Table Of ContentSpringerBriefs in Computer Science
Guangtao Xue · Yi-Chao Chen · Feng Lyu · Minglu Li
Robust Network
Compressive Sensing
SpringerBriefs in Computer Science
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Guangtao Xue (cid:129) Yi-Chao Chen (cid:129) Feng Lyu (cid:129)
Minglu Li
Robust Network
Compressive Sensing
GuangtaoXue Yi-ChaoChen
Shanghai,China Shanghai,China
FengLyu MingluLi
Hunan,China Jinhua,China
ISSN2191-5768 ISSN2191-5776 (electronic)
SpringerBriefsinComputerScience
ISBN978-3-031-16828-4 ISBN978-3-031-16829-1 (eBook)
https://doi.org/10.1007/978-3-031-16829-1
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Preface
The networks are constantly generating a wealth of rich and diverse information.
This information creates exciting opportunities for network analysis and provides
insight into the complex interactions between network entities. However, network
analysisoftenfacestheproblemsof(1)under-constrained,wherethereistoolittle
data due to feasibility and cost issues in collecting data, or (2) over-constrained,
where there is too much data, so the analysis becomes unscalable. Compressive
sensing is an effective technique to solve both problems. It utilizes the underlying
data structure for analysis. Specifically, to solve the under-constrained problem,
compressive sensing technologies can be applied to reconstruct the missing ele-
mentsorpredictthefuturedata;tosolvetheover-constraintproblem,compressive
sensingtechnologiescanbeappliedtoidentifysignificantelements.
To well support compressive sensing in network data analysis, a robust and
generalframeworkisneededtosupportdiverseapplications,yetthisischallenging
for real-world data where noise, anomalies, and lack of synchronization are
common. First, the number of unknowns for network analysis can be much larger
thanthenumberofmeasurementswehave.Forexample,trafficengineeringrequires
knowing the complete traffic matrix between all source and destination pairs in
order to properly configure traffic and avoid congestion. However, measuring the
flow between all source and destination pairs is very expensive or even infeasible.
Reconstructingdatafromasmallnumberofmeasurementsisanunder-constrained
problem.Inaddition,real-worlddataarecomplexandheterogeneousandoftenvio-
latethelow-levelassumptionsrequiredbyexistingcompressivesensingtechniques.
Such violations significantly reduce the applicability and effectiveness of existing
compressive sensing methods. Third, synchronization of network data reduces the
data ranks and increases spatial locality. However, periodic time series exhibit
not only misalignment but also different frequencies, which makes it difficult to
synchronizedatainthetimeandfrequencydomains.
In this monograph, we investigate compressive sensing techniques to provide a
robust and general framework for network data analytics. Our goal is to build a
compressivesensingframeworkformissingdatainterpolation,anomalydetection,
data segmentation, and activity recognition, and to demonstrate its benefits. In
v
vi Preface
Chap.1,weintroducecompressivesensing,includingitsdefinition,limitation,and
howitsupportsdifferentnetworkanalysisapplications.InChap.2,todemonstrate
the feasibility of compressive sensing in network analytics, we apply it to detect
anomaliesinthecustomercarecalldatasetfromaTier1ISPintheUnitedStates.
A regression-based model is applied to find the relationship between calls and
events. We show that compressive sensing is effective in identifying important
factors and can leverage the low-rank structure and temporal stability to improve
the detection accuracy. In Chap.3, we show that there are several challenges in
applyingcompressivesensingtoreal-worlddata.Understandingthereasonsbehind
the challenges is important for designing methods and mitigating their impact.
Therefore, we analyze a wide range of real-world traces, and our analysis shows
that there are different factors that contribute to the violation of the low-rank
property in real data. In particular, we find that (1) noise, errors, and anomalies,
and (2) asynchrony in the time and frequency domains lead to network-induced
ambiguity and can easily cause low-rank matrices to become higher-ranked. To
addresstheproblemofnoise,errors,andanomalies,inChap.4,weproposearobust
compressivesensingtechnique.Itexplicitlyaccountsforanomaliesbydecomposing
real-worlddatarepresentedinmatrixformintoalow-rankmatrix,asparseanomaly
matrix,anerrorterm,andasmallnoisematrix.InChap.5,toaddresstheproblemof
lackofsynchronization,weproposeadata-drivensynchronizationalgorithm.Itcan
eliminate misalignment while taking into account the heterogeneity of real-world
data in both time and frequency domains. The data-driven synchronization can be
appliedtoanycompressivesensingtechniqueandisgeneraltoanyreal-worlddata.
We show that the combination of the two techniques can reduce the ranks of real-
worlddata,improvetheeffectivenessofcompressivesensing,andhaveawiderange
ofapplications.
Shanghai,China GuangtaoXue
Shanghai,China Yi-ChaoChen
Hunan,China FengLyu
Zhejiang,China MingluLi
Contents
1 Introduction ................................................................... 1
1.1 ApplyCompressiveSensingtoReal-WorldData...................... 2
1.2 UnderstandtheLimitation .............................................. 3
1.3 ImproveCompressiveSensingforReal-WorldData .................. 3
1.4 AimoftheMonograph.................................................. 4
2 EventDetectionSystem ...................................................... 7
2.1 ProblemFormulation.................................................... 7
2.2 OurApproach............................................................ 12
2.2.1 ProblemFormulation ........................................... 12
2.2.2 OurRegression.................................................. 13
2.2.3 ReducingCategories............................................ 14
2.2.4 CombiningMultipleClassifiers ................................ 17
2.3 Evaluation................................................................ 18
2.4 ExternalData:SocialMedia............................................ 21
2.5 Conclusion............................................................... 23
References...................................................................... 23
3 LimitationofCompressiveSensing......................................... 25
3.1 Datasets.................................................................. 25
3.2 Analysis.................................................................. 28
3.2.1 AnomaliesIncreaseRanks...................................... 28
3.2.2 LackofSynchronizationIncreasesRanks ..................... 31
3.2.3 TemporalStabilityVariesAcrossTraces....................... 32
3.3 Conclusion............................................................... 33
References...................................................................... 33
4 RobustCompressiveSensing ................................................ 35
4.1 LENSDecomposition................................................... 35
4.1.1 LENSDecompositionFramework ............................. 35
4.1.2 OptimizationAlgorithm ........................................ 39
4.1.3 SettingParameters .............................................. 41
vii
viii Contents
4.2 Evaluation................................................................ 43
4.2.1 EvaluationMethodology........................................ 43
4.2.2 PerformanceResults ............................................ 45
4.3 Conclusion............................................................... 55
References...................................................................... 59
5 Data-DrivenSynchronization................................................ 61
5.1 Motivation ............................................................... 61
5.2 Data-DrivenSynchronization........................................... 61
5.3 Applications ............................................................. 65
5.3.1 Interpolation..................................................... 65
5.3.2 Segmentation.................................................... 67
5.3.3 ActivityRecognition............................................ 69
5.4 Evaluation................................................................ 70
5.4.1 EvaluationofSynchronization ................................. 70
5.4.2 EvaluationofInterpolationAccuracy.......................... 73
5.4.3 EvaluationofSegmentation .................................... 75
5.4.4 EvaluationofActivityRecognition ............................ 82
5.4.5 SummaryofEvaluationResults................................ 82
5.5 ExistingSychronizationApproaches................................... 83
5.6 Conclusion............................................................... 83
References...................................................................... 83
6 ConclusionandFutureResearchDirection................................ 85
A AlternatingDirectionMethod............................................... 87
A.1 Algorithm................................................................ 87
Acronyms
ADL Activitiesfordailyliving
ADM Alternatingdirectionmethod
AP Accesspoint
ColRandLoss Droprandomcolumns
CSI Channelstateinformation
DDoS Distributeddenialofservice
ETT Expectedtransmissiontime
EWMA Exponentialweightedmovingaverage
FLP Florida/PuertoRicoarea
IVR Interactivevoiceresponse
KNN K-nearestneighbors
LENS Thealgorithmtodecomposeamatrixintoalow-rankmatrix,a
sparseanomalymatrix,anerrormatrix,andadensebutsmall
noisematrix
MRC Maximumratiocombining
NCCO Nationalcallcenteroperations
NMAE Normalizedmeanabsoluteerror
PCA Principalcomponentanalysis
PureRandLoss Elementsinamatrixaredroppedindependentlywitharandom
lossrate
RowRandLoss Droprandomrows
RSSI Receivedsignalstrengthindicator
RT Retweets
SRMF Sparsityregularizedmatrixfactorization
STFT Short-timeFouriertransform
SVD Singularvaluedecomposition
TF-IDF Termfrequency-inversedocumentfrequency
xxElemRandLoss xx%ofrowsinamatrixareselectedandtheelementsinthese
selectedrowsaredroppedwithaprobability
ix
