship between Number of Objectsand Recognition Rate for Fixed Signal-to-Noise Ratio(SNR)

621 Relationship between the Number of Animals andRecognition Rate Assuming that there is one human sce-narios including 1ndash5 animals are considered (see Table 2)e experimental simulation results are shown in Figure 7

As can be seen from Figure 7 the correct recognitionrates achieved by the traditional NN KNN SVM and SRCare relatively low As the number of animals increases the

traditional methods struggle to recognize the special objectcorrectly e proposed method outperforms these tradi-tional methods and exhibits better anti-interference ability

622 Relationship between Number of Humans and Rec-ognition Rate For the case of only one animal experimentswith 1ndash5 humans are considered (see Table 3) e exper-imental simulation results are shown in Figure 8

From Figure 8 we can see that an increase in the numberof humans enhances the recognition rate of variousmethods However the recognition rate of the methodproposed in this paper is consistently 100 which is ob-viously superior to that of traditional methods

63 Experiment 3 Verification of Relationship between SNRandRecognitionRate For WSNs reducing the transmissionpower of the signal can effectively extend the networklifetime In this experiment the number of humans andanimals is known and we analyze the impact of differentSNRs on the recognition performance e experimentalcondition settings are listed in Table 4 and the simulationresults are shown in Figure 9

It can be seen from Figure 9 that changes in the SNR havelittle effect on the recognition rates of the various methods

Sparserepresentation

Fusion samples Multiclassdiscriminant

Special objectrecognition

Output

ConstructdictionaryPretreatmentTraining

samples

Calculate normof each class

Figure 5 Flowchart of special object recognition method for multisource fusion samples

Table 1 Number of training and test samples

Training sample Test sampleHuman 50 50Squatting human 50 50Animal (dog) 50 50

+ =

Coe

ffici

ent

ndash02

0

02

04

06

50 100 1500Atomic terms

Figure 6 Coefficient distribution of fusion samples


e experimental results show that the proposed methodoutperforms the traditional methods and we can extend theservice life of the network by reducing the transmissionpower of the network nodes without affecting the recog-nition rate

64 Experiment 4 Verification of Relationship betweenNumber of Animals and False Alarm Rate In border regionsor special monitoring areas there may be long periods

Table 2 Parameter settings for experiment 2(1)

SNR (dB) 15Number of human 1Number of animals 1 2 3 4 5

Number of humans 1

SVMKNNNN

SRCImproved method

2 3 4 51Number of animals

0

20

40

60

80

100

Reco

gniti

on ra

te (

)

Figure 7 Relationship between number of animals and recogni-tion rate


SNR (dB) 15Number of human 1 2 3 4 5Number of animals 1

Number of animals 1

SVMKNNNN

SRCImproved method

2 3 4 51Number of humans

0

20

40

60

80

100

Reco

gniti

on ra

te (

)

Figure 8 Relationship between number of people and recognitionrate

Table 4 Parameter settings for experiment 3

SNR (dB) 5 10 15 20 25Number of human 1Number of animals 1 or 3

SVMKNNNN

SRCImproved method

10 15 20 255SNR (dB)

0

20

40

60

80

100

Reco

gniti

on ra

te (

)(a)

SVMKNNNN

SRCImproved method

0

20

40

60

80

100

Reco

gniti

on ra

te (

)

10 15 20 255SNR (dB)

(b)

Figure 9 Relationship of SNR and recognition rate (a) Number ofhumans 1 number of animals 1 (b) Number of humans 1number of animals 3


without humans passing through during which only ani-mals will be detected erefore it is very important tocorrectly judge that no humans are present thus reducingthe false alarm rate of the system e experimental con-ditions are listed in Table 5 and the simulation results areshown in Figure 10

As can be seen from Figure 10 when the SNR is 15 dB or20 dB the false alarm rate of the proposed method is slightlyhigher than that of traditional methods However as thenumber of animals increases the animal class information inthe fusion sample increases which reduces the possibility offalse alarmse experimental results show that an increase inthe number of animals will not increase the false alarm ratebut will actually help to reduce the false alarm rate

In summary the traditional recognition methods mainlyfocus on the test samples of a single classWhen the samples arecomposed of multiple classes the other classes in the fusionsample produce interference that affects their correct recog-nition performance e proposed method is based on sparserepresentation theory When the samples are composed ofmultiple classes we can effectively separate the fusion samplesin the sparse domain According to the coefficient distributionwe can then judge the class combination in the fusion samplee experimental results verify the validity of this method frommany aspects of recognition tasks

7 Conclusions

According to the characteristics of the profile detection systemcombined with WSN and sparse representation theory wehave proposed amethod of multisource data processing and anassociated mathematical model Based on this model a novel

special object recognition method has been developedCompared with traditional methods the method described inthis paper achieves better performance in many aspects ofrecognition Moreover in practical applications the systemparameters (such as the transmission power of the networknodes) can be adjusted to satisfy the actual requirements

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

is work was supported by the Key Projects of NaturalScience Research in Universities in Anhui (no KJ2017A531)the Opening Foundation of Key Laboratory of IntelligentComputing amp Signal Processing (Anhui University) Min-istry of Education and Key Discipline Construction Projectof Hefei University (no 2018xk03) We thank Stuart Jen-kinson PhD from Liwen Bianji Edanz Group China forediting the English text of a draft of this manuscript

References

[1] J Russomanno David C Srikan E Kenny et al ldquoTesting andevaluation of profiling sensors for perimeter securityrdquo ITEAvol 31 no 1 pp 121ndash130 2010


SNR (dB) 15 or 20Number of human 0Number of animals 1 2 3 4 5

SVMKNNNN

SRCImproved method

0

20

40

60

80

100

False

alar

m ra

te (

)


(a)

SVMKNNNN

SRCImproved method

0

20

40

60

80

100

False

alar

m ra

te (

)


(b)

Figure 10 Relationship between number of animals and recognition rate (a) SNR 15 dB (a) SNR 20 dB


[2] B Sartain Ronald A Keith T Alexander et al ldquoLong-waveinfrared profile feature extractor (PFx) sensorrdquo in Proceedingsof SPIE 2009 Unattended Ground Sea and Air SensorTechnologies and Applications XI vol 7333 pp 733311ndash733317 Orlando FL USA May 2009

[3] D J Russomanno S Chari E L Jacobs and C HalfordldquoNear-IR sparse detector sensor for intelligent electronic fenceapplicationsrdquo IEEE Sensors Journal vol 10 no 6pp 1106-1107 2010

[4] C Srikant H Carl E Jacobs et al ldquoClassification of humansand animals using an infrared profiling sensorrdquo in Proceed-ings of SPIE 2009 Unattended Ground Sea and Air SensorTechnologies and Applications XI Orlando FL USA May2009

[5] D Russomanno S Chari and C Halford ldquoSparse detectorimaging sensor with two-class silhouette classificationrdquoSensors vol 8 no 12 pp 7996ndash8015 2008

[6] R K Reynolds S Chari and D J Russomanno ldquoEmbeddedreal-time classifier for profiling sensors and custom detectorconfigurationrdquo in Proceedings of the SPIE GroundAirMultisensor Interoperability Integration and Networking forPersistent ISR II Orlando FL USA May 2011

[7] C-J Zha N Sun and C Zhang ldquoSpecial object recognitionbased on sparse representationrdquo Journal of Jilin University(Engineering and Technology Edition) vol 43 no 1pp 256ndash260 2013

[8] W Wei and X Lihong ldquoA modified sparse representationmethod for facial expression recognitionrdquo ComputationalIntelligence and Neuroscience vol 2016 Article ID 568760212 pages 2016

[9] E R Oliveros G Coello P Marrero-Fernandez et alldquoEvaluation of K-SVD method in Facial expression recog-nition based on sparse representation problemsrdquo Interna-tional Conference on Articulated Motion amp DeformableObjects Springer Berlin Germany 2016

[10] J Wright Y Yang Allen G Arvind et al ldquoRobust facerecognition via sparse representationrdquo IEEE TransactionsPAMI vol 31 no 2 pp 1ndash18 2009

[11] D Granato J S Santos B L Ferreira G B Escher andR M Maggio ldquoUse of principal component analysis (PCA)and hierarchical cluster analysis (HCA) for multivariate as-sociation between bioactive compounds and functionalproperties in foods a critical perspectiverdquo Trends in FoodScience amp Technology vol 72 pp 83ndash90 2018

[12] D Russomanno M Yeasin E Jacobs et al ldquoSparse detectorsensor profiling experiments for broad-scale classificationrdquoin Proceedings of SPIE 2008 Unattended Ground Sea and AirSensor Technologies and Applications XI Orlando FL USAMay 2008

[13] J Wang C Luo H Huang H Zhao and S WangldquoTransferring pre-trained deep CNNs for remote sceneclassification with general features learned from linear PCAnetworkrdquo Remote Sensing vol 9 no 3 p 225 2017

[14] H Gao H Zhang Z Li et al ldquoOptimality analysis on partiall1-minimization recoveryrdquo Journal of Global Optimizationvol 70 no 1 pp 1ndash12 2017

[15] S U H Qazi L X Shi L M Tao and S Q Yang ldquoA l1-minimization based approach for hyperspectral data classi-ficationrdquo Key Engineering Materials vol 500 pp 675ndash6812012

[16] D L Donoho M Elad and V N Temlyakov ldquoStable recoveryof sparse overcomplete representations in the presence ofnoiserdquo IEEE Transactions on Information Geory vol 52no 1 pp 6ndash18 2006

[17] R Rubinstein A M Bruckstein and M Elad ldquoDictionariesfor sparse representation modelingrdquo Proceedings of the IEEEvol 98 no 6 pp 1045ndash1057 2010

[18] M R Sheri and D Chatterjee ldquoOptimal dictionary for leastsquares representationrdquo Journal of Machine Learning Re-search vol 18 pp 1ndash28 2017

[19] D Crystal ldquoA dictionary of linguistics and phoneticsrdquoModern Language Journal vol 76 no 3 pp 310-311 2015

[20] J H FriedmanGe Elements of Statistical Learning SpringerBerlin Germany 2001


is paper mainly studies the profile classification ofthree kinds of moving objects humans squatting humansand animals (namely dogs) In practice when objects enterthe sensorrsquos field of view their position speed attitude andother conditions are different To obtain a better recognitioneffect samples of various angles speeds and attitudes en-tering the field of view are collected for training as shown inFigure 2

3 Sample Feature Extraction and Data Fusion

31 Feature Extraction According to Zha et al [7] theprofile detection system of the network monitoring node inthe wireless monitoring network expresses an object profilesample P as an S times L matrix e number of columns of eachsample matrix is different and there is a large amount ofredundant information Sending the sample matrix signaldirectly through the network wastes network resources andis inconvenient for data processing because of the differentdimensions of the matrix formed by P To solve theseproblems we use principal component analysis (PCA)[11ndash13] to pretreat the sample data e specific process is asfollows

(1) Input sample matrix P isin RStimesL(2) Calculate the covariance

CXX E PTminus E PT

1113872 11138731113872 1113873(P minus E(P))1113960 1113961 (1)

(3) Determine eigenvalues and eigenvectors

CXX UΛUT (2)

namely the eigenvaluesΛ λ1 λ2 middot middot middot λL1113858 1113859 and thecorresponding eigenvectors U μ1 μ2 μL1113858 1113859

(4) Construct transformation matrix select the eigen-vectors corresponding to the k(kleL) largest ei-genvalues to construct the transformation matrixnamely

Uk μ1 μ2 μk1113858 1113859 ieUk isin RLtimesk

(3)

(5) Dimension reduction

Pand

UTkP

T (4)

(6) Output matrix vectorization

y vec(PΛ

) isin Rc(c k times S) (5)

After pretreatment the vector y is taken as the featuresample of the object and sent to the sink node for datafusion

32 Multisource Data Fusion Model Suppose that thewireless sensor network (WSN) contains N networkmonitoring nodes and that the jth network node acquires thefeature sample of the object as yj isin Rc(1le jleN) e sinknode receives the feature sample of each network node andperforms data fusion e network topology is shown inFigure 3 To reduce the computational complexity of the datafusion process we adopt the method of superposition toachieve fusion us the fusion sample can be expressed asfollows

r y1 + y2 + middot middot middot + yN 1113944N

j1yj (6)

Considering the signal transmission power channelfading noise interference and other factors associated witheach network node equation (6) can be rewritten as follows

r ρ1

radicmiddot α1 middot y1 +

ρ2

radicmiddot α2 middot y2 + middot middot middot +

ρN

radicmiddot αN middot yN( 1113857 + n

1113944N

j1

ρj

1113968 αjyj + n

(7)

where r isin Rc and the parameters ρj and αj(1le jleN) are thesignal transmission power and channel link gain of the jthnetwork node respectively and n is the additive whiteGaussian noise When the dimension of the feature sampleof each network node is large and the amount of data to betransmitted needs to be further reduced the feature samplecan be projected into a low-dimensional space through theprojection matrix Ψ isin Rdtimesc(dlt c) e signal model isshown in Figure 4 e mathematical model of the fusionsamples can be written as follows

rand

1113944

N

j1

ρj

1113968αjΨyj + n 1113944

N

j1

ρj

1113968αjyand

j + n (8)

Sensors

Figure 1 Profile detection system


where yand

j Ψyj isin Rd



r y1 + y2 + y3 (9)


y1 A1x1

y2 A2x2

y3 A3x3

⎧⎪⎪⎨

⎪⎪⎩(10)


Terminal


Sink node

Monitoringarea



Datafusion

Reco

gniti

on

Pretreatment

Output

P1

PN Projectionmatrix

y1

yN

y1

yN


(a) (b) (c) (d) (e) (f )



r 11139443

i1yi 1113944

3

i1Aixi A1A2A31113858 1113859

x1x2x3

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Aaxa

(11)


2 xT3 ]T It can be


xanda argminxa

xa

1

st r minus Aaxa

22 le ε

(12)












xanda argminxa

xa

1

st r minus Aaxa

22 le ε

(13)


sj δj xand

a1113874 1113875

1 for j 1 T (14)



identity(r) jsj

xand1

ge τ j 1 T

1113868111386811138681113868111386811138681113868111386811138681113868

⎧⎨

⎩

⎫⎬

⎭ (15)























Output


samples





+ =

Coe

ffici

ent

ndash02

0

02

04

06








Number of humans 1

SVMKNNNN

SRCImproved method


0

20

40

60

80

100

Reco

gniti

on ra

te (

)




Number of animals 1

SVMKNNNN

SRCImproved method


0

20

40

60

80

100

Reco

gniti

on ra

te (

)




SVMKNNNN

SRCImproved method

10 15 20 255SNR (dB)

0

20

40

60

80

100

Reco

gniti

on ra

te (

)(a)

SVMKNNNN

SRCImproved method

0

20

40

60

80

100

Reco

gniti

on ra

te (

)

10 15 20 255SNR (dB)

(b)






7 Conclusions



Data Availability




Acknowledgments


References




SVMKNNNN

SRCImproved method

0

20

40

60

80

100

False

alar

m ra

te (

)


(a)

SVMKNNNN

SRCImproved method

0

20

40

60

80

100

False

alar

m ra

te (

)


(b)























where yand

j Ψyj isin Rd



r y1 + y2 + y3 (9)


y1 A1x1

y2 A2x2

y3 A3x3

⎧⎪⎪⎨

⎪⎪⎩(10)


Terminal


Sink node

Monitoringarea



Datafusion

Reco

gniti

on

Pretreatment

Output

P1

PN Projectionmatrix

y1

yN

y1

yN


(a) (b) (c) (d) (e) (f )



r 11139443

i1yi 1113944

3

i1Aixi A1A2A31113858 1113859

x1x2x3

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Aaxa

(11)


2 xT3 ]T It can be


xanda argminxa

xa

1

st r minus Aaxa

22 le ε

(12)












xanda argminxa

xa

1

st r minus Aaxa

22 le ε

(13)


sj δj xand

a1113874 1113875

1 for j 1 T (14)



identity(r) jsj

xand1

ge τ j 1 T

1113868111386811138681113868111386811138681113868111386811138681113868

⎧⎨

⎩

⎫⎬

⎭ (15)























Output


samples





+ =

Coe

ffici

ent

ndash02

0

02

04

06








Number of humans 1

SVMKNNNN

SRCImproved method


0

20

40

60

80

100

Reco

gniti

on ra

te (

)




Number of animals 1

SVMKNNNN

SRCImproved method


0

20

40

60

80

100

Reco

gniti

on ra

te (

)




SVMKNNNN

SRCImproved method

10 15 20 255SNR (dB)

0

20

40

60

80

100

Reco

gniti

on ra

te (

)(a)

SVMKNNNN

SRCImproved method

0

20

40

60

80

100

Reco

gniti

on ra

te (

)

10 15 20 255SNR (dB)

(b)






7 Conclusions



Data Availability




Acknowledgments


References




SVMKNNNN

SRCImproved method

0

20

40

60

80

100

False

alar

m ra

te (

)


(a)

SVMKNNNN

SRCImproved method

0

20

40

60

80

100

False

alar

m ra

te (

)


(b)























r 11139443

i1yi 1113944

3

i1Aixi A1A2A31113858 1113859

x1x2x3

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Aaxa

(11)


2 xT3 ]T It can be


xanda argminxa

xa

1

st r minus Aaxa

22 le ε

(12)












xanda argminxa

xa

1

st r minus Aaxa

22 le ε

(13)


sj δj xand

a1113874 1113875

1 for j 1 T (14)



identity(r) jsj

xand1

ge τ j 1 T

1113868111386811138681113868111386811138681113868111386811138681113868

⎧⎨

⎩

⎫⎬

⎭ (15)























Output


samples





+ =

Coe

ffici

ent

ndash02

0

02

04

06








Number of humans 1

SVMKNNNN

SRCImproved method


0

20

40

60

80

100

Reco

gniti

on ra

te (

)




Number of animals 1

SVMKNNNN

SRCImproved method


0

20

40

60

80

100

Reco

gniti

on ra

te (

)




SVMKNNNN

SRCImproved method

10 15 20 255SNR (dB)

0

20

40

60

80

100

Reco

gniti

on ra

te (

)(a)

SVMKNNNN

SRCImproved method

0

20

40

60

80

100

Reco

gniti

on ra

te (

)

10 15 20 255SNR (dB)

(b)






7 Conclusions



Data Availability




Acknowledgments


References




SVMKNNNN

SRCImproved method

0

20

40

60

80

100

False

alar

m ra

te (

)


(a)

SVMKNNNN

SRCImproved method

0

20

40

60

80

100

False

alar

m ra

te (

)


(b)




































Output


samples





+ =

Coe

ffici

ent

ndash02

0

02

04

06








Number of humans 1

SVMKNNNN

SRCImproved method


0

20

40

60

80

100

Reco

gniti

on ra

te (

)




Number of animals 1

SVMKNNNN

SRCImproved method


0

20

40

60

80

100

Reco

gniti

on ra

te (

)




SVMKNNNN

SRCImproved method

10 15 20 255SNR (dB)

0

20

40

60

80

100

Reco

gniti

on ra

te (

)(a)

SVMKNNNN

SRCImproved method

0

20

40

60

80

100

Reco

gniti

on ra

te (

)

10 15 20 255SNR (dB)

(b)






7 Conclusions



Data Availability




Acknowledgments


References




SVMKNNNN

SRCImproved method

0

20

40

60

80

100

False

alar

m ra

te (

)


(a)

SVMKNNNN

SRCImproved method

0

20

40

60

80

100

False

alar

m ra

te (

)


(b)



























Number of humans 1

SVMKNNNN

SRCImproved method


0

20

40

60

80

100

Reco

gniti

on ra

te (

)




Number of animals 1

SVMKNNNN

SRCImproved method


0

20

40

60

80

100

Reco

gniti

on ra

te (

)




SVMKNNNN

SRCImproved method

10 15 20 255SNR (dB)

0

20

40

60

80

100

Reco

gniti

on ra

te (

)(a)

SVMKNNNN

SRCImproved method

0

20

40

60

80

100

Reco

gniti

on ra

te (

)

10 15 20 255SNR (dB)

(b)






7 Conclusions



Data Availability




Acknowledgments


References




SVMKNNNN

SRCImproved method

0

20

40

60

80

100

False

alar

m ra

te (

)


(a)

SVMKNNNN

SRCImproved method

0

20

40

60

80

100

False

alar

m ra

te (

)


(b)


























7 Conclusions



Data Availability




Acknowledgments


References




SVMKNNNN

SRCImproved method

0

20

40

60

80

100

False

alar

m ra

te (

)


(a)

SVMKNNNN

SRCImproved method

0

20

40

60

80

100

False

alar

m ra

te (

)


(b)























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