A Tunable Radial Basis Function Model for Nonlinear System Identification Using Particle Swarm Optimisation

Size: px
Start display at page:

Download "A Tunable Radial Basis Function Model for Nonlinear System Identification Using Particle Swarm Optimisation"

Transcription

1 A Tunable Radal Bass Functon Model for Nonlnear System Identfcaton Usng Partcle Swarm Optmsaton S. Chen, X. Hong, B.L. Lu and C.J. Harrs Abstract A tunable radal bass functon (RBF) networ model s proposed for nonlnear system dentfcaton usng partcle swarm optmsaton (PSO). At each stage of orthogonal forward regresson (OFR) model constructon, PSO optmses one RBF unt s centre vector and dagonal covarance matrx by mnmsng the leave-one-out (LOO) mean square error (MSE). Ths PSO aded OFR automatcally determnes how many tunable RBF nodes are suffcent for modellng. Compared wth the-state-of-the-art local regularsaton asssted orthogonal least squares algorthm based on the LOO MSE crteron for constructng fxed-node RBF networ models, the PSO tuned RBF model constructon produces more parsmonous RBF models wth better generalsaton performance and s computatonally more effcent. I. INTRODUCTION The radal bass functon (RBF) networ s a popular neural networ archtecture for nonlnear system dentfcaton [1]. In ths applcaton, the parameters of a RBF networ, ncludng nodes centre vectors and varances or covarance matrces as well as connectng weghts, can be estmated based on nonlnear optmsaton usng gradent-descent algorthms [2], [3], the expectaton-maxmsaton algorthm [4], [5] or the populaton-based evolutonary algorthms [6], [7]. However, these nonlnear estmaton methods are computatonally expensve and, moreover, the RBF model structure or the number of RBF nodes has to be determned va other means, typcally based on costly cross valdaton. Clusterng algorthms can alternatvely be appled to fnd the RBF centre vectors as well as the assocated bass functon varances [8] [10]. The remanng RBF weghts can then be determned usng the smple lnear least squares (LS) estmate. However, the number of the clusters agan has to be determned va other means, such as cross valdaton. A most popular approach for dentfyng RBF models s to formulate the problem as a lnear regresson by consderng the tranng nput data ponts as canddate RBF centres and to employ a common varance for every RBF node. A parsmonous RBF networ can then be dentfed effcently usng the orthogonal least squares (OLS) algorthm [11] [14]. Smlarly, the support vector machne (SVM) and other sparse ernel modellng methods [15] [17] also place the ernel centres to the tranng nput data ponts and adopt a common ernel varance for every ernel. A sparse ernel model s then sought. Snce the common varance n ths S. Chen and C.J. Harrs are wth School of Electroncs and Computer Scence, Unversty of Southampton, Southampton SO17 1BJ, UK X. Hong s wth School of Systems Engneerng, Unversty of Readng, Readng RG6 6AY, UK B.L. Lu s wth Department of Manufacturng Engneerng and Engneerng Management, Cty Unversty of Hong Kong, Hong Kong, Chna fxed-node RBF model s not provded by the learnng algorthms, t must be determned va cross valdaton. For the ernel methods, such as the SVM, two more hyperparameters must also be specfed va cross valdaton. Our prevous results [14] show that the local regularsaton asssted OLS (LROLS) algorthm based on the leave-one-out (LOO) cross valdaton compares favourably wth other ernel methods, n terms of model sparsty and generalsaton performance as well as effcency of model constructon. Ths LROLS-LOO algorthm [14] offers a state-of-the-art constructon method for fxed-node RBF models. Ths paper consders the tunable RBF model, where each RBF node has a tunable centre vector and an adjustable dagonal covarance matrx. We do not attempt to optmse all the RBF parameters together, as t s a too large and complex nonlnear optmsaton tas. Instead, we adopt an orthogonal forward regresson (OFR) to optmse RBF unts one by one based on the LOO mean square error (MSE). Specfcally, we use partcle swarm optmsaton (PSO) [18], [19] to optmse one RBF node s centre vector and covarance matrx at each stage of the OFR. PSO s a populaton based stochastc optmsaton technque [18], [19] nspred by socal behavour of brd flocng or fsh schools. It s becomng popular due to ts smplcty n mplementaton, ablty to qucly converge to a reasonably good soluton and ts robustness aganst local mnma. The method has been appled to many optmsaton problems successfully [7], [19] [25]. We demonstrate that the proposed PSO aded OFR algorthm for tunable-node RBF models not only produces sparser models and better generalsaton performance but also offers computatonal advantages n model constructon, compared wth the state-of-the-art LROLS-LOO constructon algorthm for fxed-node RBF models [14]. II. IDENTIFICATION USING TUNABLE RBF MODELS Consder the class of dscrete-tme nonlnear systems that can be represented by the followng NARX structure y = f s (y 1,,y my,u 1,,u mu ) + e = f s (x ) + e (1) where u and y are the system nput and output varables, respectvely, m u and m y are the nown lags for u and y, respectvely, e s a zero-mean uncorrelated observaton nose, f s ( ) denotes the unnown system mappng, and x = [x 1, x 2, x m, ] T = [y 1 y my u 1 u mu ] T (2)

2 denotes the system nput vector wth the nown dmenson m = m y + m u. The NARX system (1) s a specal case of the followng generc NARMAX system [26] y = f s (y 1,,y my,u 1,,u mu, e 1,,e me ) + e. (3) The technques developed for the NARX structure can be extended to the general NARMAX system [11], [26], [27]. Gven the tranng data set D K = {x,y } K =1, the tas s to dentfy the system (1) usng the RBF networ model ŷ (M) ˆf (M) = ˆf (M) RBF (x ) = M θ p (x ) = p T M()θ M (4) where RBF ( ) denotes the mappng of the M-term RBF model, M s the number of RBF unts, θ M = [θ 1 θ 2 θ M ] T s the RBF weght vector, and p T M() = [p 1 (x ) p 2 (x ) p M (x )] (5) s the response vector of the M RBF nodes to the nput x. We consder the general RBF regressor of the form ( ) p (x) = ϕ (x µ ) T Σ 1 (x µ ), (6) where µ and Σ = dag{σ 2,1,σ2,2,,σ,m} are the centre vector and dagonal covarance matrx of the th RBF node, respectvely, ϕ( ) s the chosen RBF bass functon. In ths study, the Gaussan bass functon s employed. Let us defne the modellng error at the th tranng data pont (x,y ) as ε (M) = y ŷ (M). (7) Then the regresson model (4) over the tranng set D K can be wrtten n the matrx form y = P M θ M + ε (M), (8) where y = [y 1 y 2 y K ] T s the desred output vector, ε (M) = [ε (M) 1 ε (M) 2 ε (M) K ]T s the modellng error vector of the M-term model, and the regresson matrx P M = [p 1 p 2 p M ] wth the th regressor gven by p = [p (x 1 ) p (x 2 ) p (x K )] T, (9) where 1 M. Note that p s the th column of P M whle p T M () denotes the th row of P M. A. Orthogonal Decomposton Let an orthogonal decomposton of P M be P M = W M A M, where W M = [w 1 w 2 w M ] wth the orthogonal columns that satsfy w Tw l = 0 for l and 1 α 1,2 α 1,M. A M = αm 1,M. (10) The regresson model (8) can alternatvely be presented as y = W M g M + ε (M), (11) where g M = [g 1 g 2 g M ] T satsfes the trangular system A M θ M = g M. Snce the space spanned by the orgnal model bases p ( ), 1 M, s dentcal to the space spanned by the orthogonal model bases, the RBF model output can equvalently be expressed as ŷ (M) = w T M()g M, (12) where w T M () = [w 1() w 2 () w M ()] s the th row of W M. Orthogonal decomposton can be carred out usng the Gram-Schmdt procedure [11]. Usng the model (11) nstead of the orgnal one (8) facltates an effcent OFR model constructon. In partcular, calculaton of the LOO MSE becomes very fast, mang t possble to construct the model by drectly optmsng the model generalsaton capablty rather than mnmsng the tranng MSE [14]. B. OFR Based on LOO Cross Valdaton The evaluaton of model generalsaton capablty s drectly based on the concept of cross valdaton [28], and a commonly used cross valdaton s the LOO cross valdaton wth ts assocated LOO test MSE [29]. Consder the OFR modellng process that has produced the n-node RBF model. Denote the constructed n columns of regressors as W n = [w 1 w 2 w n ], the th model output of ths n-node RBF model dentfed usng the entre tranng data set D K as ŷ (n) = n g w (), (13) and the correspondng th modellng error as ε (n) = y ŷ (n). If we remove the th data pont from the tranng set D K and use the remanng K 1 data ponts D K \(x,y ) to dentfy the n-node RBF model nstead, the test error of the resultng model can be calculated on the data pont (x,y ) not used n tranng. Ths LOO modellng error, denoted as ε (n, ), s gven by [29] ε (n, ) = ε (n) /η(n), (14) where η (n) s referred to as the LOO error weghtng [29]. The LOO MSE for the n-node RBF model s defned as J n = 1 K K ( =1 ε (n, ) ) 2. (15) The LOO MSE J n s a measure of the model generalsaton capablty [28], [29]. For the model (11), J n can be computed very effcently because ε (n) and η (n) can be calculated recursvely usng [14] n = y g w () = ε (n 1) g n w n () (16) and η (n) ε (n) = 1 n w 2 () w T w + λ = η(n 1) w2 n() w T nw n + λ, (17)

3 respectvely, where λ 0 s a small regularsaton parameter [14]. The regularsaton parameter can smply be set to λ = 0 (no regularsaton) or a very small value (10 6 ). We can use an OFR procedure based on ths LOO MSE to construct the RBF nodes one by one. At the nth stage of the constructon, the nth RBF node s determned by mnmsng J n wth respect to µ n and Σ n mn J n (µ n,σ n ). (18) µ n,σ n In the next secton, we wll detal how to use PSO to perform ths optmsaton. The LOO MSE J n s locally convex wth respect to the model sze n [14]. Thus, there exsts an optmal number of RBF nodes M such that: for n M J n decreases as the model sze n ncreases whle J M J M+1. (19) Therefore, ths OFR constructon process s automatcally termnated when the condton (19) s met, yeldng a very small model set contanng only M RBF nodes. After constructng the M-node RBF model usng ths OFR procedure, we may apply the LROLS-LOO algorthm of [14] to automatcally update ndvdual regularsaton parameter for each RBF weght whch may further reduce the model sze. Ths refnement wth the LROLS-LOO algorthm requres a very small amount of computaton snce the regresson matrx P M s completely specfed wth only a few columns. III. PARTICLE SWARM OPTIMISATION AIDED OFR The tas at the nth stage of the OFR for constructng a tunable RBF networ s to solve the optmsaton problem (18). Ths optmsaton problem s non-convex wth respect to µ n and Σ n, and we adopt PSO [18], [19] to determne µ n and Σ n. Our study demonstrates that PSO s partcularly suted for the optmsaton tas (18). A. Partcle Swarm Optmsaton In a PSO algorthm [19], a group of S partcles that represent potental solutons are ntalsed over the search space randomly. Each partcle has a ftness value assocated wth t, based on the related cost functon of the optmsaton problem, and ths ftness value s evaluated at each teraton. The best poston, pb, vsted by each partcle provdes the partcle the so-called cogntve nformaton, whle the best poston vsted so far among the entre group, gb, offers the socal nformaton. The pbs and gb are updated at each teraton. Each partcle has ts own velocty to drect ts flyng, whch reles on ts prevous speed as well as ts cogntve and socal nformaton. In each teraton, the velocty and the poston of the partcle are updated based on the followng equatons = ξ v [l] + rand() c 1 (pb [l] u [l] ) +rand() c 2 (gb [l] u [l] ), (20) = u [l] +, (21) l teraton ndex, 1 l L, L s the maxmum number of teratons partcle ndex, 1 S, S s the partcle sze v [l] velocty of th partcle at lth teraton. The jth elements of v [l] are n range [ V jmax, V jmax ] ξ nerta weght c j the acceleraton coeffcents, j = 1,2 rand() unform random number between 0 and 1 u [l] pb [l] gb [l] poston of th partcle at lth teraton. The jth elements of u [l] are n range [U jmn, U jmax ] best poston that the th partcle has vsted upto lth teraton best poston that all the partcles have vsted upto lth teraton It s reported n [20] that usng a tme varyng acceleraton coeffcent (TVAC) enhances the performance of PSO. The reason s that at the ntal stages, a large cogntve component and a small socal component help partcles to wander around the search space and to avod local mnma. In the later stages, a small cogntve component and a large socal component help partcles to converge qucly to a global mnmum. We adopt ths TVAC mechansm n whch c 1 for the cogntve component s reduced from 2.5 to 0.5 and c 2 for the socal component vares from 0.5 to 2.5 durng the teratve procedure accordng to c 1 = l 1.0 L and c 2 = l 1.0 L, (22) respectvely. In our experment, we have found out that usng a random nerta weght, ξ = rand(), acheves better performance than usng ξ = 0 or constant ξ. If the velocty n (20) approaches zero, t s rentalsed randomly to proportonal to the maxmum velocty j = ±rand() γ V jmax, (23) where j denotes the jth element of and γ = 0.1 s a constant. B. PSO Aded OFR for Tunable RBF Model The procedure of usng the PSO aded OFR to determne the nth RBF node s now summarsed. Let u be the vector that contans µ n and Σ n. The dmenson of u s thus 2m. The search space s specfed by { = mn{x Ujmn j,,1 K}, 1 j m, (24) U jmax = max{x j,,1 K}, U jmn = σ 2 mn, U jmax = σ 2 max, 1 + m j 2m. (25) The velocty bounds are defned by V jmax = 0.5 (U jmax U jmn ), 1 j 2m. (26) Gve the followng ntal condtons } ε (0) = y and η (0) = 1, 1 K, J 0 = 1 N yt y = 1 K N =1 y2. (27) Specfy the number of teratons L and the partcle sze S.

4 Intalsaton. Randomly generate the partcles u [0], 1 S, n the search space defned by (24) and (25). Set the ntal veloctes v [0] = 0 2m, 1 S, where 0 2m denotes the zero vector of dmenson 2m. Intalse J n (gb [0] ) and J n (pb [0] ), 1 S, to a value larger than J 0. Iteraton loop. For (l = 0; l L; l + +) { Orthogonalsaton and cost functon evaluaton. 1) For 1 S, generate p ) n from u [l], the canddates for the nth model column, accordng to (9), and orthogonalse them accordng to [11] α ) j,n = wt j p ) n/w T j w j, 1 j < n, (28) ( gn ) = n 1 wn ) = p ) n α ) j,n w j, (29) w ) n j=1 ) ( T ( ) T y/ wn ) w ) n + λ ). (30) 2) For 1 S, calculate the LOO cost for each u [l] ε (n) η (n) () = ε(n 1) wn ) ()gn ), 1 K, (31) ( ) 2 wn ) () () = η(n 1) ( ) T, 1 K, ) wn + λ J ) n = 1 K w ) n ( K =1 ε (n) η (n) ) (32) 2 (), (33) () where wn ) () s the th element of wn ). Update cogntve and socal nformaton. 1) For ( = 1; S; ++) If (Jn ) < J n (pb [l] )) J n (pb [l] ) = J) n ; = u [l] pb [l] End f; 2) Fnd ; = arg mn 1 S J n(pb [l] ). If (J n (pb [l] ) < J n(gb [l] )) J n (gb [l] ) = J n (pb [l] ); gb [l] = pb [l] ; End f; Update veloctes and postons of partcles 1) For ( = 1; S; ++) = rand() v [l] + rand() c 1 (pb [l] u [l] +rand() c 2 (gb [l] u [l] ); For (j = 1; j 2m; j++) If ( j == 0) If (rand() < 0.5) j = rand() γ V jmax ; Else j = rand() γ V jmax ; End f; ) End f; If ( j > V jmax ) j = V jmax ; Else f ( j < V jmax ) v l+1 End f; j = V jmax ; 2) For ( = 1; S; ++) = u [l] + ; For (j = 1; j 2m; j++) If ( j > U jmax ) j = U jmax ; Else f ( j < U jmn ) j = U jmn ; End f } End of teraton loop Ths yelds the soluton u = gb [L],.e. µ n and Σ n of the nth RBF node, the nth model column p n, the orthogonalsaton coeffcents α j,n, 1 j < n, the correspondng orthogonal model column w n, and the weght g n, as well as the n- term modellng errors ε (n) and the assocated LOO error weghtngs η (n) for 1 K. C. Computatonal Complexty Comparson We compare the computatonal complexty of the proposed PSO aded OFR algorthm for tunable RBF models wth that of the LROLS-LOO algorthm for fxed-node RBF models [14]. The LROLS-LOO algorthm nvolves a few teratons. The frst teraton wors on the K K full regresson matrx and selects a subset of M RBF nodes, where M K. The computatonal complexty of the algorthm s domnated by ths frst teraton, and the complexty of the rest teratons s neglgble. For the LROLS-LOO algorthm, t can be verfy that the computatonal complexty of one model column orthogonalsaton and the assocated LOO cost functon evaluaton s O(K). Thus, we can characterse the complexty of the algorthm by the requred number of the LOO cost functon evaluatons and assocated model column orthogonalsatons, whch s gven by C LROLS LOO M +1 (K ( 1)) ( M + 1 ) K, (34) where the second approxmaton arrves because M K. Snce for the PSO aded OFR algorthm, the computatonal requrement of one model column orthogonalsaton and the assocated LOO cost functon evaluaton s also O(K), we can also characterse the computatonal requrements of the algorthm by the number of the LOO cost functon evaluatons and assocated model column orthogonalsatons.

5 TABLE I COMPARISON OF THE TWO GAUSSIAN RBF NETWORK MODELS OBTAINED BY THE LROLS-LOO AND PSO-OFR ALGORITHMS. Algorthm RBF type Model sze Tranng MSE Test MSE complexty LROLS-LOO fxed O(500) PSO-OFR tunable O(500) Ths number s gven as C PSO OFR (M + 1) S L, (35) where M s the constructed model sze, S the partcle sze and L the number of teratons. Snce the model sze M s usually much smaller than the model sze M obtaned by the LROLS-LOO algorthm, we always have C PSO OFR < C LROLS LOO whenever K S L. Thus, the PSO aded OFR algorthm for constructng tunable-node RBF models has clearly computatonal advantages over the LROLS-LOO algorthm for selectng fxed-node RBF models when the sze of the tranng data set s large. Note that the PSO algorthm s very effcent. Our expermental results have shown that typcally L = 20 and S = 10 to 20 are often suffcent. Furthermore, the complexty of (35) s the true complexty of the PSO aded OFR algorthm, whle the complexty of (34) s the complexty of the LROLS-LOO algorthm gven a RBF varance. Snce the RBF varance s not provded by the LROLS-LOO algorthm, t must be determned based cross valdaton. Tang ths fact nto account, computatonal advantages of the proposed PSO aded OFR algorthm becomes even more sgnfcant. (b) Fg. 1. Lqud level data: (a) system nput u, and (b) system output y. (a) IV. LIQUID LEVEL DATA SET MODELLING The data set was collected from a nonlnear lqud level system, whch conssted of a DC water pump feedng a concal flas whch n turn fed a square tan. The system nput u was the voltage to the pump motor and the system output y was the water level n the concal flas [30]. Fg. 1 shows the 1000 data ponts of the data set used n ths experment. From the data set, 1000 data ponts {x,y } were constructed wth x gven by x = [y 1 y 2 y 3 u 1 u 2 u 3 u 4 ] T. (36) The frst 500 pars of the data were used for tranng and the remanng 500 pars for testng the constructed model. For the fxed-node RBF model wth every tranng nput data used as a candadate RBF centre vector, an approprate RBF varance was found to be σ 2 = 2.0 va a grd search based cross valdaton usng the LROLS-LOO algorthm [14]. Wth σ 2 = 2.0, the LROLS-LOO algorthm automatcally selected a model set of M = 30 nodes from the canddate set of K = 500 potental nodes. The results obtaned by the LROLS-LOO algorthm are gven n Table I, where the complexty was computed as C LROLS LOO = = for the gven σ 2 = 2.0. For constructng the tunable-node RBF model, we set the partcle sze to S = 10 and the number of teratons to L = 20. The PSO aded OFR algorthm automatcally constructed a model set of M = 20 nodes. The results produced by the the PSO aded OFR are also lsted n Table I, where the complexty was gven by C PSO OFR = = Fg. 2 shows the model predcton ŷ and the predcton error ε = y ŷ produced by the 20-node RBF model constructed usng the PSO aded OFR algorthm. For ths example, the PSO aded OFR algorthm has clear advantages over the benchmar LROLS-LOO algorthm, n terms of model sze and generalsaton capablty as well as complexty of model constructon. V. CONCLUSIONS In ths contrbuton we have proposed a novel PSO aded OFR algorthm to construct tunable-node RBF networ models for nonlnear system dentfcaton. Unle the standard fxed-node RBF model where the RBF centre vectors are placed at the tranng nput data ponts and a common RBF varance s used for every RBF node, the proposed algorthm optmses one RBF node s centre vector and dagonal covarance matrx by mnmsng the LOO MSE at each stage of the OFR. The model constructon procedure automatcally determnes how many tunable nodes are suffcent, and PSO ensures that ths model constructon procedure s computatonally very effcent. Usng the best exstng algorthm for fxed-node RBF models, the LROLS-LOO algorthm, as

6 (a) (b) Fg. 2. Modellng of the lqud level data by the 20-node RBF networ constructed usng the PSO aded OFR: (a) model predcton ŷ supermposed on system output y, and (b) model predcton error ε = y ŷ. the benchmar, t has been shown that the proposed PSO aded OFR algorthm for constructng tunable-node RBF models offers clear advantages over the benchmar LROLS- LOO algorthm for constructng fxed-node RBF models, n terms of more parsmonous model and better generalsaton performance as well as more effcent model constructon. REFERENCES [1] S. Chen, S.A. Bllngs, C.F.N. Cowan and P.M. Grant, Non-lnear systems dentfcaton usng radal bass functons, Int. J. Systems Sc., Vol.21, pp , [2] S. Chen, C.F.N. Cowan, S.A. Bllngs and P.M. Grant, Parallel recursve predcton error algorthm for tranng layered neural networs, Int. J. Control, Vol.51, pp , [3] S. McLoone, M.D. Brown, G. Irwn and A. Lghtbody, A hybrd lnear/nonlnear tranng algorthm for feedforward neural networs, IEEE Trans. Neural Networs, Vol.9, No.4, pp , [4] Z.R. Yang and S. Chen, Robust maxmum lelhood tranng of heteroscedastc probablstc neural networs, Neural Networs, Vol.11, pp , [5] M.-W. Ma and S.-Y. Kung, Estmaton of ellptcal bass functon parameters by the EM algorthm wth applcaton to speaer verfcaton, IEEE Trans. Neural Networs, Vol.11, No.4, pp , [6] J. Gonzalez, I. Rojas, J. Ortega, H. Pomares, F.J. Fernandez and A.F. Daz, Multobjectve evolutonary optmzaton of the sze, shape, and poston parameters of radal bass functon networs for functon approxmaton, IEEE Trans. Neural Networs, Vol.14, No.6, pp , [7] H.-M. Feng, Self-generaton RBFNs usng evolutonal PSO learnng, Neurocomputng, Vol.70, No.1-3, pp , [8] J. Moody and C.J. Daren, Fast learnng n networs of locally-tuned processng unts, Neural Computaton, Vol.1, pp , [9] S. Chen, S.A. Bllngs and P.M. Grant, Recursve hybrd algorthm for non-lnear system dentfcaton usng radal bass functon networs, Int. J. Control, Vol.55, pp , [10] S. Chen, Nonlnear tme seres modellng and predcton usng Gaussan RBF networs wth enhanced clusterng and RLS learnng, Electroncs Letters, Vol.31, No.2, pp , [11] S. Chen, S.A. Bllngs and W. Luo, Orthogonal least squares methods and ther applcaton to non-lnear system dentfcaton, Int. J. Control, Vol.50, No.5, pp , [12] S. Chen, C.F.N. Cowan and P.M. Grant, Orthogonal least squares learnng algorthm for radal bass functon networs, IEEE Trans. Neural Networs, Vol.2, No.2, pp , [13] S. Chen, X. Hong and C.J. Harrs, Sparse ernel regresson modellng usng combned locally regularzed orthogonal least squares and D- optmalty expermental desgn, IEEE Trans. Automatc Control, Vol.48, No.6, pp , [14] S. Chen, X. Hong, C.J. Harrs and P.M. Sharey, Sparse modellng usng orthogonal forward regresson wth PRESS statstc and regularzaton, IEEE Trans. Systems, Man and Cybernetcs, Part B, Vol.34, No.2, pp , [15] V. Vapn, The Nature of Statstcal Learnng Theory. New Yor: Sprnger-Verlag, [16] M.E. Tppng, Sparse Bayesan learnng and the relevance vector machne, J. Machne Learnng Research, Vol.1, pp , [17] B. Schölopf and A.J. Smola, Learnng wth Kernels: Support Vector Machnes, Regularzaton, Optmzaton, and Beyond. Cambrdge, MA: MIT Press, [18] J. Kennedy and R. Eberhart, Partcle swarm optmzaton, n Proc IEEE Int. Conf. Neural Networs (Perth, Australa), Nov.27- Dec.1, 1995, Vol.4, pp [19] J. Kennedy and R. Eberhart, Swarm Intellgence. Morgan Kaufmann, [20] A. Ratnaweera, S.K. Halgamuge and H.C. Watson, Self-organzng herarchcal partcle swarm optmzer wth tme-varyng acceleraton coeffcents, IEEE Trans. Evolutonary Computaton, Vol.8, No.3, pp , [21] S.M. Guru, S.K. Halgamuge and S. Fernando, Partcle swarm optmsers for cluster formaton n wreless sensor networs, n Proc Int. Conf. Intellgent Sensors, Sensor Networs and Informaton Processng (Melbourne, Australa), Dec.5-8, 2005, pp [22] K.K. Soo, Y.M. Su, W.S. Chan, L. Yang and R.S. Chen, Partcleswarm-optmzaton-based multuser detector for CDMA communcatons, IEEE Trans. Vehcular Technology, Vol.56, No.5, pp , [23] T.-Y. Sun, C.-C. Lu, T.-Y. Tsa and S.-T. Hseh, Adequate determnaton of a band of wavelet threshold for nose cancellaton usng partcle swarm optmzaton, n Proc. CEC 2008 (Hong Kong, Chna), June 1-6, 2008, pp [24] F.A. Guerra and L.S. Coelho, Mult-step ahead nonlnear dentfcaton of Lorenz s chaotc system usng radal bass functon neural networ wth learnng by clusterng and partcle swarm optmszaton, Chaos, Soltons and Fractals, Vol.35, No.5, pp , [25] W.-F. Leong and G.G. Yen, PSO-based multobjectve optmzaton wth dynamc populaton sze and adaptve local archves, IEEE Trans. Systems, Man and Cybernetcs, Part B, Vol.38, No.5, pp , [26] S. Chen and S.A. Bllngs, Representaton of non-lnear systems: The NARMAX model, Int. J. Control, Vol.49, No.3, pp , [27] S. Chen, S.A. Bllngs, C.F.N. Cowan and P.M. Grant, Practcal dentfcaton of NARMAX models usng radal bass functons, Int. J. Control, Vol.52, pp , [28] M. Stone, Cross valdaton choce and assessment of statstcal predctons, J. Royal Statstcs Socety Seres B, Vol.36, pp , [29] R.H. Myers, Classcal and Modern Regresson wth Applcatons. 2nd Edton, Boston: PWS-KENT, [30] S.A. Bllngs and W.S.F. Voon, A predcton-error and stepwseregresson estmaton algorthm for non-lnear systems, Int. J. Control, Vol.44, pp , 1986.

Forecasting the Direction and Strength of Stock Market Movement

Forecasting the Direction and Strength of Stock Market Movement Forecastng the Drecton and Strength of Stock Market Movement Jngwe Chen Mng Chen Nan Ye cjngwe@stanford.edu mchen5@stanford.edu nanye@stanford.edu Abstract - Stock market s one of the most complcated systems

More information

The Development of Web Log Mining Based on Improve-K-Means Clustering Analysis

The Development of Web Log Mining Based on Improve-K-Means Clustering Analysis The Development of Web Log Mnng Based on Improve-K-Means Clusterng Analyss TngZhong Wang * College of Informaton Technology, Luoyang Normal Unversty, Luoyang, 471022, Chna wangtngzhong2@sna.cn Abstract.

More information

Patterns Antennas Arrays Synthesis Based on Adaptive Particle Swarm Optimization and Genetic Algorithms

Patterns Antennas Arrays Synthesis Based on Adaptive Particle Swarm Optimization and Genetic Algorithms IJCSI Internatonal Journal of Computer Scence Issues, Vol. 1, Issue 1, No 2, January 213 ISSN (Prnt): 1694-784 ISSN (Onlne): 1694-814 www.ijcsi.org 21 Patterns Antennas Arrays Synthess Based on Adaptve

More information

Gender Classification for Real-Time Audience Analysis System

Gender Classification for Real-Time Audience Analysis System Gender Classfcaton for Real-Tme Audence Analyss System Vladmr Khryashchev, Lev Shmaglt, Andrey Shemyakov, Anton Lebedev Yaroslavl State Unversty Yaroslavl, Russa vhr@yandex.ru, shmaglt_lev@yahoo.com, andrey.shemakov@gmal.com,

More information

What is Candidate Sampling

What is Candidate Sampling What s Canddate Samplng Say we have a multclass or mult label problem where each tranng example ( x, T ) conssts of a context x a small (mult)set of target classes T out of a large unverse L of possble

More information

8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by

8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by 6 CHAPTER 8 COMPLEX VECTOR SPACES 5. Fnd the kernel of the lnear transformaton gven n Exercse 5. In Exercses 55 and 56, fnd the mage of v, for the ndcated composton, where and are gven by the followng

More information

Logistic Regression. Lecture 4: More classifiers and classes. Logistic regression. Adaboost. Optimization. Multiple class classification

Logistic Regression. Lecture 4: More classifiers and classes. Logistic regression. Adaboost. Optimization. Multiple class classification Lecture 4: More classfers and classes C4B Machne Learnng Hlary 20 A. Zsserman Logstc regresson Loss functons revsted Adaboost Loss functons revsted Optmzaton Multple class classfcaton Logstc Regresson

More information

v a 1 b 1 i, a 2 b 2 i,..., a n b n i.

v a 1 b 1 i, a 2 b 2 i,..., a n b n i. SECTION 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS 455 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS All the vector spaces we have studed thus far n the text are real vector spaces snce the scalars are

More information

Document Clustering Analysis Based on Hybrid PSO+K-means Algorithm

Document Clustering Analysis Based on Hybrid PSO+K-means Algorithm Document Clusterng Analyss Based on Hybrd PSO+K-means Algorthm Xaohu Cu, Thomas E. Potok Appled Software Engneerng Research Group, Computatonal Scences and Engneerng Dvson, Oak Rdge Natonal Laboratory,

More information

A hybrid global optimization algorithm based on parallel chaos optimization and outlook algorithm

A hybrid global optimization algorithm based on parallel chaos optimization and outlook algorithm Avalable onlne www.ocpr.com Journal of Chemcal and Pharmaceutcal Research, 2014, 6(7):1884-1889 Research Artcle ISSN : 0975-7384 CODEN(USA) : JCPRC5 A hybrd global optmzaton algorthm based on parallel

More information

CS 2750 Machine Learning. Lecture 3. Density estimation. CS 2750 Machine Learning. Announcements

CS 2750 Machine Learning. Lecture 3. Density estimation. CS 2750 Machine Learning. Announcements Lecture 3 Densty estmaton Mlos Hauskrecht mlos@cs.ptt.edu 5329 Sennott Square Next lecture: Matlab tutoral Announcements Rules for attendng the class: Regstered for credt Regstered for audt (only f there

More information

Causal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting

Causal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting Causal, Explanatory Forecastng Assumes cause-and-effect relatonshp between system nputs and ts output Forecastng wth Regresson Analyss Rchard S. Barr Inputs System Cause + Effect Relatonshp The job of

More information

Calculation of Sampling Weights

Calculation of Sampling Weights Perre Foy Statstcs Canada 4 Calculaton of Samplng Weghts 4.1 OVERVIEW The basc sample desgn used n TIMSS Populatons 1 and 2 was a two-stage stratfed cluster desgn. 1 The frst stage conssted of a sample

More information

Luby s Alg. for Maximal Independent Sets using Pairwise Independence

Luby s Alg. for Maximal Independent Sets using Pairwise Independence Lecture Notes for Randomzed Algorthms Luby s Alg. for Maxmal Independent Sets usng Parwse Independence Last Updated by Erc Vgoda on February, 006 8. Maxmal Independent Sets For a graph G = (V, E), an ndependent

More information

A Binary Particle Swarm Optimization Algorithm for Lot Sizing Problem

A Binary Particle Swarm Optimization Algorithm for Lot Sizing Problem Journal o Economc and Socal Research 5 (2), -2 A Bnary Partcle Swarm Optmzaton Algorthm or Lot Szng Problem M. Fath Taşgetren & Yun-Cha Lang Abstract. Ths paper presents a bnary partcle swarm optmzaton

More information

Vision Mouse. Saurabh Sarkar a* University of Cincinnati, Cincinnati, USA ABSTRACT 1. INTRODUCTION

Vision Mouse. Saurabh Sarkar a* University of Cincinnati, Cincinnati, USA ABSTRACT 1. INTRODUCTION Vson Mouse Saurabh Sarkar a* a Unversty of Cncnnat, Cncnnat, USA ABSTRACT The report dscusses a vson based approach towards trackng of eyes and fngers. The report descrbes the process of locatng the possble

More information

Exhaustive Regression. An Exploration of Regression-Based Data Mining Techniques Using Super Computation

Exhaustive Regression. An Exploration of Regression-Based Data Mining Techniques Using Super Computation Exhaustve Regresson An Exploraton of Regresson-Based Data Mnng Technques Usng Super Computaton Antony Daves, Ph.D. Assocate Professor of Economcs Duquesne Unversty Pttsburgh, PA 58 Research Fellow The

More information

Support Vector Machines

Support Vector Machines Support Vector Machnes Max Wellng Department of Computer Scence Unversty of Toronto 10 Kng s College Road Toronto, M5S 3G5 Canada wellng@cs.toronto.edu Abstract Ths s a note to explan support vector machnes.

More information

Forecasting the Demand of Emergency Supplies: Based on the CBR Theory and BP Neural Network

Forecasting the Demand of Emergency Supplies: Based on the CBR Theory and BP Neural Network 700 Proceedngs of the 8th Internatonal Conference on Innovaton & Management Forecastng the Demand of Emergency Supples: Based on the CBR Theory and BP Neural Network Fu Deqang, Lu Yun, L Changbng School

More information

Module 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur

Module 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..

More information

L10: Linear discriminants analysis

L10: Linear discriminants analysis L0: Lnear dscrmnants analyss Lnear dscrmnant analyss, two classes Lnear dscrmnant analyss, C classes LDA vs. PCA Lmtatons of LDA Varants of LDA Other dmensonalty reducton methods CSCE 666 Pattern Analyss

More information

LSSVM-ABC Algorithm for Stock Price prediction Osman Hegazy 1, Omar S. Soliman 2 and Mustafa Abdul Salam 3

LSSVM-ABC Algorithm for Stock Price prediction Osman Hegazy 1, Omar S. Soliman 2 and Mustafa Abdul Salam 3 LSSVM-ABC Algorthm for Stock Prce predcton Osman Hegazy 1, Omar S. Solman 2 and Mustafa Abdul Salam 3 1, 2 (Faculty of Computers and Informatcs, Caro Unversty, Egypt) 3 (Hgher echnologcal Insttute (H..I),

More information

Feature selection for intrusion detection. Slobodan Petrović NISlab, Gjøvik University College

Feature selection for intrusion detection. Slobodan Petrović NISlab, Gjøvik University College Feature selecton for ntruson detecton Slobodan Petrovć NISlab, Gjøvk Unversty College Contents The feature selecton problem Intruson detecton Traffc features relevant for IDS The CFS measure The mrmr measure

More information

Financial market forecasting using a two-step kernel learning method for the support vector regression

Financial market forecasting using a two-step kernel learning method for the support vector regression Ann Oper Res (2010) 174: 103 120 DOI 10.1007/s10479-008-0357-7 Fnancal market forecastng usng a two-step kernel learnng method for the support vector regresson L Wang J Zhu Publshed onlne: 28 May 2008

More information

Damage detection in composite laminates using coin-tap method

Damage detection in composite laminates using coin-tap method Damage detecton n composte lamnates usng con-tap method S.J. Km Korea Aerospace Research Insttute, 45 Eoeun-Dong, Youseong-Gu, 35-333 Daejeon, Republc of Korea yaeln@kar.re.kr 45 The con-tap test has the

More information

Project Networks With Mixed-Time Constraints

Project Networks With Mixed-Time Constraints Project Networs Wth Mxed-Tme Constrants L Caccetta and B Wattananon Western Australan Centre of Excellence n Industral Optmsaton (WACEIO) Curtn Unversty of Technology GPO Box U1987 Perth Western Australa

More information

An Interest-Oriented Network Evolution Mechanism for Online Communities

An Interest-Oriented Network Evolution Mechanism for Online Communities An Interest-Orented Network Evoluton Mechansm for Onlne Communtes Cahong Sun and Xaopng Yang School of Informaton, Renmn Unversty of Chna, Bejng 100872, P.R. Chna {chsun,yang}@ruc.edu.cn Abstract. Onlne

More information

Logical Development Of Vogel s Approximation Method (LD-VAM): An Approach To Find Basic Feasible Solution Of Transportation Problem

Logical Development Of Vogel s Approximation Method (LD-VAM): An Approach To Find Basic Feasible Solution Of Transportation Problem INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME, ISSUE, FEBRUARY ISSN 77-866 Logcal Development Of Vogel s Approxmaton Method (LD- An Approach To Fnd Basc Feasble Soluton Of Transportaton

More information

Lecture 2: Single Layer Perceptrons Kevin Swingler

Lecture 2: Single Layer Perceptrons Kevin Swingler Lecture 2: Sngle Layer Perceptrons Kevn Sngler kms@cs.str.ac.uk Recap: McCulloch-Ptts Neuron Ths vastly smplfed model of real neurons s also knon as a Threshold Logc Unt: W 2 A Y 3 n W n. A set of synapses

More information

SCHEDULING OF CONSTRUCTION PROJECTS BY MEANS OF EVOLUTIONARY ALGORITHMS

SCHEDULING OF CONSTRUCTION PROJECTS BY MEANS OF EVOLUTIONARY ALGORITHMS SCHEDULING OF CONSTRUCTION PROJECTS BY MEANS OF EVOLUTIONARY ALGORITHMS Magdalena Rogalska 1, Wocech Bożeko 2,Zdzsław Heduck 3, 1 Lubln Unversty of Technology, 2- Lubln, Nadbystrzycka 4., Poland. E-mal:rogalska@akropols.pol.lubln.pl

More information

PSYCHOLOGICAL RESEARCH (PYC 304-C) Lecture 12

PSYCHOLOGICAL RESEARCH (PYC 304-C) Lecture 12 14 The Ch-squared dstrbuton PSYCHOLOGICAL RESEARCH (PYC 304-C) Lecture 1 If a normal varable X, havng mean µ and varance σ, s standardsed, the new varable Z has a mean 0 and varance 1. When ths standardsed

More information

benefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).

benefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ). REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or

More information

Face Verification Problem. Face Recognition Problem. Application: Access Control. Biometric Authentication. Face Verification (1:1 matching)

Face Verification Problem. Face Recognition Problem. Application: Access Control. Biometric Authentication. Face Verification (1:1 matching) Face Recognton Problem Face Verfcaton Problem Face Verfcaton (1:1 matchng) Querymage face query Face Recognton (1:N matchng) database Applcaton: Access Control www.vsage.com www.vsoncs.com Bometrc Authentcaton

More information

A Secure Password-Authenticated Key Agreement Using Smart Cards

A Secure Password-Authenticated Key Agreement Using Smart Cards A Secure Password-Authentcated Key Agreement Usng Smart Cards Ka Chan 1, Wen-Chung Kuo 2 and Jn-Chou Cheng 3 1 Department of Computer and Informaton Scence, R.O.C. Mltary Academy, Kaohsung 83059, Tawan,

More information

Least Squares Fitting of Data

Least Squares Fitting of Data Least Squares Fttng of Data Davd Eberly Geoetrc Tools, LLC http://www.geoetrctools.co/ Copyrght c 1998-2016. All Rghts Reserved. Created: July 15, 1999 Last Modfed: January 5, 2015 Contents 1 Lnear Fttng

More information

Recurrence. 1 Definitions and main statements

Recurrence. 1 Definitions and main statements Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.

More information

1 Example 1: Axis-aligned rectangles

1 Example 1: Axis-aligned rectangles COS 511: Theoretcal Machne Learnng Lecturer: Rob Schapre Lecture # 6 Scrbe: Aaron Schld February 21, 2013 Last class, we dscussed an analogue for Occam s Razor for nfnte hypothess spaces that, n conjuncton

More information

Inequality and The Accounting Period. Quentin Wodon and Shlomo Yitzhaki. World Bank and Hebrew University. September 2001.

Inequality and The Accounting Period. Quentin Wodon and Shlomo Yitzhaki. World Bank and Hebrew University. September 2001. Inequalty and The Accountng Perod Quentn Wodon and Shlomo Ytzha World Ban and Hebrew Unversty September Abstract Income nequalty typcally declnes wth the length of tme taen nto account for measurement.

More information

A New Task Scheduling Algorithm Based on Improved Genetic Algorithm

A New Task Scheduling Algorithm Based on Improved Genetic Algorithm A New Task Schedulng Algorthm Based on Improved Genetc Algorthm n Cloud Computng Envronment Congcong Xong, Long Feng, Lxan Chen A New Task Schedulng Algorthm Based on Improved Genetc Algorthm n Cloud Computng

More information

The Greedy Method. Introduction. 0/1 Knapsack Problem

The Greedy Method. Introduction. 0/1 Knapsack Problem The Greedy Method Introducton We have completed data structures. We now are gong to look at algorthm desgn methods. Often we are lookng at optmzaton problems whose performance s exponental. For an optmzaton

More information

Biometric Signature Processing & Recognition Using Radial Basis Function Network

Biometric Signature Processing & Recognition Using Radial Basis Function Network Bometrc Sgnature Processng & Recognton Usng Radal Bass Functon Network Ankt Chadha, Neha Satam, and Vbha Wal Abstract- Automatc recognton of sgnature s a challengng problem whch has receved much attenton

More information

Imperial College London

Imperial College London F. Fang 1, C.C. Pan 1, I.M. Navon 2, M.D. Pggott 1, G.J. Gorman 1, P.A. Allson 1 and A.J.H. Goddard 1 1 Appled Modellng and Computaton Group Department of Earth Scence and Engneerng Imperal College London,

More information

GRAVITY DATA VALIDATION AND OUTLIER DETECTION USING L 1 -NORM

GRAVITY DATA VALIDATION AND OUTLIER DETECTION USING L 1 -NORM GRAVITY DATA VALIDATION AND OUTLIER DETECTION USING L 1 -NORM BARRIOT Jean-Perre, SARRAILH Mchel BGI/CNES 18.av.E.Beln 31401 TOULOUSE Cedex 4 (France) Emal: jean-perre.barrot@cnes.fr 1/Introducton The

More information

A Binary Quantum-behaved Particle Swarm Optimization Algorithm with Cooperative Approach

A Binary Quantum-behaved Particle Swarm Optimization Algorithm with Cooperative Approach IJCSI Internatonal Journal of Computer Scence Issues, Vol., Issue, No, January 3 ISSN (Prnt): 694-784 ISSN (Onlne): 694-84 www.ijcsi.org A Bnary Quantum-behave Partcle Swarm Optmzaton Algorthm wth Cooperatve

More information

+ + + - - This circuit than can be reduced to a planar circuit

+ + + - - This circuit than can be reduced to a planar circuit MeshCurrent Method The meshcurrent s analog of the nodeoltage method. We sole for a new set of arables, mesh currents, that automatcally satsfy KCLs. As such, meshcurrent method reduces crcut soluton to

More information

Ants Can Schedule Software Projects

Ants Can Schedule Software Projects Ants Can Schedule Software Proects Broderck Crawford 1,2, Rcardo Soto 1,3, Frankln Johnson 4, and Erc Monfroy 5 1 Pontfca Unversdad Católca de Valparaíso, Chle FrstName.Name@ucv.cl 2 Unversdad Fns Terrae,

More information

PERRON FROBENIUS THEOREM

PERRON FROBENIUS THEOREM PERRON FROBENIUS THEOREM R. CLARK ROBINSON Defnton. A n n matrx M wth real entres m, s called a stochastc matrx provded () all the entres m satsfy 0 m, () each of the columns sum to one, m = for all, ()

More information

Period and Deadline Selection for Schedulability in Real-Time Systems

Period and Deadline Selection for Schedulability in Real-Time Systems Perod and Deadlne Selecton for Schedulablty n Real-Tme Systems Thdapat Chantem, Xaofeng Wang, M.D. Lemmon, and X. Sharon Hu Department of Computer Scence and Engneerng, Department of Electrcal Engneerng

More information

An Enhanced Super-Resolution System with Improved Image Registration, Automatic Image Selection, and Image Enhancement

An Enhanced Super-Resolution System with Improved Image Registration, Automatic Image Selection, and Image Enhancement An Enhanced Super-Resoluton System wth Improved Image Regstraton, Automatc Image Selecton, and Image Enhancement Yu-Chuan Kuo ( ), Chen-Yu Chen ( ), and Chou-Shann Fuh ( ) Department of Computer Scence

More information

Performance Analysis and Coding Strategy of ECOC SVMs

Performance Analysis and Coding Strategy of ECOC SVMs Internatonal Journal of Grd and Dstrbuted Computng Vol.7, No. (04), pp.67-76 http://dx.do.org/0.457/jgdc.04.7..07 Performance Analyss and Codng Strategy of ECOC SVMs Zhgang Yan, and Yuanxuan Yang, School

More information

Hybrid-Learning Methods for Stock Index Modeling

Hybrid-Learning Methods for Stock Index Modeling Hybrd-Learnng Methods for Stock Index Modelng 63 Chapter IV Hybrd-Learnng Methods for Stock Index Modelng Yuehu Chen, Jnan Unversty, Chna Ajth Abraham, Chung-Ang Unversty, Republc of Korea Abstract The

More information

Ring structure of splines on triangulations

Ring structure of splines on triangulations www.oeaw.ac.at Rng structure of splnes on trangulatons N. Vllamzar RICAM-Report 2014-48 www.rcam.oeaw.ac.at RING STRUCTURE OF SPLINES ON TRIANGULATIONS NELLY VILLAMIZAR Introducton For a trangulated regon

More information

A GENERAL APPROACH FOR SECURITY MONITORING AND PREVENTIVE CONTROL OF NETWORKS WITH LARGE WIND POWER PRODUCTION

A GENERAL APPROACH FOR SECURITY MONITORING AND PREVENTIVE CONTROL OF NETWORKS WITH LARGE WIND POWER PRODUCTION A GENERAL APPROACH FOR SECURITY MONITORING AND PREVENTIVE CONTROL OF NETWORKS WITH LARGE WIND POWER PRODUCTION Helena Vasconcelos INESC Porto hvasconcelos@nescportopt J N Fdalgo INESC Porto and FEUP jfdalgo@nescportopt

More information

Lecture 5,6 Linear Methods for Classification. Summary

Lecture 5,6 Linear Methods for Classification. Summary Lecture 5,6 Lnear Methods for Classfcaton Rce ELEC 697 Farnaz Koushanfar Fall 2006 Summary Bayes Classfers Lnear Classfers Lnear regresson of an ndcator matrx Lnear dscrmnant analyss (LDA) Logstc regresson

More information

Intelligent Method for Cloud Task Scheduling Based on Particle Swarm Optimization Algorithm

Intelligent Method for Cloud Task Scheduling Based on Particle Swarm Optimization Algorithm Unversty of Nzwa, Oman December 9-11, 2014 Page 39 THE INTERNATIONAL ARAB CONFERENCE ON INFORMATION TECHNOLOGY (ACIT2014) Intellgent Method for Cloud Task Schedulng Based on Partcle Swarm Optmzaton Algorthm

More information

A Multi-Camera System on PC-Cluster for Real-time 3-D Tracking

A Multi-Camera System on PC-Cluster for Real-time 3-D Tracking The 23 rd Conference of the Mechancal Engneerng Network of Thaland November 4 7, 2009, Chang Ma A Mult-Camera System on PC-Cluster for Real-tme 3-D Trackng Vboon Sangveraphunsr*, Krtsana Uttamang, and

More information

APPLICATION OF PROBE DATA COLLECTED VIA INFRARED BEACONS TO TRAFFIC MANEGEMENT

APPLICATION OF PROBE DATA COLLECTED VIA INFRARED BEACONS TO TRAFFIC MANEGEMENT APPLICATION OF PROBE DATA COLLECTED VIA INFRARED BEACONS TO TRAFFIC MANEGEMENT Toshhko Oda (1), Kochro Iwaoka (2) (1), (2) Infrastructure Systems Busness Unt, Panasonc System Networks Co., Ltd. Saedo-cho

More information

RESEARCH ON DUAL-SHAKER SINE VIBRATION CONTROL. Yaoqi FENG 1, Hanping QIU 1. China Academy of Space Technology (CAST) yaoqi.feng@yahoo.

RESEARCH ON DUAL-SHAKER SINE VIBRATION CONTROL. Yaoqi FENG 1, Hanping QIU 1. China Academy of Space Technology (CAST) yaoqi.feng@yahoo. ICSV4 Carns Australa 9- July, 007 RESEARCH ON DUAL-SHAKER SINE VIBRATION CONTROL Yaoq FENG, Hanpng QIU Dynamc Test Laboratory, BISEE Chna Academy of Space Technology (CAST) yaoq.feng@yahoo.com Abstract

More information

Stock volatility forecasting using Swarm optimized Hybrid Network

Stock volatility forecasting using Swarm optimized Hybrid Network Web Ste: www.jettcs.org Emal: edtor@jettcs.org, edtorjettcs@gmal.com Volume 2, Issue 3, May June 23 ISSN 2278-686 Stock volatlty forecastng usng Swarm optmzed Hybrd Network Puspanjal Mohapatra, Soumya

More information

A Fast Incremental Spectral Clustering for Large Data Sets

A Fast Incremental Spectral Clustering for Large Data Sets 2011 12th Internatonal Conference on Parallel and Dstrbuted Computng, Applcatons and Technologes A Fast Incremental Spectral Clusterng for Large Data Sets Tengteng Kong 1,YeTan 1, Hong Shen 1,2 1 School

More information

A study on the ability of Support Vector Regression and Neural Networks to Forecast Basic Time Series Patterns

A study on the ability of Support Vector Regression and Neural Networks to Forecast Basic Time Series Patterns A study on the ablty of Support Vector Regresson and Neural Networks to Forecast Basc Tme Seres Patterns Sven F. Crone, Jose Guajardo 2, and Rchard Weber 2 Lancaster Unversty, Department of Management

More information

Fault tolerance in cloud technologies presented as a service

Fault tolerance in cloud technologies presented as a service Internatonal Scentfc Conference Computer Scence 2015 Pavel Dzhunev, PhD student Fault tolerance n cloud technologes presented as a servce INTRODUCTION Improvements n technques for vrtualzaton and performance

More information

1. Measuring association using correlation and regression

1. Measuring association using correlation and regression How to measure assocaton I: Correlaton. 1. Measurng assocaton usng correlaton and regresson We often would lke to know how one varable, such as a mother's weght, s related to another varable, such as a

More information

Statistical Approach for Offline Handwritten Signature Verification

Statistical Approach for Offline Handwritten Signature Verification Journal of Computer Scence 4 (3): 181-185, 2008 ISSN 1549-3636 2008 Scence Publcatons Statstcal Approach for Offlne Handwrtten Sgnature Verfcaton 2 Debnath Bhattacharyya, 1 Samr Kumar Bandyopadhyay, 2

More information

A Comparative Study of Data Clustering Techniques

A Comparative Study of Data Clustering Techniques A COMPARATIVE STUDY OF DATA CLUSTERING TECHNIQUES A Comparatve Study of Data Clusterng Technques Khaled Hammouda Prof. Fakhreddne Karray Unversty of Waterloo, Ontaro, Canada Abstract Data clusterng s a

More information

A DYNAMIC CRASHING METHOD FOR PROJECT MANAGEMENT USING SIMULATION-BASED OPTIMIZATION. Michael E. Kuhl Radhamés A. Tolentino-Peña

A DYNAMIC CRASHING METHOD FOR PROJECT MANAGEMENT USING SIMULATION-BASED OPTIMIZATION. Michael E. Kuhl Radhamés A. Tolentino-Peña Proceedngs of the 2008 Wnter Smulaton Conference S. J. Mason, R. R. Hll, L. Mönch, O. Rose, T. Jefferson, J. W. Fowler eds. A DYNAMIC CRASHING METHOD FOR PROJECT MANAGEMENT USING SIMULATION-BASED OPTIMIZATION

More information

INVESTIGATION OF VEHICULAR USERS FAIRNESS IN CDMA-HDR NETWORKS

INVESTIGATION OF VEHICULAR USERS FAIRNESS IN CDMA-HDR NETWORKS 21 22 September 2007, BULGARIA 119 Proceedngs of the Internatonal Conference on Informaton Technologes (InfoTech-2007) 21 st 22 nd September 2007, Bulgara vol. 2 INVESTIGATION OF VEHICULAR USERS FAIRNESS

More information

Dynamic Pricing for Smart Grid with Reinforcement Learning

Dynamic Pricing for Smart Grid with Reinforcement Learning Dynamc Prcng for Smart Grd wth Renforcement Learnng Byung-Gook Km, Yu Zhang, Mhaela van der Schaar, and Jang-Won Lee Samsung Electroncs, Suwon, Korea Department of Electrcal Engneerng, UCLA, Los Angeles,

More information

A COPMARISON OF PARTICLE SWARM OPTIMIZATION AND THE GENETIC ALGORITHM

A COPMARISON OF PARTICLE SWARM OPTIMIZATION AND THE GENETIC ALGORITHM A COPMARISON OF PARTICLE SWARM OPTIMIZATION AND THE GENETIC ALGORITHM Rana Hassan * Babak Cohanm Olver de Weck Massachusetts Insttute of Technology, Cambrdge, MA, 39 Gerhard Venter Vanderplaats Research

More information

Comparison of Weighted Sum Fitness Functions for PSO Optimization of Wideband Medium-gain Antennas

Comparison of Weighted Sum Fitness Functions for PSO Optimization of Wideband Medium-gain Antennas 54 ZHOGKU MA, G. A. E. VAEBOSCH, COMPARISO OF WEIGHTE SUM FITESS FUCTIOS FOR PSO Comparson of Weghted Sum Ftness Functons for PSO Optmzaton of Wdeband Medum-gan Antennas Zhongkun MA, Guy A. E. VAEBOSCH

More information

NPAR TESTS. One-Sample Chi-Square Test. Cell Specification. Observed Frequencies 1O i 6. Expected Frequencies 1EXP i 6

NPAR TESTS. One-Sample Chi-Square Test. Cell Specification. Observed Frequencies 1O i 6. Expected Frequencies 1EXP i 6 PAR TESTS If a WEIGHT varable s specfed, t s used to replcate a case as many tmes as ndcated by the weght value rounded to the nearest nteger. If the workspace requrements are exceeded and samplng has

More information

Modelling of Web Domain Visits by Radial Basis Function Neural Networks and Support Vector Machine Regression

Modelling of Web Domain Visits by Radial Basis Function Neural Networks and Support Vector Machine Regression Modellng of Web Doman Vsts by Radal Bass Functon Neural Networks and Support Vector Machne Regresson Vladmír Olej, Jana Flpová Insttute of System Engneerng and Informatcs Faculty of Economcs and Admnstraton,

More information

Single and multiple stage classifiers implementing logistic discrimination

Single and multiple stage classifiers implementing logistic discrimination Sngle and multple stage classfers mplementng logstc dscrmnaton Hélo Radke Bttencourt 1 Dens Alter de Olvera Moraes 2 Vctor Haertel 2 1 Pontfíca Unversdade Católca do Ro Grande do Sul - PUCRS Av. Ipranga,

More information

SOLVING CARDINALITY CONSTRAINED PORTFOLIO OPTIMIZATION PROBLEM BY BINARY PARTICLE SWARM OPTIMIZATION ALGORITHM

SOLVING CARDINALITY CONSTRAINED PORTFOLIO OPTIMIZATION PROBLEM BY BINARY PARTICLE SWARM OPTIMIZATION ALGORITHM SOLVIG CARDIALITY COSTRAIED PORTFOLIO OPTIMIZATIO PROBLEM BY BIARY PARTICLE SWARM OPTIMIZATIO ALGORITHM Aleš Kresta Klíčová slova: optmalzace portfola, bnární algortmus rojení částc Key words: portfolo

More information

Risk-based Fatigue Estimate of Deep Water Risers -- Course Project for EM388F: Fracture Mechanics, Spring 2008

Risk-based Fatigue Estimate of Deep Water Risers -- Course Project for EM388F: Fracture Mechanics, Spring 2008 Rsk-based Fatgue Estmate of Deep Water Rsers -- Course Project for EM388F: Fracture Mechancs, Sprng 2008 Chen Sh Department of Cvl, Archtectural, and Envronmental Engneerng The Unversty of Texas at Austn

More information

MAPP. MERIS level 3 cloud and water vapour products. Issue: 1. Revision: 0. Date: 9.12.1998. Function Name Organisation Signature Date

MAPP. MERIS level 3 cloud and water vapour products. Issue: 1. Revision: 0. Date: 9.12.1998. Function Name Organisation Signature Date Ttel: Project: Doc. No.: MERIS level 3 cloud and water vapour products MAPP MAPP-ATBD-ClWVL3 Issue: 1 Revson: 0 Date: 9.12.1998 Functon Name Organsaton Sgnature Date Author: Bennartz FUB Preusker FUB Schüller

More information

Testing and Debugging Resource Allocation for Fault Detection and Removal Process

Testing and Debugging Resource Allocation for Fault Detection and Removal Process Internatonal Journal of New Computer Archtectures and ther Applcatons (IJNCAA) 4(4): 93-00 The Socety of Dgtal Informaton and Wreless Communcatons, 04 (ISSN: 0-9085) Testng and Debuggng Resource Allocaton

More information

Fast Fuzzy Clustering of Web Page Collections

Fast Fuzzy Clustering of Web Page Collections Fast Fuzzy Clusterng of Web Page Collectons Chrstan Borgelt and Andreas Nürnberger Dept. of Knowledge Processng and Language Engneerng Otto-von-Guercke-Unversty of Magdeburg Unverstätsplatz, D-396 Magdeburg,

More information

IMPACT ANALYSIS OF A CELLULAR PHONE

IMPACT ANALYSIS OF A CELLULAR PHONE 4 th ASA & μeta Internatonal Conference IMPACT AALYSIS OF A CELLULAR PHOE We Lu, 2 Hongy L Bejng FEAonlne Engneerng Co.,Ltd. Bejng, Chna ABSTRACT Drop test smulaton plays an mportant role n nvestgatng

More information

Point cloud to point cloud rigid transformations. Minimizing Rigid Registration Errors

Point cloud to point cloud rigid transformations. Minimizing Rigid Registration Errors Pont cloud to pont cloud rgd transformatons Russell Taylor 600.445 1 600.445 Fall 000-014 Copyrght R. H. Taylor Mnmzng Rgd Regstraton Errors Typcally, gven a set of ponts {a } n one coordnate system and

More information

Bayesian Network Based Causal Relationship Identification and Funding Success Prediction in P2P Lending

Bayesian Network Based Causal Relationship Identification and Funding Success Prediction in P2P Lending Proceedngs of 2012 4th Internatonal Conference on Machne Learnng and Computng IPCSIT vol. 25 (2012) (2012) IACSIT Press, Sngapore Bayesan Network Based Causal Relatonshp Identfcaton and Fundng Success

More information

NMT EE 589 & UNM ME 482/582 ROBOT ENGINEERING. Dr. Stephen Bruder NMT EE 589 & UNM ME 482/582

NMT EE 589 & UNM ME 482/582 ROBOT ENGINEERING. Dr. Stephen Bruder NMT EE 589 & UNM ME 482/582 NMT EE 589 & UNM ME 482/582 ROBOT ENGINEERING Dr. Stephen Bruder NMT EE 589 & UNM ME 482/582 7. Root Dynamcs 7.2 Intro to Root Dynamcs We now look at the forces requred to cause moton of the root.e. dynamcs!!

More information

Conversion between the vector and raster data structures using Fuzzy Geographical Entities

Conversion between the vector and raster data structures using Fuzzy Geographical Entities Converson between the vector and raster data structures usng Fuzzy Geographcal Enttes Cdála Fonte Department of Mathematcs Faculty of Scences and Technology Unversty of Combra, Apartado 38, 3 454 Combra,

More information

Investigation of Modified Bee Colony Algorithm with Particle and Chaos Theory

Investigation of Modified Bee Colony Algorithm with Particle and Chaos Theory Internatonal Journal of Control and Automaton, pp. 311-3 http://dx.do.org/10.1457/jca.015.8..30 Investgaton of Modfed Bee Colony Algorthm wth Partcle and Chaos Theory Guo Cheng Shangluo College, Zhangye,

More information

How Sets of Coherent Probabilities May Serve as Models for Degrees of Incoherence

How Sets of Coherent Probabilities May Serve as Models for Degrees of Incoherence 1 st Internatonal Symposum on Imprecse Probabltes and Ther Applcatons, Ghent, Belgum, 29 June 2 July 1999 How Sets of Coherent Probabltes May Serve as Models for Degrees of Incoherence Mar J. Schervsh

More information

Optimal Choice of Random Variables in D-ITG Traffic Generating Tool using Evolutionary Algorithms

Optimal Choice of Random Variables in D-ITG Traffic Generating Tool using Evolutionary Algorithms Optmal Choce of Random Varables n D-ITG Traffc Generatng Tool usng Evolutonary Algorthms M. R. Mosav* (C.A.), F. Farab* and S. Karam* Abstract: Impressve development of computer networks has been requred

More information

Course outline. Financial Time Series Analysis. Overview. Data analysis. Predictive signal. Trading strategy

Course outline. Financial Time Series Analysis. Overview. Data analysis. Predictive signal. Trading strategy Fnancal Tme Seres Analyss Patrck McSharry patrck@mcsharry.net www.mcsharry.net Trnty Term 2014 Mathematcal Insttute Unversty of Oxford Course outlne 1. Data analyss, probablty, correlatons, vsualsaton

More information

Data Broadcast on a Multi-System Heterogeneous Overlayed Wireless Network *

Data Broadcast on a Multi-System Heterogeneous Overlayed Wireless Network * JOURNAL OF INFORMATION SCIENCE AND ENGINEERING 24, 819-840 (2008) Data Broadcast on a Mult-System Heterogeneous Overlayed Wreless Network * Department of Computer Scence Natonal Chao Tung Unversty Hsnchu,

More information

Logistic Regression. Steve Kroon

Logistic Regression. Steve Kroon Logstc Regresson Steve Kroon Course notes sectons: 24.3-24.4 Dsclamer: these notes do not explctly ndcate whether values are vectors or scalars, but expects the reader to dscern ths from the context. Scenaro

More information

ONLINE ANOMALY DETECTION WITH CONSTANT FALSE ALARM RATE

ONLINE ANOMALY DETECTION WITH CONSTANT FALSE ALARM RATE 2015 IEEE INTERNATIONAL WORKSHOP ON MACHINE LEARNING FOR SIGNAL PROCESSING, SEPT. 17 20, 2014, BOSTON, USA ONLINE ANOMALY DETECTION WITH CONSTANT FALSE ALARM RATE Huseyn Ozkan Fath Ozkan Ibrahm Delbalta

More information

1. Fundamentals of probability theory 2. Emergence of communication traffic 3. Stochastic & Markovian Processes (SP & MP)

1. Fundamentals of probability theory 2. Emergence of communication traffic 3. Stochastic & Markovian Processes (SP & MP) 6.3 / -- Communcaton Networks II (Görg) SS20 -- www.comnets.un-bremen.de Communcaton Networks II Contents. Fundamentals of probablty theory 2. Emergence of communcaton traffc 3. Stochastc & Markovan Processes

More information

Data Visualization by Pairwise Distortion Minimization

Data Visualization by Pairwise Distortion Minimization Communcatons n Statstcs, Theory and Methods 34 (6), 005 Data Vsualzaton by Parwse Dstorton Mnmzaton By Marc Sobel, and Longn Jan Lateck* Department of Statstcs and Department of Computer and Informaton

More information

DEFINING %COMPLETE IN MICROSOFT PROJECT

DEFINING %COMPLETE IN MICROSOFT PROJECT CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMI-SP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,

More information

Loop Parallelization

Loop Parallelization - - Loop Parallelzaton C-52 Complaton steps: nested loops operatng on arrays, sequentell executon of teraton space DECLARE B[..,..+] FOR I :=.. FOR J :=.. I B[I,J] := B[I-,J]+B[I-,J-] ED FOR ED FOR analyze

More information

"Research Note" APPLICATION OF CHARGE SIMULATION METHOD TO ELECTRIC FIELD CALCULATION IN THE POWER CABLES *

Research Note APPLICATION OF CHARGE SIMULATION METHOD TO ELECTRIC FIELD CALCULATION IN THE POWER CABLES * Iranan Journal of Scence & Technology, Transacton B, Engneerng, ol. 30, No. B6, 789-794 rnted n The Islamc Republc of Iran, 006 Shraz Unversty "Research Note" ALICATION OF CHARGE SIMULATION METHOD TO ELECTRIC

More information

A Genetic Programming Based Stock Price Predictor together with Mean-Variance Based Sell/Buy Actions

A Genetic Programming Based Stock Price Predictor together with Mean-Variance Based Sell/Buy Actions Proceedngs of the World Congress on Engneerng 28 Vol II WCE 28, July 2-4, 28, London, U.K. A Genetc Programmng Based Stock Prce Predctor together wth Mean-Varance Based Sell/Buy Actons Ramn Rajaboun and

More information

Improved Mining of Software Complexity Data on Evolutionary Filtered Training Sets

Improved Mining of Software Complexity Data on Evolutionary Filtered Training Sets Improved Mnng of Software Complexty Data on Evolutonary Fltered Tranng Sets VILI PODGORELEC Insttute of Informatcs, FERI Unversty of Marbor Smetanova ulca 17, SI-2000 Marbor SLOVENIA vl.podgorelec@un-mb.s

More information

A heuristic task deployment approach for load balancing

A heuristic task deployment approach for load balancing Xu Gaochao, Dong Yunmeng, Fu Xaodog, Dng Yan, Lu Peng, Zhao Ja Abstract A heurstc task deployment approach for load balancng Gaochao Xu, Yunmeng Dong, Xaodong Fu, Yan Dng, Peng Lu, Ja Zhao * College of

More information

Review of Hierarchical Models for Data Clustering and Visualization

Review of Hierarchical Models for Data Clustering and Visualization Revew of Herarchcal Models for Data Clusterng and Vsualzaton Lola Vcente & Alfredo Velldo Grup de Soft Computng Seccó d Intel lgènca Artfcal Departament de Llenguatges Sstemes Informàtcs Unverstat Poltècnca

More information

The Network flow Motoring System based on Particle Swarm Optimized

The Network flow Motoring System based on Particle Swarm Optimized The Network flow Motorng System based on Partcle Swarm Optmzed Neural Network Adult Educaton College, Hebe Unversty of Archtecture, Zhangjakou Hebe 075000, Chna Abstract The compatblty of the commercal

More information