DISTRIBUTED PROCESSING OVER ADAPTIVE NETWORKS. Cassio G. Lopes and Ali H. Sayed
|
|
- Kevin Barton
- 5 years ago
- Views:
Transcription
1 DISTRIBUTED PROCESSIG OVER ADAPTIVE ETWORKS Casso G Lopes and A H Sayed Department of Eectrca Engneerng Unversty of Caforna Los Angees, CA, 995 Ema: {casso, sayed@eeucaedu ABSTRACT Dstrbuted adaptve agorthms are proposed based on ncrementa and dffuson strateges Adaptaton rues that are sutabe for rng topooges and genera topooges are descrbed Both dstrbuted LMS and RLS mpementatons are consdered n order to endow a networ of nodes wth earnng abtes; thus resutng n a networ that s an adaptve entty n ts own rght ITRODUCTIO Dstrbuted and sensor networs are emergng as a formdabe technoogy for a varety of appcatons, rangng from precson agrcuture, to envronment surveance, to target ocazaton However, the advantages advocated by the use of dstrbuted and cooperatve processng [] demand adaptve processng capabtes at the dstrbuted nodes n order to be abe to cope wth tme varatons n the envronment and the networ In addton, the adaptve processors shoud enabe the networ to respond to such varatons n rea-tme and to adjust ts performance accordngy Inspred by ncrementa strateges [], we propose dstrbuted processng strateges over what we refer to as adaptve networs (eg, []) The proposed strateges requre the adaptve nodes to share nformaton ony ocay and to expot both spata and tempora nformaton n a cooperatve fashon Dfferent cooperaton poces w ead to dfferent dstrbuted agorthms Each node across an -node networ s assumed to have access to tme reazatons {d (), u,, of zero-mean random data {d, u, wth d () a scaar measurement and u, a regresson row vector; both at tme see Fgure The nodes shoud use the data to estmate some unnown common vector w o Rather than expect each node to functon ndependenty of the other nodes, the nodes w nstead coaborate wth each other n an adaptve manner n order to acheve three objectves: () mprove goba performance wth reduced communcaton; () aow the nodes to converge to the desred estmate wthout the need to share goba nformaton; () endow the networ wth earnng abtes Recenty the authors proposed a scheme [] that mpements a dstrbuted ncrementa gradent agorthm n whch an nta vector estmate s updated aong a coaboraton cyce over the networ Each oca fter updates the estmate receved from the prevous neghbor wth ts oca data and passes the estmate to the next node +, operatng over a coaboraton cyce - see Ths matera was based on wor supported n part by the atona Scence Foundaton under awards ECS-88 and ECS- The wor of Mr Lopes was aso supported by a feowshp from CAPES, Braz, under award 8/- Fg A dstrbuted networ wth nodes Fgure further ahead Ths approach requres mted communcatons and ncreases the networ autonomy [] The networ may aso earn at an enhanced pace as compared to a standard gradentdescent souton In ths paper, we propose a east-squares framewor that equps the nodes wth a RLS-type adaptaton rue, whe eepng the same cooperaton strategy, yedng to a dstrbuted and recursve eastsquares souton (drls) The resutng agorthm conveys an exact goba east-squares estmate, for the unnown vector w o, to every node n the networ Ths scheme further aows an aternatve drls mpementaton wth decreased communcaton requrements, savng energy compared wth ts exact counterpart It aso has the strng feature that n steady-state, both agorthms present smar performance n the mean-square error sense When more communcaton and energy resources are avaabe, the topoogy constrants mped by the aforementoned agorthms can be removed by resortng to a dffuson cooperatve scheme, where the adaptve processor at node updates ts estmate usng a avaabe estmates from the neghbors, as we as oca data and ts own past estmate see Fgure DISTRIBUTED ESTIMATIO We are nterested n estmatng an unnown vector w o from measurements coected at nodes n a networ (see Fg ) Each node has access to reazatons of zero-mean data {d, u, =,,, where d s a scaar and u s M We coect the
2 regresson and measurement data nto goba matrces: U = co{u, u,, u ( M) () d = co{d, d,, d ( ) () and pose the mnmum mean-square error estmaton probem: mn w J(w), where J(w) = E d Uw () The optma souton w o satsfes the norma equatons []: where R u = E U U = X = R du = R u w o () R u,, R du = E U d = X = R du, (5) Computng w o from () requres every node to have access to the goba statstca nformaton {R u, R du, thus dranng communcatons and computatona resources In [] we proposed a dstrbuted souton (ncrementa LMS) that aows cooperaton among nodes through mted oca communcatons, whe equppng the nodes wth adaptve mechansms to respond to tme-varatons n the underyng sgna statstcs ICREMETAL LMS ADAPTATIO In ths secton, we revew the dstrbuted ncrementa LMS agorthm [], whch s a startng pont for the ater deveopments The agorthm s obtaned as foows We start from the standard gradent-descent mpementaton w = w µ [ J(w )] () for sovng the norma equatons (), where µ > s a sutaby chosen step-sze parameter, w s an estmate for w o at teraton, and J( ) denotes the gradent vector of J(w) evauated at w For µ suffcenty sma we w have w w o as Ths teratve souton coud be apped at every node or centray at some centra node A dstrbuted verson can be motvated as foows The cost functon J(w) can be decomposed as: J(w) = X = J (w), where J (w) = E d u w () whch aows us to rewrte () as w = w µ " X = J (w )# (8) ow et be a oca estmate of wo at node and tme and assgn the nta condton w Then w can be evauated by teratng through the nodes n the foowng manner: = ψ() µ [ J (w )], =,, (9) At the end of the procedure (9), the ast node w contan the goba estmate w from (8), e, w Ths scheme st requres EMSE (db) Incrementa Souton () Souton (9) 8 Iteraton Fg Excess mean square error (EMSE) performance for both the dstrbuted ncrementa souton () and the centrazed souton (9) at node a nodes to share the goba nformaton w A fuy dstrbuted souton can be acheved by resortng to ncrementa strateges, whch woud requre each node n (9) to evauate ts parta gradent J ( ) at ts oca estmate, nstead of w Ths approach eads to the ncrementa agorthm: = ψ() µ [ J ( ) ], =,, () Ths cooperatve scheme requres each node to communcate ony wth ts mmedate neghbor over a pre-defned path Moreover, t s an estabshed resut n optmzaton theory that the ncrementa souton () can outperform the souton (9) as ustrated n Fg The fgure compares the excess mean square error (EMSE) of both agorthms for a networ wth = nodes and usng Gaussan regressors wth R u, = I The bacground nose s whte and Gaussan wth σ v = The curves are obtaned by averagng over 5 experments wth µ = 5 ow usng nstantaneous approxmatons ˆR du, = d ()u, and ˆR u, = u,u, n (), and aowng for dfferent step-szes at dfferent nodes, eads to a dstrbuted ncrementa LMS agorthm, summarzed beow: 8 >< >: w = ψ() + µ u, w d () u, () wth =,, In ths agorthm, a weght estmate s crcuated through a path defned over the networ and updated by oca adaptve fters usng oca data see Fg node: {d (), u, node: {d (), u, node: - {d - (), u -, node: + {d + (), u +, node: {d (), u, ode, Tme ( ) Remote nput Loca nput ψ (from node -) (sensors) { d ( ), u, ( ( ) ) ψ + µ u d u ψ ( ) * ( ),, ( ) ψ Toward neghbor node + ode output (ready to use) Fg The structure of ncrementa LMS
3 EXACT DISTRIBUTED RLS ADAPTATIO We formuate n ths secton a east-squares souton for estmatng the unnown parameter vector w o At each tme nstant, the networ has access to the foowng space-tme data: y = d () d () d () 5 and H = u, u, u, 5 () We can then see an estmate for w o by sovng a reguarzed eastsquares probem of the form []: mn w w Πw + Y H w () where Π > s a reguarzaton matrx and Y and H coect a the data that are avaabe up to tme : Y = y y y 5 and H = H H H 5 () One coud aso ncorporate weghtng nto () to account for spata reevance, tempora reevance, and node reevance Here we contnue wthout weghtng n order to convey the man dea We are thus nterested n dervng a dstrbuted mpementaton of the east-squares souton Some reated wor has been recenty proposed where a goba east-squares souton s acheved ony approxmatey at each node, and the agorthm demands arge communcaton and energy resources [5] We proceed nstead as foows Assume that w s the souton to the foowng eastsquares (LS) probem usng the data that are avaabe up to tme : mn w Πw + Y H w w (5) We are nterested n updatng w to w by accountng for the ncomng data bocs y and H at tme An agorthm that updates w ncrementay s gven by: w ; P, P for = : e () = d () u, = ψ() + P, +u, P, u u,e (), P, = P, P,u, u,p, +u, P, u, end w ; P P, () Smary to the ncrementa LMS n Secton, agorthm () nduces a cyce across the networ, aong whch the estmate w s spatay updated by sequentay vstng every node once At each node, the estmate at tme s the LS souton that s based on the data bocs Y and H and the data coected aong the path up to that node, namey mn ψ ψ Πψ + Y H ψ = () where now Y = Y d () d () d () 5 and H = H u, u, u, 5 (8) At the end of the cyce, w contan the desred souton w If we start from = wth w = and P = Π and repeatedy appy (), then w be the souton to () The dstrbuted RLS (drls) agorthm () can be motvated as foows ote frst that the souton for () s gven by []: wth P, = Partton Y and H as foows: Y Y = and H = d () = P,H Y (9) Π + H H () H u, () Then a spata recurson for P, can be found by substtutng () nto (): P, = Π + H H = Π + H H + u,u, = P, + u,u, () whch, by appyng the matrx nverson emma, eads to P, = P, P,u,u, P, + u, P, u (), Substtutng () and () nto (9) we get: = P, H Y + u,d () = P, H {z Y = + P, u, whch eads to wth u,p, u, + u, P, u, P, u,u, P + u, P, u, H, = ψ() + P, d () Y {z = + u, P, u u,e () (), e () = d () u, (5) Groupng (), (), and (5) eads to () The agorthm structure s reatvey smpe and t can be understood as a standard east-squares souton unwrapped aong the coaboraton cyce However, the nodes are exposed to data wth dstnct spata and nose profes Ths varaton refects tsef n the performance of the agorthm, whch w be studed esewhere
4 5 LOW-COMMUICATIO DISTRIBUTED RLS ADAPTATIO The agorthm proposed n the prevous secton mpements exact RLS dstrbutvey, whereby the nodes share nformaton about the oca weght estmates { and the matrces {P, A ess compex souton that ony shares nformaton about the weght estmates can be obtaned by requrng the matrces {P, to evove ocay Ths strategy eads to: w for = : e () = d () u, P, = = ψ() + end w P, +u, P, u, u,e () P, P, u, u,p, +u, P, u, () To ustrate the operaton of both agorthms drls and ts owcommuncaton counterpart (LC-dRLS), we consder a networ wth = 5 nodes where each oca fter has M = taps The system evoves for teratons and the resuts are averaged over ndependent experments The steady-state meansquare error vaues are obtaned by averagng the ast 5 tme sampes Each node accesses tme-correated spatay ndependent Gaussan regressors u, wth correaton functons r () = σ u, (α ), =,, M, wth {α and {σ u, randomy chosen n [, ) and depcted n Fg The bacground nose v () has varance σ v, = across the networ ote n Fg 5 that both dstrbuted RLS agorthms have smar performance n the mean-square error sense, suggestng that the ow-communcaton mpementaton can be a qute compettve suboptma mpementaton DIFFUSIO LMS ADAPTATIO When more communcaton and energy resources are avaabe, we may tae advantage of the networ connectvty and devse more sophstcated peer-to-peer cooperaton rues We expore a smpe dffuson protoco (see Fg ) Each ndvdua node consuts ts peer nodes from the neghborhood ( ) and combnes ther past estmates {ψ ( ) ; ( ) wth ts own past estmate ψ ( ) The node generates an aggregated estmate φ ( ) and feeds t n ts oca adaptve fter Ths strategy can be expressed as foows: φ ( ) = f ψ ( ) ; ( ) = φ ( ) + µu, for some combner f ( ) d () u, φ ( ) () ode power profe σ U () Correaton Index α ode ode Fg etwor statstca profe Steady state experments Fg A networ wth dffuson cooperaton strategy In ths wor we expore a smpe combnng rue n whch the aggregated estmate s generated by averagng oca and neghbors prevous estmates, e, X φ ( ) = a(, ) ψ ( ) = φ ( ) + µu, d () u, φ ( ) (8) MSE (db) drls LC drls 8 ode Fg 5 MSE performance for both agorthms drls and LC-dRLS across the networ where a(, ) = /deg(), wth deg() denotng the degree of node (number of ncdent ns at ths node, ncudng tsef) Ths scheme expots networ connectvty eadng to more robust agorthms Furthermore, snce more nformaton s aggregated n the oca adaptve fter updates, ndvdua nodes can attan better earnng behavor when compared to the non-cooperatve case, provded that the combners f are we desgned To ustrate ths fact, we run a smuaton exampe wth a networ of = adaptve fters wth M = taps each The topoogy s presented n Fg, whe the networ statstca profe s presented n Fg 8 The neghborhood of a node s the set of nodes drecty connected to t, ncudng tsef
5 o coop Dffuson EMSE per node (db) ode Fg etwor topoogy (sef-oops omtted) for the dffuson LMS exampe etwor Statstcs 8 α σ u, 8 ode 8 σ v, 8 ode Fg 8 etwor statstca profe: regressors power and correaton ndces (eft) and nose power (rght) Fg Steady-state EMSE per node for dffuson LMS COCLUDIG REMARKS We have descrbed adaptve schemes to perform dstrbuted estmaton n a cooperatve fashon When communcaton and energy resources are scarce, the ncrementa LMS scheme may be used When more powerfu processors are avaabe at the nodes, dstrbuted RLS mpementatons wth mted cooperaton can be empoyed For genera topooges, and wth more energy and communcaton resources, one can resort to dffuson LMS strateges The dffuson technques can aso be extended to recursve eastsquares formuatons, whch we w examne esewhere 8 REFERECES EMSE goba (db) o coop Dffuson 5 Tme [] D Estrn, G Potte and M Srvastava Intrumentng the word wth wreess sensor networs, Proc IEEE ICASSP, pp -, Sat Lae Cty, UT, May [] D Bertseas, A new cass of ncrementa gradent methods for eastsquares probems, SIAM J Optm, vo, no, pp 9-9, ov 99 [] C Lopes and A H Sayed, Dstrbuted adaptve ncrementa strateges: formuaton and performance anayss, Proc ICASSP, Tououse, France, May [] A H Sayed Fundamentas of Adaptve Fterng, Wey, J, [5] L Xao, S Boyd and S La, A scheme for robust dstrbuted sensor fuson based on average consensus, Fourth IPS, Los Angees, UCLA, Apr 5, pp - Fg 9 Dffuson LMS - Transent goba EMSE We compare the dffuson LMS wth the non-cooperatve case, n whch the adaptve fters evove ndependenty accessng oca data and consutng ther own past estmates ony We use the goba EMSE average, defned as ζ g = X = ζ (9) as a fgure of mert, where ζ s the oca EMSE at node Fgure 9 shows the goba earnng behavor and Fgure 9 presents the networ ndvdua EMSE profe n steady-state Despte some osses at a few nodes, as for ths case n node 9, on average, the entre system benefts from cooperaton
Associative Memories
Assocatve Memores We consder now modes for unsupervsed earnng probems, caed auto-assocaton probems. Assocaton s the task of mappng patterns to patterns. In an assocatve memory the stmuus of an ncompete
More informationResearch on Complex Networks Control Based on Fuzzy Integral Sliding Theory
Advanced Scence and Technoogy Letters Vo.83 (ISA 205), pp.60-65 http://dx.do.org/0.4257/ast.205.83.2 Research on Compex etworks Contro Based on Fuzzy Integra Sdng Theory Dongsheng Yang, Bngqng L, 2, He
More informationDelay tomography for large scale networks
Deay tomography for arge scae networks MENG-FU SHIH ALFRED O. HERO III Communcatons and Sgna Processng Laboratory Eectrca Engneerng and Computer Scence Department Unversty of Mchgan, 30 Bea. Ave., Ann
More informationNested case-control and case-cohort studies
Outne: Nested case-contro and case-cohort studes Ørnuf Borgan Department of Mathematcs Unversty of Oso NORBIS course Unversty of Oso 4-8 December 217 1 Radaton and breast cancer data Nested case contro
More informationExample: Suppose we want to build a classifier that recognizes WebPages of graduate students.
Exampe: Suppose we want to bud a cassfer that recognzes WebPages of graduate students. How can we fnd tranng data? We can browse the web and coect a sampe of WebPages of graduate students of varous unverstes.
More informationNeural network-based athletics performance prediction optimization model applied research
Avaabe onne www.jocpr.com Journa of Chemca and Pharmaceutca Research, 04, 6(6):8-5 Research Artce ISSN : 0975-784 CODEN(USA) : JCPRC5 Neura networ-based athetcs performance predcton optmzaton mode apped
More informationImage Classification Using EM And JE algorithms
Machne earnng project report Fa, 2 Xaojn Sh, jennfer@soe Image Cassfcaton Usng EM And JE agorthms Xaojn Sh Department of Computer Engneerng, Unversty of Caforna, Santa Cruz, CA, 9564 jennfer@soe.ucsc.edu
More informationOn Uplink-Downlink Sum-MSE Duality of Multi-hop MIMO Relay Channel
On Upn-Downn Sum-MSE Duat of Mut-hop MIMO Rea Channe A Cagata Cr, Muhammad R. A. handaer, Yue Rong and Yngbo ua Department of Eectrca Engneerng, Unverst of Caforna Rversde, Rversde, CA, 95 Centre for Wreess
More informationSupplementary Material: Learning Structured Weight Uncertainty in Bayesian Neural Networks
Shengyang Sun, Changyou Chen, Lawrence Carn Suppementary Matera: Learnng Structured Weght Uncertanty n Bayesan Neura Networks Shengyang Sun Changyou Chen Lawrence Carn Tsnghua Unversty Duke Unversty Duke
More informationApplication of Particle Swarm Optimization to Economic Dispatch Problem: Advantages and Disadvantages
Appcaton of Partce Swarm Optmzaton to Economc Dspatch Probem: Advantages and Dsadvantages Kwang Y. Lee, Feow, IEEE, and Jong-Bae Par, Member, IEEE Abstract--Ths paper summarzes the state-of-art partce
More informationCorrespondence. Performance Evaluation for MAP State Estimate Fusion I. INTRODUCTION
Correspondence Performance Evauaton for MAP State Estmate Fuson Ths paper presents a quanttatve performance evauaton method for the maxmum a posteror (MAP) state estmate fuson agorthm. Under dea condtons
More informationMARKOV CHAIN AND HIDDEN MARKOV MODEL
MARKOV CHAIN AND HIDDEN MARKOV MODEL JIAN ZHANG JIANZHAN@STAT.PURDUE.EDU Markov chan and hdden Markov mode are probaby the smpest modes whch can be used to mode sequenta data,.e. data sampes whch are not
More informationGreyworld White Balancing with Low Computation Cost for On- Board Video Capturing
reyword Whte aancng wth Low Computaton Cost for On- oard Vdeo Capturng Peng Wu Yuxn Zoe) Lu Hewett-Packard Laboratores Hewett-Packard Co. Pao Ato CA 94304 USA Abstract Whte baancng s a process commony
More informationDistributed Moving Horizon State Estimation of Nonlinear Systems. Jing Zhang
Dstrbuted Movng Horzon State Estmaton of Nonnear Systems by Jng Zhang A thess submtted n parta fufment of the requrements for the degree of Master of Scence n Chemca Engneerng Department of Chemca and
More informationResearch Article H Estimates for Discrete-Time Markovian Jump Linear Systems
Mathematca Probems n Engneerng Voume 213 Artce ID 945342 7 pages http://dxdoorg/11155/213/945342 Research Artce H Estmates for Dscrete-Tme Markovan Jump Lnear Systems Marco H Terra 1 Gdson Jesus 2 and
More informationSubgradient Methods and Consensus Algorithms for Solving Convex Optimization Problems
Proceedngs of the 47th IEEE Conference on Decson and Contro Cancun, Mexco, Dec. 9-11, 2008 Subgradent Methods and Consensus Agorthms for Sovng Convex Optmzaton Probems Björn Johansson, Tamás Kevczy, Mae
More informationLecture Notes on Linear Regression
Lecture Notes on Lnear Regresson Feng L fl@sdueducn Shandong Unversty, Chna Lnear Regresson Problem In regresson problem, we am at predct a contnuous target value gven an nput feature vector We assume
More informationPolite Water-filling for Weighted Sum-rate Maximization in MIMO B-MAC Networks under. Multiple Linear Constraints
2011 IEEE Internatona Symposum on Informaton Theory Proceedngs Pote Water-fng for Weghted Sum-rate Maxmzaton n MIMO B-MAC Networks under Mutpe near Constrants An u 1, Youjan u 2, Vncent K. N. au 3, Hage
More informationA finite difference method for heat equation in the unbounded domain
Internatona Conerence on Advanced ectronc Scence and Technoogy (AST 6) A nte derence method or heat equaton n the unbounded doman a Quan Zheng and Xn Zhao Coege o Scence North Chna nversty o Technoogy
More informationOptimum Selection Combining for M-QAM on Fading Channels
Optmum Seecton Combnng for M-QAM on Fadng Channes M. Surendra Raju, Ramesh Annavajjaa and A. Chockangam Insca Semconductors Inda Pvt. Ltd, Bangaore-56000, Inda Department of ECE, Unversty of Caforna, San
More informationA General Column Generation Algorithm Applied to System Reliability Optimization Problems
A Genera Coumn Generaton Agorthm Apped to System Reabty Optmzaton Probems Lea Za, Davd W. Cot, Department of Industra and Systems Engneerng, Rutgers Unversty, Pscataway, J 08854, USA Abstract A genera
More informationInterference Alignment and Degrees of Freedom Region of Cellular Sigma Channel
2011 IEEE Internatona Symposum on Informaton Theory Proceedngs Interference Agnment and Degrees of Freedom Regon of Ceuar Sgma Channe Huaru Yn 1 Le Ke 2 Zhengdao Wang 2 1 WINLAB Dept of EEIS Unv. of Sc.
More informationL-Edge Chromatic Number Of A Graph
IJISET - Internatona Journa of Innovatve Scence Engneerng & Technoogy Vo. 3 Issue 3 March 06. ISSN 348 7968 L-Edge Chromatc Number Of A Graph Dr.R.B.Gnana Joth Assocate Professor of Mathematcs V.V.Vannaperuma
More informationLower Bounding Procedures for the Single Allocation Hub Location Problem
Lower Boundng Procedures for the Snge Aocaton Hub Locaton Probem Borzou Rostam 1,2 Chrstoph Buchhem 1,4 Fautät für Mathemat, TU Dortmund, Germany J. Faban Meer 1,3 Uwe Causen 1 Insttute of Transport Logstcs,
More informationOn the Power Function of the Likelihood Ratio Test for MANOVA
Journa of Mutvarate Anayss 8, 416 41 (00) do:10.1006/jmva.001.036 On the Power Functon of the Lkehood Rato Test for MANOVA Dua Kumar Bhaumk Unversty of South Aabama and Unversty of Inos at Chcago and Sanat
More informationIV. Performance Optimization
IV. Performance Optmzaton A. Steepest descent algorthm defnton how to set up bounds on learnng rate mnmzaton n a lne (varyng learnng rate) momentum learnng examples B. Newton s method defnton Gauss-Newton
More informationOptimization of JK Flip Flop Layout with Minimal Average Power of Consumption based on ACOR, Fuzzy-ACOR, GA, and Fuzzy-GA
Journa of mathematcs and computer Scence 4 (05) - 5 Optmzaton of JK Fp Fop Layout wth Mnma Average Power of Consumpton based on ACOR, Fuzzy-ACOR, GA, and Fuzzy-GA Farshd Kevanan *,, A Yekta *,, Nasser
More informationCOXREG. Estimation (1)
COXREG Cox (972) frst suggested the modes n whch factors reated to fetme have a mutpcatve effect on the hazard functon. These modes are caed proportona hazards (PH) modes. Under the proportona hazards
More informationLower bounds for the Crossing Number of the Cartesian Product of a Vertex-transitive Graph with a Cycle
Lower bounds for the Crossng Number of the Cartesan Product of a Vertex-transtve Graph wth a Cyce Junho Won MIT-PRIMES December 4, 013 Abstract. The mnmum number of crossngs for a drawngs of a gven graph
More informationA DIMENSION-REDUCTION METHOD FOR STOCHASTIC ANALYSIS SECOND-MOMENT ANALYSIS
A DIMESIO-REDUCTIO METHOD FOR STOCHASTIC AALYSIS SECOD-MOMET AALYSIS S. Rahman Department of Mechanca Engneerng and Center for Computer-Aded Desgn The Unversty of Iowa Iowa Cty, IA 52245 June 2003 OUTLIE
More informationarxiv: v1 [cs.gt] 28 Mar 2017
A Dstrbuted Nash qubrum Seekng n Networked Graphca Games Farzad Saehsadaghan, and Lacra Pave arxv:7009765v csgt 8 Mar 07 Abstract Ths paper consders a dstrbuted gossp approach for fndng a Nash equbrum
More informationThe Application of BP Neural Network principal component analysis in the Forecasting the Road Traffic Accident
ICTCT Extra Workshop, Bejng Proceedngs The Appcaton of BP Neura Network prncpa component anayss n Forecastng Road Traffc Accdent He Mng, GuoXucheng &LuGuangmng Transportaton Coege of Souast Unversty 07
More informationOn the Equality of Kernel AdaTron and Sequential Minimal Optimization in Classification and Regression Tasks and Alike Algorithms for Kernel
Proceedngs of th European Symposum on Artfca Neura Networks, pp. 25-222, ESANN 2003, Bruges, Begum, 2003 On the Equaty of Kerne AdaTron and Sequenta Mnma Optmzaton n Cassfcaton and Regresson Tasks and
More informationGlobally Optimal Multisensor Distributed Random Parameter Matrices Kalman Filtering Fusion with Applications
Sensors 2008, 8, 8086-8103; DOI: 10.3390/s8128086 OPEN ACCESS sensors ISSN 1424-8220 www.mdp.com/journa/sensors Artce Gobay Optma Mutsensor Dstrbuted Random Parameter Matrces Kaman Fterng Fuson wth Appcatons
More informationEstimation: Part 2. Chapter GREG estimation
Chapter 9 Estmaton: Part 2 9. GREG estmaton In Chapter 8, we have seen that the regresson estmator s an effcent estmator when there s a lnear relatonshp between y and x. In ths chapter, we generalzed the
More informationThe Entire Solution Path for Support Vector Machine in Positive and Unlabeled Classification 1
Abstract The Entre Souton Path for Support Vector Machne n Postve and Unabeed Cassfcaton 1 Yao Lmn, Tang Je, and L Juanz Department of Computer Scence, Tsnghua Unversty 1-308, FIT, Tsnghua Unversty, Bejng,
More informationDSCOVR: Randomized Primal-Dual Block Coordinate Algorithms for Asynchronous Distributed Optimization
DSCOVR: Randomzed Prma-Dua Boc Coordnate Agorthms for Asynchronous Dstrbuted Optmzaton Ln Xao Mcrosoft Research AI Redmond, WA 9805, USA Adams We Yu Machne Learnng Department, Carnege Meon Unversty Pttsburgh,
More informationThe line method combined with spectral chebyshev for space-time fractional diffusion equation
Apped and Computatona Mathematcs 014; 3(6): 330-336 Pubshed onne December 31, 014 (http://www.scencepubshnggroup.com/j/acm) do: 10.1164/j.acm.0140306.17 ISS: 3-5605 (Prnt); ISS: 3-5613 (Onne) The ne method
More informationQuantum Runge-Lenz Vector and the Hydrogen Atom, the hidden SO(4) symmetry
Quantum Runge-Lenz ector and the Hydrogen Atom, the hdden SO(4) symmetry Pasca Szrftgser and Edgardo S. Cheb-Terrab () Laboratore PhLAM, UMR CNRS 85, Unversté Le, F-59655, France () Mapesoft Let's consder
More informationCyclic Codes BCH Codes
Cycc Codes BCH Codes Gaos Feds GF m A Gaos fed of m eements can be obtaned usng the symbos 0,, á, and the eements beng 0,, á, á, á 3 m,... so that fed F* s cosed under mutpcaton wth m eements. The operator
More informationCSci 6974 and ECSE 6966 Math. Tech. for Vision, Graphics and Robotics Lecture 21, April 17, 2006 Estimating A Plane Homography
CSc 6974 and ECSE 6966 Math. Tech. for Vson, Graphcs and Robotcs Lecture 21, Aprl 17, 2006 Estmatng A Plane Homography Overvew We contnue wth a dscusson of the major ssues, usng estmaton of plane projectve
More informationMAXIMUM NORM STABILITY OF DIFFERENCE SCHEMES FOR PARABOLIC EQUATIONS ON OVERSET NONMATCHING SPACE-TIME GRIDS
MATHEMATICS OF COMPUTATION Voume 72 Number 242 Pages 619 656 S 0025-57180201462-X Artce eectroncay pubshed on November 4 2002 MAXIMUM NORM STABILITY OF DIFFERENCE SCHEMES FOR PARABOLIC EQUATIONS ON OVERSET
More informationDecentralized Adaptive Control for a Class of Large-Scale Nonlinear Systems with Unknown Interactions
Decentrazed Adaptve Contro for a Cass of Large-Scae onnear Systems wth Unknown Interactons Bahram Karm 1, Fatemeh Jahangr, Mohammad B. Menhaj 3, Iman Saboor 4 1. Center of Advanced Computatona Integence,
More informationRetrodirective Distributed Transmit Beamforming with Two-Way Source Synchronization
Retrodrectve Dstrbuted Transmt Beamformng wth Two-Way Source Synchronzaton Robert D. Preuss and D. Rchard Brown III Abstract Dstrbuted transmt beamformng has recenty been proposed as a technque n whch
More informationCOMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS
Avalable onlne at http://sck.org J. Math. Comput. Sc. 3 (3), No., 6-3 ISSN: 97-537 COMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS
More informationNetworked Cooperative Distributed Model Predictive Control Based on State Observer
Apped Mathematcs, 6, 7, 48-64 ubshed Onne June 6 n ScRes. http://www.scrp.org/journa/am http://dx.do.org/.436/am.6.73 Networed Cooperatve Dstrbuted Mode redctve Contro Based on State Observer Ba Su, Yanan
More informationSupervised Learning. Neural Networks and Back-Propagation Learning. Credit Assignment Problem. Feedforward Network. Adaptive System.
Part 7: Neura Networ & earnng /2/05 Superved earnng Neura Networ and Bac-Propagaton earnng Produce dered output for tranng nput Generaze reaonaby & appropratey to other nput Good exampe: pattern recognton
More informationDeriving the Dual. Prof. Bennett Math of Data Science 1/13/06
Dervng the Dua Prof. Bennett Math of Data Scence /3/06 Outne Ntty Grtty for SVM Revew Rdge Regresson LS-SVM=KRR Dua Dervaton Bas Issue Summary Ntty Grtty Need Dua of w, b, z w 2 2 mn st. ( x w ) = C z
More informationLOW BIAS INTEGRATED PATH ESTIMATORS. James M. Calvin
Proceedngs of the 007 Wnter Smulaton Conference S G Henderson, B Bller, M-H Hseh, J Shortle, J D Tew, and R R Barton, eds LOW BIAS INTEGRATED PATH ESTIMATORS James M Calvn Department of Computer Scence
More informationSingular Value Decomposition: Theory and Applications
Sngular Value Decomposton: Theory and Applcatons Danel Khashab Sprng 2015 Last Update: March 2, 2015 1 Introducton A = UDV where columns of U and V are orthonormal and matrx D s dagonal wth postve real
More informationUncertainty Specification and Propagation for Loss Estimation Using FOSM Methods
Uncertanty Specfcaton and Propagaton for Loss Estmaton Usng FOSM Methods J.W. Baer and C.A. Corne Dept. of Cv and Envronmenta Engneerng, Stanford Unversty, Stanford, CA 94305-400 Keywords: Sesmc, oss estmaton,
More informationA General Distributed Dual Coordinate Optimization Framework for Regularized Loss Minimization
Journa of Machne Learnng Research 18 17 1-5 Submtted 9/16; Revsed 1/17; Pubshed 1/17 A Genera Dstrbuted Dua Coordnate Optmzaton Framework for Reguarzed Loss Mnmzaton Shun Zheng Insttute for Interdscpnary
More informationTransfer Functions. Convenient representation of a linear, dynamic model. A transfer function (TF) relates one input and one output: ( ) system
Transfer Functons Convenent representaton of a lnear, dynamc model. A transfer functon (TF) relates one nput and one output: x t X s y t system Y s The followng termnology s used: x y nput output forcng
More informationWAVELET-BASED IMAGE COMPRESSION USING SUPPORT VECTOR MACHINE LEARNING AND ENCODING TECHNIQUES
WAVELE-BASED IMAGE COMPRESSION USING SUPPOR VECOR MACHINE LEARNING AND ENCODING ECHNIQUES Rakb Ahmed Gppsand Schoo of Computng and Informaton echnoogy Monash Unversty, Gppsand Campus Austraa. Rakb.Ahmed@nfotech.monash.edu.au
More informationInformation Weighted Consensus
Informaton Weghted Consensus A. T. Kamal, J. A. Farrell and A. K. Roy-Chowdhury Unversty of Calforna, Rversde, CA-92521 Abstract Consensus-based dstrbuted estmaton schemes are becomng ncreasngly popular
More informationThe Concept of Beamforming
ELG513 Smart Antennas S.Loyka he Concept of Beamformng Generc representaton of the array output sgnal, 1 where w y N 1 * = 1 = w x = w x (4.1) complex weghts, control the array pattern; y and x - narrowband
More informationQUARTERLY OF APPLIED MATHEMATICS
QUARTERLY OF APPLIED MATHEMATICS Voume XLI October 983 Number 3 DIAKOPTICS OR TEARING-A MATHEMATICAL APPROACH* By P. W. AITCHISON Unversty of Mantoba Abstract. The method of dakoptcs or tearng was ntroduced
More informationMultispectral Remote Sensing Image Classification Algorithm Based on Rough Set Theory
Proceedngs of the 2009 IEEE Internatona Conference on Systems Man and Cybernetcs San Antono TX USA - October 2009 Mutspectra Remote Sensng Image Cassfcaton Agorthm Based on Rough Set Theory Yng Wang Xaoyun
More informationA Class of Distributed Optimization Methods with Event-Triggered Communication
A Cass of Dstrbuted Optmzaton Methods wth Event-Trggered Communcaton Martn C. Mene Mchae Ubrch Sebastan Abrecht the date of recept and acceptance shoud be nserted ater Abstract We present a cass of methods
More informationAndre Schneider P622
Andre Schneder P6 Probem Set #0 March, 00 Srednc 7. Suppose that we have a theory wth Negectng the hgher order terms, show that Souton Knowng β(α and γ m (α we can wrte β(α =b α O(α 3 (. γ m (α =c α O(α
More informationA parametric Linear Programming Model Describing Bandwidth Sharing Policies for ABR Traffic
parametrc Lnear Programmng Mode Descrbng Bandwdth Sharng Poces for BR Traffc I. Moschoos, M. Logothets and G. Kokknaks Wre ommuncatons Laboratory, Dept. of Eectrca & omputer Engneerng, Unversty of Patras,
More informationAdaptive and Iterative Least Squares Support Vector Regression Based on Quadratic Renyi Entropy
daptve and Iteratve Least Squares Support Vector Regresson Based on Quadratc Ren Entrop Jngqng Jang, Chu Song, Haan Zhao, Chunguo u,3 and Yanchun Lang Coege of Mathematcs and Computer Scence, Inner Mongoa
More informationSupporting Information
Supportng Informaton The neural network f n Eq. 1 s gven by: f x l = ReLU W atom x l + b atom, 2 where ReLU s the element-wse rectfed lnear unt, 21.e., ReLUx = max0, x, W atom R d d s the weght matrx to
More informationComparison of the Population Variance Estimators. of 2-Parameter Exponential Distribution Based on. Multiple Criteria Decision Making Method
Appled Mathematcal Scences, Vol. 7, 0, no. 47, 07-0 HIARI Ltd, www.m-hkar.com Comparson of the Populaton Varance Estmators of -Parameter Exponental Dstrbuton Based on Multple Crtera Decson Makng Method
More informationI. INTRODUCTION WIRELESS sensing and control systems have received
IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 23, NO. 6, NOVEMBER 2015 2167 Mutpe-Loop Sef-Trggered Mode Predctve Contro for Network Schedung and Contro Erk Henrksson, Dane E. Quevedo, Senor Member,
More informationProblem Set 9 Solutions
Desgn and Analyss of Algorthms May 4, 2015 Massachusetts Insttute of Technology 6.046J/18.410J Profs. Erk Demane, Srn Devadas, and Nancy Lynch Problem Set 9 Solutons Problem Set 9 Solutons Ths problem
More informationDownlink Power Allocation for CoMP-NOMA in Multi-Cell Networks
Downn Power Aocaton for CoMP-NOMA n Mut-Ce Networs Md Shpon A, Eram Hossan, Arafat A-Dwe, and Dong In Km arxv:80.0498v [eess.sp] 6 Dec 207 Abstract Ths wor consders the probem of dynamc power aocaton n
More informationAdaptive Beamforming in Multi path fading Channels for Voice Enhancements
Adaptve Beamformng n ut path fadng Channes for Voce Enhancements usnan Abbas Internatona Isamc Unversty Isamabad Waqas Ahmed Internatona Isamc Unversty Isamabad Shehzad Ashraf Internatona Isamc Unversty
More informationREAL-TIME IMPACT FORCE IDENTIFICATION OF CFRP LAMINATED PLATES USING SOUND WAVES
8 TH INTERNATIONAL CONERENCE ON COMPOSITE MATERIALS REAL-TIME IMPACT ORCE IDENTIICATION O CRP LAMINATED PLATES USING SOUND WAVES S. Atobe *, H. Kobayash, N. Hu 3 and H. ukunaga Department of Aerospace
More informationChapter - 2. Distribution System Power Flow Analysis
Chapter - 2 Dstrbuton System Power Flow Analyss CHAPTER - 2 Radal Dstrbuton System Load Flow 2.1 Introducton Load flow s an mportant tool [66] for analyzng electrcal power system network performance. Load
More informationDynamic Programming. Preview. Dynamic Programming. Dynamic Programming. Dynamic Programming (Example: Fibonacci Sequence)
/24/27 Prevew Fbonacc Sequence Longest Common Subsequence Dynamc programmng s a method for solvng complex problems by breakng them down nto smpler sub-problems. It s applcable to problems exhbtng the propertes
More informationECE559VV Project Report
ECE559VV Project Report (Supplementary Notes Loc Xuan Bu I. MAX SUM-RATE SCHEDULING: THE UPLINK CASE We have seen (n the presentaton that, for downlnk (broadcast channels, the strategy maxmzng the sum-rate
More informationXin Li Department of Information Systems, College of Business, City University of Hong Kong, Hong Kong, CHINA
RESEARCH ARTICLE MOELING FIXE OS BETTING FOR FUTURE EVENT PREICTION Weyun Chen eartment of Educatona Informaton Technoogy, Facuty of Educaton, East Chna Norma Unversty, Shangha, CHINA {weyun.chen@qq.com}
More informationMarkov Chain Monte Carlo Lecture 6
where (x 1,..., x N ) X N, N s called the populaton sze, f(x) f (x) for at least one {1, 2,..., N}, and those dfferent from f(x) are called the tral dstrbutons n terms of mportance samplng. Dfferent ways
More informationPower Allocation for Distributed BLUE Estimation with Full and Limited Feedback of CSI
Power Allocaton for Dstrbuted BLUE Estmaton wth Full and Lmted Feedback of CSI Mohammad Fanae, Matthew C. Valent, and Natala A. Schmd Lane Department of Computer Scence and Electrcal Engneerng West Vrgna
More informationLinear Approximation with Regularization and Moving Least Squares
Lnear Approxmaton wth Regularzaton and Movng Least Squares Igor Grešovn May 007 Revson 4.6 (Revson : March 004). 5 4 3 0.5 3 3.5 4 Contents: Lnear Fttng...4. Weghted Least Squares n Functon Approxmaton...
More informationDynamic Systems on Graphs
Prepared by F.L. Lews Updated: Saturday, February 06, 200 Dynamc Systems on Graphs Control Graphs and Consensus A network s a set of nodes that collaborates to acheve what each cannot acheve alone. A network,
More informationA Hybrid Variational Iteration Method for Blasius Equation
Avalable at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 1932-9466 Vol. 10, Issue 1 (June 2015), pp. 223-229 Applcatons and Appled Mathematcs: An Internatonal Journal (AAM) A Hybrd Varatonal Iteraton Method
More informationFor now, let us focus on a specific model of neurons. These are simplified from reality but can achieve remarkable results.
Neural Networks : Dervaton compled by Alvn Wan from Professor Jtendra Malk s lecture Ths type of computaton s called deep learnng and s the most popular method for many problems, such as computer vson
More informationSampling-based Approach for Design Optimization in the Presence of Interval Variables
0 th Word Congress on Structura and Mutdscpnary Optmzaton May 9-4, 03, Orando, orda, USA Sampng-based Approach for Desgn Optmzaton n the Presence of nterva Varabes Davd Yoo and kn Lee Unversty of Connectcut,
More informationParametric fractional imputation for missing data analysis. Jae Kwang Kim Survey Working Group Seminar March 29, 2010
Parametrc fractonal mputaton for mssng data analyss Jae Kwang Km Survey Workng Group Semnar March 29, 2010 1 Outlne Introducton Proposed method Fractonal mputaton Approxmaton Varance estmaton Multple mputaton
More informationApproximate merging of a pair of BeÂzier curves
COMPUTER-AIDED DESIGN Computer-Aded Desgn 33 (1) 15±136 www.esever.com/ocate/cad Approxmate mergng of a par of BeÂzer curves Sh-Mn Hu a,b, *, Rou-Feng Tong c, Tao Ju a,b, Ja-Guang Sun a,b a Natona CAD
More informationOutline and Reading. Dynamic Programming. Dynamic Programming revealed. Computing Fibonacci. The General Dynamic Programming Technique
Outlne and Readng Dynamc Programmng The General Technque ( 5.3.2) -1 Knapsac Problem ( 5.3.3) Matrx Chan-Product ( 5.3.1) Dynamc Programmng verson 1.4 1 Dynamc Programmng verson 1.4 2 Dynamc Programmng
More informationNONLINEAR SYSTEM IDENTIFICATION BASE ON FW-LSSVM
Journa of heoretca and Apped Informaton echnoogy th February 3. Vo. 48 No. 5-3 JAI & LLS. A rghts reserved. ISSN: 99-8645 www.jatt.org E-ISSN: 87-395 NONLINEAR SYSEM IDENIFICAION BASE ON FW-LSSVM, XIANFANG
More informationGrover s Algorithm + Quantum Zeno Effect + Vaidman
Grover s Algorthm + Quantum Zeno Effect + Vadman CS 294-2 Bomb 10/12/04 Fall 2004 Lecture 11 Grover s algorthm Recall that Grover s algorthm for searchng over a space of sze wors as follows: consder the
More informationChapter 6. Rotations and Tensors
Vector Spaces n Physcs 8/6/5 Chapter 6. Rotatons and ensors here s a speca knd of near transformaton whch s used to transforms coordnates from one set of axes to another set of axes (wth the same orgn).
More informationOptimal and Suboptimal Linear Receivers for Time-Hopping Impulse Radio Systems
MITSUBISHI ELECTRIC RESEARCH LABORATORIES http://www.mer.com Optma and Suboptma Lnear Recevers for Tme-Hoppng Impuse Rado Systems Snan Gezc Hsash Kbayash H. Vncent Poor Andreas F. Mosch TR2004-052 May
More informationISSN: ISO 9001:2008 Certified International Journal of Engineering and Innovative Technology (IJEIT) Volume 3, Issue 1, July 2013
ISSN: 2277-375 Constructon of Trend Free Run Orders for Orthogonal rrays Usng Codes bstract: Sometmes when the expermental runs are carred out n a tme order sequence, the response can depend on the run
More informationVQ widely used in coding speech, image, and video
at Scalar quantzers are specal cases of vector quantzers (VQ): they are constraned to look at one sample at a tme (memoryless) VQ does not have such constrant better RD perfomance expected Source codng
More informationA Derivative-Free Algorithm for Bound Constrained Optimization
Computatona Optmzaton and Appcatons, 21, 119 142, 2002 c 2002 Kuwer Academc Pubshers. Manufactured n The Netherands. A Dervatve-Free Agorthm for Bound Constraned Optmzaton STEFANO LUCIDI ucd@ds.unroma.t
More informationBoundary Value Problems. Lecture Objectives. Ch. 27
Boundar Vaue Probes Ch. 7 Lecture Obectves o understand the dfference between an nta vaue and boundar vaue ODE o be abe to understand when and how to app the shootng ethod and FD ethod. o understand what
More informationStructure and Drive Paul A. Jensen Copyright July 20, 2003
Structure and Drve Paul A. Jensen Copyrght July 20, 2003 A system s made up of several operatons wth flow passng between them. The structure of the system descrbes the flow paths from nputs to outputs.
More informationJournal of Multivariate Analysis
Journa of Mutvarate Anayss 3 (04) 74 96 Contents sts avaabe at ScenceDrect Journa of Mutvarate Anayss journa homepage: www.esever.com/ocate/jmva Hgh-dmensona sparse MANOVA T. Tony Ca a, Yn Xa b, a Department
More informationOn balancing multiple video streams with distributed QoS control in mobile communications
On balancng multple vdeo streams wth dstrbuted QoS control n moble communcatons Arjen van der Schaaf, José Angel Lso Arellano, and R. (Inald) L. Lagendjk TU Delft, Mekelweg 4, 68 CD Delft, The Netherlands
More informationNeural networks. Nuno Vasconcelos ECE Department, UCSD
Neural networs Nuno Vasconcelos ECE Department, UCSD Classfcaton a classfcaton problem has two types of varables e.g. X - vector of observatons (features) n the world Y - state (class) of the world x X
More informationAchieving Optimal Throughput Utility and Low Delay with CSMA-like Algorithms: A Virtual Multi-Channel Approach
IEEE/AM TRANSATIONS ON NETWORKING, VOL. X, NO. XX, XXXXXXX 20X Achevng Optma Throughput Utty and Low Deay wth SMA-ke Agorthms: A Vrtua Mut-hanne Approach Po-Ka Huang, Student Member, IEEE, and Xaojun Ln,
More informationEEE 241: Linear Systems
EEE : Lnear Systems Summary #: Backpropagaton BACKPROPAGATION The perceptron rule as well as the Wdrow Hoff learnng were desgned to tran sngle layer networks. They suffer from the same dsadvantage: they
More informationConsensus Algorithms and Distributed Structure Estimation in Wireless Sensor Networks. Sai Zhang
Consensus Algorthms and Dstrbuted Structure Estmaton n Wreless Sensor Networks by Sa Zhang A Dssertaton Presented n Partal Fulfllment of the Requrements for the Degree Doctor of Phlosophy Approved Aprl
More information3. Stress-strain relationships of a composite layer
OM PO I O U P U N I V I Y O F W N ompostes ourse 8-9 Unversty of wente ng. &ech... tress-stran reatonshps of a composte ayer - Laurent Warnet & emo Aerman.. tress-stran reatonshps of a composte ayer Introducton
More informationModule 3 LOSSY IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module 3 LOSSY IMAGE COMPRESSION SYSTEMS Verson ECE IIT, Kharagpur Lesson 6 Theory of Quantzaton Verson ECE IIT, Kharagpur Instructonal Objectves At the end of ths lesson, the students should be able to:
More information