Modeling Waveform Shapes with Random Effects Segmental Hidden Markov Models

Size: px
Start display at page:

Download "Modeling Waveform Shapes with Random Effects Segmental Hidden Markov Models"

Transcription

1 Modelng Waveform Shapes wth Random Effects Segmental Hdden Markov Models Seyoung Km, Padhrac Smyth Department of Computer Scence Unversty of Calforna, Irvne CA Abstract In ths paper we descrbe a general probablstc framework for modelng waveforms such as heartbeats from ECG data. The model s based on segmental hdden Markov models (as used n speech recognton) wth the addton of random effects to the generatve model. The random effects component of the model handles shape varablty across dfferent waveforms wthn a general class of waveforms of smlar shape. We show that ths probablstc model provdes a unfed framework for learnng these models from sets of waveform data as well as parsng, classfcaton, and predcton of new waveforms. We derve a computatonally effcent EM algorthm to ft the model on multple waveforms, and ntroduce a scorng method that evaluates a test waveform based on ts shape. Results on two real-world data sets demonstrate that the random effects methodology leads to mproved accuracy (compared to alternatve approaches) on classfcaton and segmentaton of real-world waveforms. Introducton Automatcally parsng and recognzng waveforms based on ther shape s a classc problem n pattern recognton (Fu, 98). Applcatons nclude automated classfcaton of heartbeat waveforms n ECG data analyss (Kosk, 986), nterpretaton of waveforms from turbulent flow experments (Bruun, 995), and dscrmnaton of nuclear events and earthquakes n sesmograph data (Bennett & Murphy, 986). Typcally n these applcatons t s mpractcal for a human to contnuously montor the -seres data n real- (or to scan large archves of such data) and there s a need for accurate and automated real- Stefan Luther Department of Appled Physcs Unversty of Twente The Netherlands s.luther@tn.utwente.nl waveform detecton. Other applcatons of waveform modelng occur n database systems and nformaton retreval, for systems that can take a waveform as an nput query and search a large database to fnd smlar waveforms that match ths query (e.g., Y & Faloutsos, ). Whle the human vsual system can easly recognze the characterstc sgnature of a partcular waveform shape (a heartbeat waveform for example) the problem can be qute dffcult for automated methods. For example, as Fgure (a) shows, there can be sgnfcant varablty n shape among waveforms belongng to the same general class. A generally useful approach to these problems s to construct a generatve model for the waveform and then use ths model to detect and parse new waveforms. For example, syntactc grammars decompose the waveform nto a set of component parts generated by a set of grammatcal rules. To model shape varablty these grammars requre the addton of a stochastc component, and to learn such models from data requres a lkelhood functon expressng the probablty of an observed set of waveforms gven a model and ts parameters. In ths general context relatvely smple statstcal grammars such as hdden Markov models (HMMs) have been pursued (e.g., Kosk, 996; Hughes et al., 3), gven that stochastc grammars wth rcher representatons are generally much more dffcult to learn. The parameters of these models can be learned from a set of examplar waveforms new waveforms can then be parsed and classfed based on the lkelhood of the new waveform gven the traned model. A potentally useful extenson of standard HMMs for shape modelng s the so-called segmental hdden Markov model, orgnally ntroduced n the speech recognton communty (Levnson, 986; Ostendorf et al., 996) and proposed for more general waveform modelng n Ge & Smyth (). The segmental model allows for the observed data wthn each segment (a sequence of states wth the same value) to follow a

2 5 5 5 (a) (c) (b) segmental HMMs waveform data (d) Fgure : Bubble-probe nteracton data: (a) a set of waveforms obtaned from bubbles that are splt by a probe durng nteracton, (b) an example of sngle waveform, (c) pecewse lnear approxmaton of (b), and (d) segmental HMMs ft to a test waveform. general parametrc regresson form, such as a lnear functon of wth addtve nose. Ths allows us to model the shape of the waveform drectly, n ths case as a sequence of pecewse lnear components, as shown n Fgure (c). A lmtaton of the standard segmental model s that t assumes that the parameters of the model are fxed. Thus, the only source of varablty n an observed waveform arses from varaton n the lengths of the segments and observaton nose added to the functonal form n each segment. The lmtaton of ths can clearly be seen n Fgure (d), where a segmental model has been traned on the data n Fgure (a) and then used to parse the specfc waveform n Fgure (b) ( parsng means nferrng the most lkely state sequence gven the model). We can see that the slopes and ntercepts provded by the model do not match the observed data partcularly well n each segment, e.g., n the frst segment the ntercept s clearly too low on the y-axs, n the second segment the slope s too small, and so forth. By usng the same fxed parameters for all waveforms, the model cannot fully account for varablty n waveform shapes. To overcome ths lmtaton, n ths paper we combne segmental HMMs wth random effects models (Lard & Ware, 98). The general dea of modelng wth random effects s to allow parameters to have ndvdual-level (or waveform-level) random varaton, whle stll beng coupled together by an overall populaton pror. By extendng the segmental HMM to nclude random effects, we can allow the slopes and ntercepts of each waveform to vary accordng to a pror dstrbuton, wthn each segment. The parameters of ths pror can be learned from data n the form of sets of waveforms n an unsupervsed manner. In fact the resultng model can be vewed as a drected graphcal model, allowng for applcaton of standard methods for nference and learnng. For example, we can n prncple learn that the slopes across multple waveforms for the frst segment n Fgure (c) tend to have a characterstc mean slope and standard devaton. The random effects approach provdes a systematc mechansm for allowng varaton n shape space n a manner that can be parametrzed. The prmary contrbutons of ths paper are to (a) propose the use of random effects segmental HMMs for general waveform modelng applcatons, (b) derve a computatonally effcent EM procedure for learnng such models (reducng complexty by a factor of T where T s the length of a waveform), (c) propose two separate lkelhood-based scores for shape and for nose (whch are then shown to mprove recognton accuracy over usng just lkelhood alone), and fnally (d) llustrate on two real waveform data sets how these models can be used for waveform parsng, classfcaton, and predcton. The closest related work s Holmes & Russell (999) who explored a smlar dea for usng a dstrbuton over parameters n segmental HMMs, n the context of speech recognton. Our work extends these deas by dervng a provably correct EM algorthm, showng how the computatonal complexty of ths EM algorthm can be sgnfcantly reduced, and generalzng the applcablty of the method. We begn our dscusson by ntroducng segmental HMMs n Secton. In Secton 3, we extend ths model to ncorporate random effects models, and descrbe the EM algorthm for parameter estmaton as well as the nference algorthms and the scorng methods for test waveforms. In Secton 4, we evaluate our model on two applcatons nvolvng bubble-probe nteracton data and ECG data, wth conclusons n Secton 5. Segmental HMMs Standard dscrete- fnte-state HMMs mpose a geometrc dstrbuton on run lengths (or segment lengths) for each state value and assume that observatons are condtonally ndependent wth a constant mean wthn such segments. Segmental HMMs relax these modelng constrants by allowng (a) arbtrary dstrbutons on run lengths and (b) segment models (regresson models) that allow the mean to be a functon of wthn each segment. A segmental HMM wth M states s descrbed by an

3 M M transton matrx, plus a duraton dstrbuton and segment dstrbuton for each state k, where k =,..., M. The transton matrx A (whch s statonary n ) has entres a kl, namely, the probablty of beng n state k at t+ gven state l at t. The ntal state dstrbuton can be ncluded n A as transtons from state to each state k. In waveform modelng, we typcally constran the transton matrx to allow only left-to-rght transtons and no self-transtons. Thus, there s an orderng on states, each state can be vsted at most once, and states can be skpped. In ths paper, we model the duraton dstrbuton of state k, usng a Posson dstrbuton, P (d θ dk ) = e λ k λ k d (d )! d =,,... (shfted to start at d = to prevent a slent state). Other choces for the duraton dstrbuton could also be used. Once the process enters state k, a duraton d s drawn, and state k produces a segment of observatons of length d from the segment dstrbuton. In what follows we assume that the shape of waveforms can be approxmated as a sequence of lnear segments, and model the rth segment of observatons of length d, y r, generated by state k, as a lnear regresson functon n, y r = X r β k + e r e r N d (, σ I d ), () where β k s a vector of regresson coeffcents, e r s a d vector of Gaussan nose wth varance σ n each component, and X r s a d desgn matrx consstng of a column of s (for the ntercept term) and a column of x values representng the values. Note that ths model can easly be generalzed to allow nonlnear polynomal functons of x that are stll lnear n the parameters β k. For smplcty, σ s assumed to be common across all states; agan ths can be relaxed. One could enforce contnuty of the mean functons across segments n the probablstc model, but ths s not dscussed n the present paper. Treatng the unobserved state sequences as mssng, we can estmate the parameters, θ = {A, θ d = {λ k k =,..., M}, θ f = {β k, (σ ) k =,..., M}}, usng the EM algorthm wth the forward-backward (F-B) algorthm as a subroutne for nference n the E step (Deng et al., 994). The F-B algorthm for segmental HMMs, modfed from that of standard HMMs to take nto account the duraton dstrbuton, recursvely computes α t (k) = P (y :t, stay n state k ends at t θ) α t (k) = P (y :t, stay n state k starts at t + θ) () n the forward pass, and β t (k) = P (y t+:t stay n state k ends at t, θ) β t (k) = P (y t+:t stay n state k starts at t +, θ) (3) n the backward pass, and returns the results to the M step as suffcent statstcs (Rabner & Juang, 993). Inference algorthms for segmental HMMs provde a natural way to evaluate the performance of the model on test data. The F-B algorthm scores a prevously unseen waveform y by calculatng the lkelhood p(y θ) = s p(y, s θ) = k α T (k). (4) In addton, the Vterb algorthm can be used to provde a segmentaton of a waveform by computng the most lkely state sequence. The addton of duraton dstrbutons n segmental HMMs ncreases the complexty of both the F-B and Vterb algorthms from O(M T ) for standard HMMs to O(M T ), where T s the length of the waveform (.e. the number of observatons). 3 Segmental HMMs wth Random Effects A random effects model s a general statstcal framework when the data generaton process can be seen as havng herarchcal structure. At each level of the generatve process, the model defnes a pror dstrbuton over the ndvdual group parameters, called random effects, of one level below. Typcally, the random effects are not observable, so the EM algorthm s a popular approach to learnng model parameters from the observed data (Dempster et al., 98; Lard & Ware, 98). By combnng segmental HMMs and random effects models we can take advantage of the strength of each n waveform modelng. 3. The Model Begnnng wth the segmental HMMs descrbed n Secton, we can extend the segment dstrbutons of the model as follows. Consder the rth segment yr of length d from the th ndvdual waveform generated by state k. Followng the dscusson n Lard & Ware (98), we descrbe the generatve model as a two-stage process. At stage one, we model the observed data yr as y r = X rβ k + X ru k + e r e r N d (, σ I d ), (5) where e r s the measurement nose, X r s a d desgn matrx for the measurements correspondng to yr, (β k + u k ) are the regresson coeffcents, and N (for N waveforms). β k represents the mean regresson parameters for segment k, and u k represents the varaton n regresson (or shape) parameters for

4 the th ndvdual waveform. At ths stage, the ndvdual random effects u k as well as β k and σ are vewed as parameters. At the second stage, u k s vewed as a random varable wth dstrbuton u k N (, Ψ k ), (6) where Ψ k s a covarance matrx, and u k s ndependent of e r. In ths setup, t can be shown that yr and u k have the followng jont dstrbuton: ( ) ( ( ) y r X u N r β k d+, k ( X r Ψ k X ) ) r + σ I d X rψ k Ψ k X. (7) r Ψ k Also, from Equaton (7), the posteror dstrbuton of u k can be wrtten as ) u k yr, β k, Ψ k, σ N (ˆβ k, Ψ ˆβ, (8) where ˆβ k = (X r X r + σ (Ψ k ) ) X r (y r X rβ k ), (9) and Ψ ˆβ k = σ (X r X r + σ (Ψ k ) ). () Fgure (a) s a plate-lke dagram that llustrates how the segment model descrbed above generates a sngle waveform segment yr when the duraton d of the state s gven. As we enter state s (that then repeats tself for d steps), the model generates the ndvdual random effects parameter vector u r from Equaton (6), and, then, generates the observed data yr = {y,..., yd } from Equaton (5). u k belongs to the ndvdual waveform, whereas Ψ, β, and σ are global parameters. 3. Inference To handle the random effects component n the F- B and Vterb algorthms for segmental HMMs, we notce from Equaton (7) that the margnal dstrbuton of a segment yr generated by state k s N d (X rβ k, X rψ k X r + σ I d ), and that ths corresponds to Equaton () wth the covarance matrx σ I d replaced by (X rψ k X r + σ I d ). Replacng the two-level segment dstrbuton wth ths margnal dstrbuton, and collapsng the herarchy nto a sngle level, as shown n Fgure (b), we can use the same F-B and Vterb algorthm as n segmental HMMs n the margnalzed space over the random effects. The F-B algorthm recursvely computes the quanttes n Equatons () and (3). These are then used n k = : N = : N Ψ s s... s d s s... s d u Ψ k β, σ y (a) y y d β, σ y (b) Fgure : Plate-lke dagrams for the segment dstrbuton of random effects segmental HMMs. Ths shows the generatve process for one segment, y,..., yd gven the duraton d of state s = s = = s d. (a) shows a two-stage model wth random effects parameters, and (b) the model after ntegratng out random effects parameters. the M step of the EM algorthm. The lkelhood of a waveform y, gven fxed parameters θ = {A, θ d, θ f = {β k, Ψ k, (σ ) k =,..., M}}, but wth states s and random effects u unknown, s evaluated as p(y θ) = s = s y y d p(y, s, u θ)du () p(y, s θ) = k α T (k). As n segmental HMMs, the Vterb algorthm can be used as a method to segment a waveform by computng the most lkely state sequence. What appears to make the nference n random effects segmental HMMs computatonally much more expensve than n segmental HMMs s the nverson of the d d covarance matrx, X rψ k X r + σ I d, of the margnal segment dstrbuton durng the evaluaton of the lkelhood of a segment. For example, n the F-B algorthm, the lkelhood of a segment y r of length d gven state k, p(y r β k, Ψ k, σ ), needs to be calculated for all possble duratons d n each of the α t (k) and β t (k) expressons at each recurson. The nave computaton of a segment lkelhood usng drect nverson of the d d covarance matrx would requre O(T 3 ) computatons, where T s the upper bound for d, leadng to an overall complexty of O(M T 5 ). Ths can be computatonally mpractcal when we have long waveforms wth a large value of T, (for example, T = 56 for the data shown n Fgure ). In the dscusson of computatonal ssues for random effects models, Dempster et al. (98) suggest an expresson for the lkelhood that s smple to evaluate. Applyng ther method to the segment dstrbuton of our model, we rewrte, usng Bayes rule, the lkelhood

5 of a segment y r generated by state k as p(y r β k, Ψ k ) = p(y r, u k β k, Ψ k, σ ) p(u k y r, β k, Ψ k, σ ), where the numerator and the denomnator of the rghthand sde are gven as Equatons (7) and (8), respectvely. The rght-hand sde of the above equaton holds for all values of u k. By settng u k to ˆβ k as gven n Equaton (9), we can smplfy the expresson for the segment lkelhood to a form that nvolves only O(d) computatons for each step, where prevously ths nvolved O(d 3 ) computatons n the case of the nave approach wth matrx nversons. Thus, the complexty of the F-B and Vterb algorthms s reduced to O(M T 3 ). As shown n Mtchell et al. (995) for segmental HMMs we can further reduce ths computatonal complexty to O(M T ) by precomputng the segment lkelhood and storng the values n a table however, ths precomputaton s not possble wth random effects models, leadng to the addtonal factor of T n the complexty term. 3.3 Parameter Estmaton In ths secton, we descrbe how to obtan maxmum lkelhood estmates of the parameters from a tranng set of multple waveforms for a random effects segmental HMM usng the EM algorthm. We can augment the observed waveform data wth both (a) state sequences and (b) random effects parameters (both are consdered to be hdden). The log lkelhood of the complete data of N waveforms, D complete = (Y, S, U) = {(y, s, u ),..., (y N, s N, u N )}, where the state sequence s mples R s segments n waveform, s: log L(θ D complete ) = = N log p(y, s, u A, θ d, θ f ) = R N s log P (s r s r, A) () = r= R N s log P (d r θ dk, k = s r) (3) = r= R N s log p(yr u k, β k, σ, k = s r, d r)(4) = r= R N s log p(u k Ψ k, k = s r ). (5) = r= As we can see from the above equaton, gven the complete data, the log lkelhood decouples nto four parts, where the transton matrx, the duraton dstrbuton parameters, the bottom level parameters β k, σ, and the top level parameters u k of random effects models appear n each of the four terms. If we had complete data, we could optmze the four sets of parameters ndependently. When only parts of the data are observed, by teratng between the E step and the M step n the EM algorthm as descrbed n the followng secton, we can fnd a soluton that locally maxmzes the lkelhood of the observed data E Step In the E step, we fnd the expected log lkelhood of the complete data, wth respect to Q(θ (t), θ) = E[log L(θ D complete )], (6) p(s, U Y, θ (t) ) = p(u S, Y, θ (t) )P (S Y, θ (t) ) R N s = p(u r s r = k, yr, θ (t) )P (s r = k yr, θ (t) ), (7) = r= where θ (t) s the estmate of the parameter vector from the prevous M step of the tth EM teraton. P (s r = k yr, θ (t) ) n Equaton (7) can be obtaned from [ the F-B algorthm. The suffcent statstcs, E u k s r = k, Y, θ (t)] [ and E u k u k s r = k, Y, θ (t)], for P (u k s r = k, yr, θ (t) ) n Equaton (7) can be drectly obtaned from Equatons (9) and (). The computatonal complexty for an E step s O(M T 3 N) where N s the number of waveforms M Step In the M step, we fnd the values of the parameters that maxmze Equaton (6). As we can see from Equatons ()-(5) and Equaton (6), the optmzaton problem decouples nto four parts each of whch nvolves a dstnct set of parameters (the equatons are omtted here due to lack of space but are provded n Km et al., 4). The computatonal complexty for each M step s O(MT 3 N). 3.4 Model Evaluaton and Score Functons An obvous choce for evaluatng a new test waveform based on a probablstc model s to compute the lkelhood of the waveform gven the parameters, as shown n Equaton (). A dfferent method that we propose n ths secton uses the fact that waveforms are scored based on two dfferent aspects of how the model fts the test waveform. Each level of the random effects model models a dfferent source of varablty. At stage two, the covarance matrx Ψ k n Equaton (6) explans the amount

6 Lkelhood =.569 Lkelhood =.395 Score shape = Score shape =.845 Score nose = Score nose = 7.74 (a) (b) Fgure 3: Scores for test waveforms from the random effects segmental HMM traned usng the data shown n Fgure (a). of nose n shape space. Unlke segmental HMMs, where the varance σ n Equaton (4) s forced to explan both shape deformatons and measurement nose, random effects models allow for modellng them separately wth a herarchcal structure. However, the lkelhood n effect mxes both lack of ft terms nto a sngle score. Consequently, smooth waveforms that are well approxmated by lnear segments wth lttle measurement nose but wth a consderable error n shape (as shown n Fgure 3(a)) can receve the same lkelhood score as waveforms wth hgh measurement nose and lttle shape deformaton from the mean shape (as shown n Fgure 3(b)). From the decomposton of the complete data lkelhood n Equatons ()-(5), we notce that Equaton (5) s a contrbuton from stage two of the random effects component, and that Equaton (4) s a contrbuton from stage one. Equatons () and (3) can be vewed as representng the shape deformaton explaned by the segmental HMM part of the model. The score decomposton s, R s Score shape = E[( log P (s r s r, A)) r= R s +( log P (d r θ dk, k = s r )) r= R s +( log p(u k Ψ k, k = s r )) y, θ], r= r= R s Score nose = E[ log p(y r u k, β k, σ, k = s r ) y, θ], where the expectaton s taken wth respect to the posteror dstrbuton of the unobserved data, p(s, u y, θ) (Equaton (7)). Fgure 3 shows examples of waveforms wth these two scores. The results from our experment n Secton 4 demonstrate that usng ths score decomposton (.e., usng both scores as features nstead of a sngle lkelhood score) mproves the recognton accuracy. 4 Experments We apply our model to two real world data sets, hotflm anemometry data n turbulent bubbly flow and ECG heartbeat data. In all of our experments, we compare the results from our new model wth those from segmental HMMs. We use several methods to evaluate the models: LogP Score We compute log p(y θ) scores (Equatons (4) and () for each model) for test waveforms y to see how well the parameters θ learned from the tranng data can model test waveforms. Segmentaton Qualty To evaluate how well the model can segment test waveforms, we frst obtan the segmentatons of test waveforms wth the Vterb algorthm, estmate the regresson coeffcents ˆβ of each segment, and calculate the mean squared dfference between the observed data and Xˆβ (good segmentatons produce low scores). One-Step-Ahead Predcton To evaluate the predctve power of the models, we use one-stepahead predcton on test waveforms. Gven all of the observatons up to step (t ) for a test waveform y, we compute the logp scores of the observed value at t and the mean squared error of the predcted values, for the next step. In all of these experments, we use fve-fold cross valdaton. To evaluate the performance of our model for classfcaton, we nclude n the test set negatve examples of the shape that we are modelng, and buld a k-nearest neghbor classfer wth varyng values for k usng the scores from the model as a feature vector for each waveform. For the model from each of the fve-fold cross valdaton runs, usng the postve examples n the test set for that model and the negatve examples, we use three-fold cross valdaton to obtan the classfcaton accuracy of the classfer. 4. Hot-flm Anemometry n Turbulent Bubbly Flow Hot-flm anemometry s a technque commonly used n turbulent bubbly flow measurements n flud physcs. Interactons between the bubbles and the probe n turbulent gas flow, such as splttng, bouncng, and penetraton, lead to characterstc nteracton waveform

7 Table : Performance on Bubble-probe Interacton Data One Step Ahead Predcton LogP Scores LogP Mean Squared Error Segmentaton Error Segmental HMMs Random Effects Segmental HMMs Table : Performance on ECG Data for Normal Heartbeats One Step Ahead Predcton LogP Scores LogP Mean Squared Error Segmentaton Error Segmental HMMs Random Effects Segmental HMMs shapes. Physcsts are nterested n detectng the occurrence and type of nteractons automatcally from such waveforms (Bruun, 995). There can be large varablty n the shape of the waveforms caused by varous factors such as velocty fluctuatons and dfferent gas fractons durng measurement. Labels are avalable for the type or class of each nteracton based on hgh-speed mage recordngs of the event obtaned smultaneously wth the nteracton sgnal. In the results of ths paper, we model waveforms for one specfc type of nteracton where the probe splts the bubble. Our data consst of 5 waveforms such as those shown n Fgures (a) and (b). We randomly sampled waveforms from ths data set to form a tranng set for each of fve-fold cross valdaton runs. Gven that Fgure (c) s a reasonable pecewse lnear approxmaton of the general shape, we subjectvely chose M = 6 as the number of states for both segmental HMMs and random effects segmental HMMs. Fgure 4(a) llustrates vsually that the qualty of the segmentatons of the waveforms usng the Vterb algorthm s much better wth random effects than wthout. Table shows a reducton of approxmately 8% n squared error from usng random effects for these segmentatons. Table also shows a sgnfcant ncrease n logp scores for the test waveforms n the models wth random effects parameters as well as sgnfcantly better one-step-ahead predctons. To evaluate the performance of the models for classfcaton, we used 7 addtonal waveforms of negatve examples labeled as bouncng, penetratng, and glancng nteracton types, and plot the classfcaton accuracy n Fgure 5. In addton to the two probablstc models, we nclude the results of usng the drect mean squared dstance between two waveforms as a dstance measure n k-nearest neghbor algorthms (as a baselne method). Usng the two decomposed scores mproves the accuracy of k-nearest neghbor classfers sgnfcantly over just usng the lkelhood. 4. ECG Data The shape of heartbeat cycles n ECG data can be used to dagnose the heart condton of a patent (Kosk, 996; Hughes et al. 3). For example, Fgure 4(b) shows the typcal shape of normal heartbeats, whereas Fgure 4(c) s taken from a heart experencng a premature ventrcular contracton. However, even among heartbeat recordngs for the same heart condton from the same ndvdual, there s a sgnfcant varablty n terms of shape and length. We chose an ECG recordng from the MIT-BIH Arrhythma database, and manually dvded t nto ndvdual waveforms to obtan 8 normal heartbeats and 8 abnormal heartbeats of a premature ventrcular contracton. waveforms from each of the resultng data sets were used to tran the models wth the number of states M = 9 n normal cases and M = 6 n abnormal cases. The results from 5-fold cross valdaton are shown n Table and 3. Agan we see a sgnfcant mprovements for the random effects model. In terms of classfcaton (detals not shown) our new models were % accurate n all experments versus an average accuracy of 98% for segmental HMMs. 5 Conclusons In ths paper, we proposed a probablstc model that extends segmental HMMs to nclude random effects. Ths model allows an ndvdual waveform to vary ts shape n a constraned manner va a pror dstrbuton over ndvdual waveform parameters. We demonstrated that random effects segmental HMMs can acheve a sgnfcant mprovement n modelng, segmentaton, and classfcaton of waveforms. Acknowledgements Ths materal s based upon work supported by the Natonal Scence Foundaton under Grant No. SCI- 564 for the OptIPuter project. We would lke to

8 Table 3: Performance on ECG Data for Premature Ventrcular Contractons One-Step-Ahead Predcton LogP Scores LogP Mean Squared Error Segmentaton Error Segmental HMMs Random Effects Segmental HMMs (a) Bubble-probe nteracton data Classfcaton accuracy (%) Mean squared error Segmental HMMs Random effects segmental HMMs (lkelhood) Random effects segmental HMMs (decomposed scores) (b) ECG data - normal heartbeats (c) ECG data - premature ventrcular contractons Fgure 4: Examples for the segmentaton of waveforms by the Vterb algorthm for segmental HMMs (left) and for random effects segmental HMMs (rght) thank Davd Van Dyk for dscussons relatng to random effects models and EM. References Bennett, T., & Murphy, J. (986). Analyss of sesmc dscrmnaton usng regonal data from western Unted States events. Bull. Ses. Soc. Am., 76: Bruun, H. (995). Hot Wre Anemometry: Prncples and Sgnal Analyss. Oxford: Oxford Unversty Press. Dempster, A., Rubn, D., & Tsutakawa, R. (98). Estmaton n covarance components models. J. Am. Stat. Assoc., 76(374): Deng, L., Aksmanovc, M., Sun, D., & Wu, J. (994). Speech recognton usng hdden Markov models wth polynomal regresson functons as nonstatonary states. IEEE Trans. Speech Audo Processng, (4): k Fgure 5: k-nearest neghbor classfcaton accuracy Ge, X., & Smyth, P. (). Deformable Markov model templates for -seres pattern matchng. In Proc. 6th ACM SIGKDD Conference, 8 9. Holmes, W., & Russell, M. (999). Probablstc-trajectory segmental HMMs. Computer Speech and Language, 3():3 37. Hughes, N., Tarassenko, L., & Roberts, S. (3). Markov models for automated ECG nterval analyss. Advances n NIPS 6. Km, S., Smyth, P. & Luther, S. (4). Modelng waveform shapes wth random effects segmental hdden Markov models, Techncal Report ICS-TR-4-5, UC Irvne. Kosk, A. (996). Modellng ECG sgnals wth hdden Markov models, Artfcal Intellgence n Medcne, 8(5): Lard, N. & Ware, J. (98). Random-effects models for longtudnal data. Bometrcs, 38(4): Levnson, S. (986). Contnuously varable duraton hdden Markov models for automatc speech recognton. Computer Speech and Language, ():9 45. Mtchell, C., Harper, M., & Jameson, L. (995). On the computatonal complexty of explct duraton HMMs. IEEE Trans. on Speech and Audo Processng, 3(3):3 7. Ostendorf, M., Dgalaks, V., & Kmball, O. (996). From HMMs to segmental models: a unfed vew of stochastc modelng for speech recognton. IEEE Trans. on Speech and Audo Processng, 4(5): Rabner, L. & Juang, B. (993). Fundamentals of Speech Recognton. Englewood Clffs, NJ: Prentce Hall. Y, B. & Faloutsos, C. (). Fast sequence ndexng for arbtrary L p norms. Proceedngs of the 6th VLDB Conference,

Modeling Waveform Shapes with Random Effects Segmental Hidden Markov Models

Modeling Waveform Shapes with Random Effects Segmental Hidden Markov Models Modeling Waveform Shapes with Random Effects Segmental Hidden Markov Models Technical Report UCI-ICS 4-5 School of Information and Computer Science University of California, Irvine Seyoung Kim, Padhraic

More information

CS 534: Computer Vision Model Fitting

CS 534: Computer Vision Model Fitting CS 534: Computer Vson Model Fttng Sprng 004 Ahmed Elgammal Dept of Computer Scence CS 534 Model Fttng - 1 Outlnes Model fttng s mportant Least-squares fttng Maxmum lkelhood estmaton MAP estmaton Robust

More information

Hermite Splines in Lie Groups as Products of Geodesics

Hermite Splines in Lie Groups as Products of Geodesics Hermte Splnes n Le Groups as Products of Geodescs Ethan Eade Updated May 28, 2017 1 Introducton 1.1 Goal Ths document defnes a curve n the Le group G parametrzed by tme and by structural parameters n the

More information

Support Vector Machines

Support Vector Machines /9/207 MIST.6060 Busness Intellgence and Data Mnng What are Support Vector Machnes? Support Vector Machnes Support Vector Machnes (SVMs) are supervsed learnng technques that analyze data and recognze patterns.

More information

Feature Reduction and Selection

Feature Reduction and Selection Feature Reducton and Selecton Dr. Shuang LIANG School of Software Engneerng TongJ Unversty Fall, 2012 Today s Topcs Introducton Problems of Dmensonalty Feature Reducton Statstc methods Prncpal Components

More information

Learning the Kernel Parameters in Kernel Minimum Distance Classifier

Learning the Kernel Parameters in Kernel Minimum Distance Classifier Learnng the Kernel Parameters n Kernel Mnmum Dstance Classfer Daoqang Zhang 1,, Songcan Chen and Zh-Hua Zhou 1* 1 Natonal Laboratory for Novel Software Technology Nanjng Unversty, Nanjng 193, Chna Department

More information

User Authentication Based On Behavioral Mouse Dynamics Biometrics

User Authentication Based On Behavioral Mouse Dynamics Biometrics User Authentcaton Based On Behavoral Mouse Dynamcs Bometrcs Chee-Hyung Yoon Danel Donghyun Km Department of Computer Scence Department of Computer Scence Stanford Unversty Stanford Unversty Stanford, CA

More information

Lecture 5: Multilayer Perceptrons

Lecture 5: Multilayer Perceptrons Lecture 5: Multlayer Perceptrons Roger Grosse 1 Introducton So far, we ve only talked about lnear models: lnear regresson and lnear bnary classfers. We noted that there are functons that can t be represented

More information

An Entropy-Based Approach to Integrated Information Needs Assessment

An Entropy-Based Approach to Integrated Information Needs Assessment Dstrbuton Statement A: Approved for publc release; dstrbuton s unlmted. An Entropy-Based Approach to ntegrated nformaton Needs Assessment June 8, 2004 Wllam J. Farrell Lockheed Martn Advanced Technology

More information

A Semi-parametric Regression Model to Estimate Variability of NO 2

A Semi-parametric Regression Model to Estimate Variability of NO 2 Envronment and Polluton; Vol. 2, No. 1; 2013 ISSN 1927-0909 E-ISSN 1927-0917 Publshed by Canadan Center of Scence and Educaton A Sem-parametrc Regresson Model to Estmate Varablty of NO 2 Meczysław Szyszkowcz

More information

SLAM Summer School 2006 Practical 2: SLAM using Monocular Vision

SLAM Summer School 2006 Practical 2: SLAM using Monocular Vision SLAM Summer School 2006 Practcal 2: SLAM usng Monocular Vson Javer Cvera, Unversty of Zaragoza Andrew J. Davson, Imperal College London J.M.M Montel, Unversty of Zaragoza. josemar@unzar.es, jcvera@unzar.es,

More information

Outline. Type of Machine Learning. Examples of Application. Unsupervised Learning

Outline. Type of Machine Learning. Examples of Application. Unsupervised Learning Outlne Artfcal Intellgence and ts applcatons Lecture 8 Unsupervsed Learnng Professor Danel Yeung danyeung@eee.org Dr. Patrck Chan patrckchan@eee.org South Chna Unversty of Technology, Chna Introducton

More information

Smoothing Spline ANOVA for variable screening

Smoothing Spline ANOVA for variable screening Smoothng Splne ANOVA for varable screenng a useful tool for metamodels tranng and mult-objectve optmzaton L. Rcco, E. Rgon, A. Turco Outlne RSM Introducton Possble couplng Test case MOO MOO wth Game Theory

More information

Content Based Image Retrieval Using 2-D Discrete Wavelet with Texture Feature with Different Classifiers

Content Based Image Retrieval Using 2-D Discrete Wavelet with Texture Feature with Different Classifiers IOSR Journal of Electroncs and Communcaton Engneerng (IOSR-JECE) e-issn: 78-834,p- ISSN: 78-8735.Volume 9, Issue, Ver. IV (Mar - Apr. 04), PP 0-07 Content Based Image Retreval Usng -D Dscrete Wavelet wth

More information

A Bilinear Model for Sparse Coding

A Bilinear Model for Sparse Coding A Blnear Model for Sparse Codng Davd B. Grmes and Rajesh P. N. Rao Department of Computer Scence and Engneerng Unversty of Washngton Seattle, WA 98195-2350, U.S.A. grmes,rao @cs.washngton.edu Abstract

More information

Simulation: Solving Dynamic Models ABE 5646 Week 11 Chapter 2, Spring 2010

Simulation: Solving Dynamic Models ABE 5646 Week 11 Chapter 2, Spring 2010 Smulaton: Solvng Dynamc Models ABE 5646 Week Chapter 2, Sprng 200 Week Descrpton Readng Materal Mar 5- Mar 9 Evaluatng [Crop] Models Comparng a model wth data - Graphcal, errors - Measures of agreement

More information

Classifier Selection Based on Data Complexity Measures *

Classifier Selection Based on Data Complexity Measures * Classfer Selecton Based on Data Complexty Measures * Edth Hernández-Reyes, J.A. Carrasco-Ochoa, and J.Fco. Martínez-Trndad Natonal Insttute for Astrophyscs, Optcs and Electroncs, Lus Enrque Erro No.1 Sta.

More information

X- Chart Using ANOM Approach

X- Chart Using ANOM Approach ISSN 1684-8403 Journal of Statstcs Volume 17, 010, pp. 3-3 Abstract X- Chart Usng ANOM Approach Gullapall Chakravarth 1 and Chaluvad Venkateswara Rao Control lmts for ndvdual measurements (X) chart are

More information

Unsupervised Learning

Unsupervised Learning Pattern Recognton Lecture 8 Outlne Introducton Unsupervsed Learnng Parametrc VS Non-Parametrc Approach Mxture of Denstes Maxmum-Lkelhood Estmates Clusterng Prof. Danel Yeung School of Computer Scence and

More information

S1 Note. Basis functions.

S1 Note. Basis functions. S1 Note. Bass functons. Contents Types of bass functons...1 The Fourer bass...2 B-splne bass...3 Power and type I error rates wth dfferent numbers of bass functons...4 Table S1. Smulaton results of type

More information

Cluster Analysis of Electrical Behavior

Cluster Analysis of Electrical Behavior Journal of Computer and Communcatons, 205, 3, 88-93 Publshed Onlne May 205 n ScRes. http://www.scrp.org/ournal/cc http://dx.do.org/0.4236/cc.205.350 Cluster Analyss of Electrcal Behavor Ln Lu Ln Lu, School

More information

Term Weighting Classification System Using the Chi-square Statistic for the Classification Subtask at NTCIR-6 Patent Retrieval Task

Term Weighting Classification System Using the Chi-square Statistic for the Classification Subtask at NTCIR-6 Patent Retrieval Task Proceedngs of NTCIR-6 Workshop Meetng, May 15-18, 2007, Tokyo, Japan Term Weghtng Classfcaton System Usng the Ch-square Statstc for the Classfcaton Subtask at NTCIR-6 Patent Retreval Task Kotaro Hashmoto

More information

Three supervised learning methods on pen digits character recognition dataset

Three supervised learning methods on pen digits character recognition dataset Three supervsed learnng methods on pen dgts character recognton dataset Chrs Flezach Department of Computer Scence and Engneerng Unversty of Calforna, San Dego San Dego, CA 92093 cflezac@cs.ucsd.edu Satoru

More information

Adaptive Transfer Learning

Adaptive Transfer Learning Adaptve Transfer Learnng Bn Cao, Snno Jaln Pan, Yu Zhang, Dt-Yan Yeung, Qang Yang Hong Kong Unversty of Scence and Technology Clear Water Bay, Kowloon, Hong Kong {caobn,snnopan,zhangyu,dyyeung,qyang}@cse.ust.hk

More information

FEATURE EXTRACTION. Dr. K.Vijayarekha. Associate Dean School of Electrical and Electronics Engineering SASTRA University, Thanjavur

FEATURE EXTRACTION. Dr. K.Vijayarekha. Associate Dean School of Electrical and Electronics Engineering SASTRA University, Thanjavur FEATURE EXTRACTION Dr. K.Vjayarekha Assocate Dean School of Electrcal and Electroncs Engneerng SASTRA Unversty, Thanjavur613 41 Jont Intatve of IITs and IISc Funded by MHRD Page 1 of 8 Table of Contents

More information

A Binarization Algorithm specialized on Document Images and Photos

A Binarization Algorithm specialized on Document Images and Photos A Bnarzaton Algorthm specalzed on Document mages and Photos Ergna Kavalleratou Dept. of nformaton and Communcaton Systems Engneerng Unversty of the Aegean kavalleratou@aegean.gr Abstract n ths paper, a

More information

Biostatistics 615/815

Biostatistics 615/815 The E-M Algorthm Bostatstcs 615/815 Lecture 17 Last Lecture: The Smplex Method General method for optmzaton Makes few assumptons about functon Crawls towards mnmum Some recommendatons Multple startng ponts

More information

Analysis of Continuous Beams in General

Analysis of Continuous Beams in General Analyss of Contnuous Beams n General Contnuous beams consdered here are prsmatc, rgdly connected to each beam segment and supported at varous ponts along the beam. onts are selected at ponts of support,

More information

Online Detection and Classification of Moving Objects Using Progressively Improving Detectors

Online Detection and Classification of Moving Objects Using Progressively Improving Detectors Onlne Detecton and Classfcaton of Movng Objects Usng Progressvely Improvng Detectors Omar Javed Saad Al Mubarak Shah Computer Vson Lab School of Computer Scence Unversty of Central Florda Orlando, FL 32816

More information

NAG Fortran Library Chapter Introduction. G10 Smoothing in Statistics

NAG Fortran Library Chapter Introduction. G10 Smoothing in Statistics Introducton G10 NAG Fortran Lbrary Chapter Introducton G10 Smoothng n Statstcs Contents 1 Scope of the Chapter... 2 2 Background to the Problems... 2 2.1 Smoothng Methods... 2 2.2 Smoothng Splnes and Regresson

More information

Tsinghua University at TAC 2009: Summarizing Multi-documents by Information Distance

Tsinghua University at TAC 2009: Summarizing Multi-documents by Information Distance Tsnghua Unversty at TAC 2009: Summarzng Mult-documents by Informaton Dstance Chong Long, Mnle Huang, Xaoyan Zhu State Key Laboratory of Intellgent Technology and Systems, Tsnghua Natonal Laboratory for

More information

Subspace clustering. Clustering. Fundamental to all clustering techniques is the choice of distance measure between data points;

Subspace clustering. Clustering. Fundamental to all clustering techniques is the choice of distance measure between data points; Subspace clusterng Clusterng Fundamental to all clusterng technques s the choce of dstance measure between data ponts; D q ( ) ( ) 2 x x = x x, j k = 1 k jk Squared Eucldean dstance Assumpton: All features

More information

Classifying Acoustic Transient Signals Using Artificial Intelligence

Classifying Acoustic Transient Signals Using Artificial Intelligence Classfyng Acoustc Transent Sgnals Usng Artfcal Intellgence Steve Sutton, Unversty of North Carolna At Wlmngton (suttons@charter.net) Greg Huff, Unversty of North Carolna At Wlmngton (jgh7476@uncwl.edu)

More information

Edge Detection in Noisy Images Using the Support Vector Machines

Edge Detection in Noisy Images Using the Support Vector Machines Edge Detecton n Nosy Images Usng the Support Vector Machnes Hlaro Gómez-Moreno, Saturnno Maldonado-Bascón, Francsco López-Ferreras Sgnal Theory and Communcatons Department. Unversty of Alcalá Crta. Madrd-Barcelona

More information

Determining the Optimal Bandwidth Based on Multi-criterion Fusion

Determining the Optimal Bandwidth Based on Multi-criterion Fusion Proceedngs of 01 4th Internatonal Conference on Machne Learnng and Computng IPCSIT vol. 5 (01) (01) IACSIT Press, Sngapore Determnng the Optmal Bandwdth Based on Mult-crteron Fuson Ha-L Lang 1+, Xan-Mn

More information

Machine Learning 9. week

Machine Learning 9. week Machne Learnng 9. week Mappng Concept Radal Bass Functons (RBF) RBF Networks 1 Mappng It s probably the best scenaro for the classfcaton of two dataset s to separate them lnearly. As you see n the below

More information

Collaboratively Regularized Nearest Points for Set Based Recognition

Collaboratively Regularized Nearest Points for Set Based Recognition Academc Center for Computng and Meda Studes, Kyoto Unversty Collaboratvely Regularzed Nearest Ponts for Set Based Recognton Yang Wu, Mchhko Mnoh, Masayuk Mukunok Kyoto Unversty 9/1/013 BMVC 013 @ Brstol,

More information

EXTENDED BIC CRITERION FOR MODEL SELECTION

EXTENDED BIC CRITERION FOR MODEL SELECTION IDIAP RESEARCH REPORT EXTEDED BIC CRITERIO FOR ODEL SELECTIO Itshak Lapdot Andrew orrs IDIAP-RR-0-4 Dalle olle Insttute for Perceptual Artfcal Intellgence P.O.Box 59 artgny Valas Swtzerland phone +4 7

More information

The Codesign Challenge

The Codesign Challenge ECE 4530 Codesgn Challenge Fall 2007 Hardware/Software Codesgn The Codesgn Challenge Objectves In the codesgn challenge, your task s to accelerate a gven software reference mplementaton as fast as possble.

More information

The Research of Support Vector Machine in Agricultural Data Classification

The Research of Support Vector Machine in Agricultural Data Classification The Research of Support Vector Machne n Agrcultural Data Classfcaton Le Sh, Qguo Duan, Xnmng Ma, Me Weng College of Informaton and Management Scence, HeNan Agrcultural Unversty, Zhengzhou 45000 Chna Zhengzhou

More information

Mathematics 256 a course in differential equations for engineering students

Mathematics 256 a course in differential equations for engineering students Mathematcs 56 a course n dfferental equatons for engneerng students Chapter 5. More effcent methods of numercal soluton Euler s method s qute neffcent. Because the error s essentally proportonal to the

More information

Improvement of Spatial Resolution Using BlockMatching Based Motion Estimation and Frame. Integration

Improvement of Spatial Resolution Using BlockMatching Based Motion Estimation and Frame. Integration Improvement of Spatal Resoluton Usng BlockMatchng Based Moton Estmaton and Frame Integraton Danya Suga and Takayuk Hamamoto Graduate School of Engneerng, Tokyo Unversty of Scence, 6-3-1, Nuku, Katsuska-ku,

More information

CLASSIFICATION OF ULTRASONIC SIGNALS

CLASSIFICATION OF ULTRASONIC SIGNALS The 8 th Internatonal Conference of the Slovenan Socety for Non-Destructve Testng»Applcaton of Contemporary Non-Destructve Testng n Engneerng«September -3, 5, Portorož, Slovena, pp. 7-33 CLASSIFICATION

More information

y and the total sum of

y and the total sum of Lnear regresson Testng for non-lnearty In analytcal chemstry, lnear regresson s commonly used n the constructon of calbraton functons requred for analytcal technques such as gas chromatography, atomc absorpton

More information

MULTISPECTRAL IMAGES CLASSIFICATION BASED ON KLT AND ATR AUTOMATIC TARGET RECOGNITION

MULTISPECTRAL IMAGES CLASSIFICATION BASED ON KLT AND ATR AUTOMATIC TARGET RECOGNITION MULTISPECTRAL IMAGES CLASSIFICATION BASED ON KLT AND ATR AUTOMATIC TARGET RECOGNITION Paulo Quntlano 1 & Antono Santa-Rosa 1 Federal Polce Department, Brasla, Brazl. E-mals: quntlano.pqs@dpf.gov.br and

More information

Wishing you all a Total Quality New Year!

Wishing you all a Total Quality New Year! Total Qualty Management and Sx Sgma Post Graduate Program 214-15 Sesson 4 Vnay Kumar Kalakband Assstant Professor Operatons & Systems Area 1 Wshng you all a Total Qualty New Year! Hope you acheve Sx sgma

More information

Machine Learning: Algorithms and Applications

Machine Learning: Algorithms and Applications 14/05/1 Machne Learnng: Algorthms and Applcatons Florano Zn Free Unversty of Bozen-Bolzano Faculty of Computer Scence Academc Year 011-01 Lecture 10: 14 May 01 Unsupervsed Learnng cont Sldes courtesy of

More information

Face Recognition University at Buffalo CSE666 Lecture Slides Resources:

Face Recognition University at Buffalo CSE666 Lecture Slides Resources: Face Recognton Unversty at Buffalo CSE666 Lecture Sldes Resources: http://www.face-rec.org/algorthms/ Overvew of face recognton algorthms Correlaton - Pxel based correspondence between two face mages Structural

More information

A Unified Framework for Semantics and Feature Based Relevance Feedback in Image Retrieval Systems

A Unified Framework for Semantics and Feature Based Relevance Feedback in Image Retrieval Systems A Unfed Framework for Semantcs and Feature Based Relevance Feedback n Image Retreval Systems Ye Lu *, Chunhu Hu 2, Xngquan Zhu 3*, HongJang Zhang 2, Qang Yang * School of Computng Scence Smon Fraser Unversty

More information

Explicit Formulas and Efficient Algorithm for Moment Computation of Coupled RC Trees with Lumped and Distributed Elements

Explicit Formulas and Efficient Algorithm for Moment Computation of Coupled RC Trees with Lumped and Distributed Elements Explct Formulas and Effcent Algorthm for Moment Computaton of Coupled RC Trees wth Lumped and Dstrbuted Elements Qngan Yu and Ernest S.Kuh Electroncs Research Lab. Unv. of Calforna at Berkeley Berkeley

More information

Discriminative Dictionary Learning with Pairwise Constraints

Discriminative Dictionary Learning with Pairwise Constraints Dscrmnatve Dctonary Learnng wth Parwse Constrants Humn Guo Zhuoln Jang LARRY S. DAVIS UNIVERSITY OF MARYLAND Nov. 6 th, Outlne Introducton/motvaton Dctonary Learnng Dscrmnatve Dctonary Learnng wth Parwse

More information

An Optimal Algorithm for Prufer Codes *

An Optimal Algorithm for Prufer Codes * J. Software Engneerng & Applcatons, 2009, 2: 111-115 do:10.4236/jsea.2009.22016 Publshed Onlne July 2009 (www.scrp.org/journal/jsea) An Optmal Algorthm for Prufer Codes * Xaodong Wang 1, 2, Le Wang 3,

More information

Problem Definitions and Evaluation Criteria for Computational Expensive Optimization

Problem Definitions and Evaluation Criteria for Computational Expensive Optimization Problem efntons and Evaluaton Crtera for Computatonal Expensve Optmzaton B. Lu 1, Q. Chen and Q. Zhang 3, J. J. Lang 4, P. N. Suganthan, B. Y. Qu 6 1 epartment of Computng, Glyndwr Unversty, UK Faclty

More information

Adjustment methods for differential measurement errors in multimode surveys

Adjustment methods for differential measurement errors in multimode surveys Adjustment methods for dfferental measurement errors n multmode surveys Salah Merad UK Offce for Natonal Statstcs ESSnet MM DCSS, Fnal Meetng Wesbaden, Germany, 4-5 September 2014 Outlne Introducton Stablsng

More information

CS434a/541a: Pattern Recognition Prof. Olga Veksler. Lecture 15

CS434a/541a: Pattern Recognition Prof. Olga Veksler. Lecture 15 CS434a/541a: Pattern Recognton Prof. Olga Veksler Lecture 15 Today New Topc: Unsupervsed Learnng Supervsed vs. unsupervsed learnng Unsupervsed learnng Net Tme: parametrc unsupervsed learnng Today: nonparametrc

More information

Empirical Distributions of Parameter Estimates. in Binary Logistic Regression Using Bootstrap

Empirical Distributions of Parameter Estimates. in Binary Logistic Regression Using Bootstrap Int. Journal of Math. Analyss, Vol. 8, 4, no. 5, 7-7 HIKARI Ltd, www.m-hkar.com http://dx.do.org/.988/jma.4.494 Emprcal Dstrbutons of Parameter Estmates n Bnary Logstc Regresson Usng Bootstrap Anwar Ftranto*

More information

Unsupervised Learning and Clustering

Unsupervised Learning and Clustering Unsupervsed Learnng and Clusterng Why consder unlabeled samples?. Collectng and labelng large set of samples s costly Gettng recorded speech s free, labelng s tme consumng 2. Classfer could be desgned

More information

A Fast Content-Based Multimedia Retrieval Technique Using Compressed Data

A Fast Content-Based Multimedia Retrieval Technique Using Compressed Data A Fast Content-Based Multmeda Retreval Technque Usng Compressed Data Borko Furht and Pornvt Saksobhavvat NSF Multmeda Laboratory Florda Atlantc Unversty, Boca Raton, Florda 3343 ABSTRACT In ths paper,

More information

Quality Improvement Algorithm for Tetrahedral Mesh Based on Optimal Delaunay Triangulation

Quality Improvement Algorithm for Tetrahedral Mesh Based on Optimal Delaunay Triangulation Intellgent Informaton Management, 013, 5, 191-195 Publshed Onlne November 013 (http://www.scrp.org/journal/m) http://dx.do.org/10.36/m.013.5601 Qualty Improvement Algorthm for Tetrahedral Mesh Based on

More information

Support Vector Machines

Support Vector Machines Support Vector Machnes Decson surface s a hyperplane (lne n 2D) n feature space (smlar to the Perceptron) Arguably, the most mportant recent dscovery n machne learnng In a nutshell: map the data to a predetermned

More information

A mathematical programming approach to the analysis, design and scheduling of offshore oilfields

A mathematical programming approach to the analysis, design and scheduling of offshore oilfields 17 th European Symposum on Computer Aded Process Engneerng ESCAPE17 V. Plesu and P.S. Agach (Edtors) 2007 Elsever B.V. All rghts reserved. 1 A mathematcal programmng approach to the analyss, desgn and

More information

Active Contours/Snakes

Active Contours/Snakes Actve Contours/Snakes Erkut Erdem Acknowledgement: The sldes are adapted from the sldes prepared by K. Grauman of Unversty of Texas at Austn Fttng: Edges vs. boundares Edges useful sgnal to ndcate occludng

More information

A Background Subtraction for a Vision-based User Interface *

A Background Subtraction for a Vision-based User Interface * A Background Subtracton for a Vson-based User Interface * Dongpyo Hong and Woontack Woo KJIST U-VR Lab. {dhon wwoo}@kjst.ac.kr Abstract In ths paper, we propose a robust and effcent background subtracton

More information

Optimizing Document Scoring for Query Retrieval

Optimizing Document Scoring for Query Retrieval Optmzng Document Scorng for Query Retreval Brent Ellwen baellwe@cs.stanford.edu Abstract The goal of ths project was to automate the process of tunng a document query engne. Specfcally, I used machne learnng

More information

Detection of an Object by using Principal Component Analysis

Detection of an Object by using Principal Component Analysis Detecton of an Object by usng Prncpal Component Analyss 1. G. Nagaven, 2. Dr. T. Sreenvasulu Reddy 1. M.Tech, Department of EEE, SVUCE, Trupath, Inda. 2. Assoc. Professor, Department of ECE, SVUCE, Trupath,

More information

Simulation Based Analysis of FAST TCP using OMNET++

Simulation Based Analysis of FAST TCP using OMNET++ Smulaton Based Analyss of FAST TCP usng OMNET++ Umar ul Hassan 04030038@lums.edu.pk Md Term Report CS678 Topcs n Internet Research Sprng, 2006 Introducton Internet traffc s doublng roughly every 3 months

More information

A New Approach For the Ranking of Fuzzy Sets With Different Heights

A New Approach For the Ranking of Fuzzy Sets With Different Heights New pproach For the ankng of Fuzzy Sets Wth Dfferent Heghts Pushpnder Sngh School of Mathematcs Computer pplcatons Thapar Unversty, Patala-7 00 Inda pushpndersnl@gmalcom STCT ankng of fuzzy sets plays

More information

High-Boost Mesh Filtering for 3-D Shape Enhancement

High-Boost Mesh Filtering for 3-D Shape Enhancement Hgh-Boost Mesh Flterng for 3-D Shape Enhancement Hrokazu Yagou Λ Alexander Belyaev y Damng We z Λ y z ; ; Shape Modelng Laboratory, Unversty of Azu, Azu-Wakamatsu 965-8580 Japan y Computer Graphcs Group,

More information

EECS 730 Introduction to Bioinformatics Sequence Alignment. Luke Huan Electrical Engineering and Computer Science

EECS 730 Introduction to Bioinformatics Sequence Alignment. Luke Huan Electrical Engineering and Computer Science EECS 730 Introducton to Bonformatcs Sequence Algnment Luke Huan Electrcal Engneerng and Computer Scence http://people.eecs.ku.edu/~huan/ HMM Π s a set of states Transton Probabltes a kl Pr( l 1 k Probablty

More information

BOOSTING CLASSIFICATION ACCURACY WITH SAMPLES CHOSEN FROM A VALIDATION SET

BOOSTING CLASSIFICATION ACCURACY WITH SAMPLES CHOSEN FROM A VALIDATION SET 1 BOOSTING CLASSIFICATION ACCURACY WITH SAMPLES CHOSEN FROM A VALIDATION SET TZU-CHENG CHUANG School of Electrcal and Computer Engneerng, Purdue Unversty, West Lafayette, Indana 47907 SAUL B. GELFAND School

More information

Classification Based Mode Decisions for Video over Networks

Classification Based Mode Decisions for Video over Networks Classfcaton Based Mode Decsons for Vdeo over Networks Deepak S. Turaga and Tsuhan Chen Advanced Multmeda Processng Lab Tranng data for Inter-Intra Decson Inter-Intra Decson Regons pdf 6 5 6 5 Energy 4

More information

Chapter 6 Programmng the fnte element method Inow turn to the man subject of ths book: The mplementaton of the fnte element algorthm n computer programs. In order to make my dscusson as straghtforward

More information

Fusion Performance Model for Distributed Tracking and Classification

Fusion Performance Model for Distributed Tracking and Classification Fuson Performance Model for Dstrbuted rackng and Classfcaton K.C. Chang and Yng Song Dept. of SEOR, School of I&E George Mason Unversty FAIRFAX, VA kchang@gmu.edu Martn Lggns Verdan Systems Dvson, Inc.

More information

Lecture #15 Lecture Notes

Lecture #15 Lecture Notes Lecture #15 Lecture Notes The ocean water column s very much a 3-D spatal entt and we need to represent that structure n an economcal way to deal wth t n calculatons. We wll dscuss one way to do so, emprcal

More information

A MOVING MESH APPROACH FOR SIMULATION BUDGET ALLOCATION ON CONTINUOUS DOMAINS

A MOVING MESH APPROACH FOR SIMULATION BUDGET ALLOCATION ON CONTINUOUS DOMAINS Proceedngs of the Wnter Smulaton Conference M E Kuhl, N M Steger, F B Armstrong, and J A Jones, eds A MOVING MESH APPROACH FOR SIMULATION BUDGET ALLOCATION ON CONTINUOUS DOMAINS Mark W Brantley Chun-Hung

More information

SVM-based Learning for Multiple Model Estimation

SVM-based Learning for Multiple Model Estimation SVM-based Learnng for Multple Model Estmaton Vladmr Cherkassky and Yunqan Ma Department of Electrcal and Computer Engneerng Unversty of Mnnesota Mnneapols, MN 55455 {cherkass,myq}@ece.umn.edu Abstract:

More information

7/12/2016. GROUP ANALYSIS Martin M. Monti UCLA Psychology AGGREGATING MULTIPLE SUBJECTS VARIANCE AT THE GROUP LEVEL

7/12/2016. GROUP ANALYSIS Martin M. Monti UCLA Psychology AGGREGATING MULTIPLE SUBJECTS VARIANCE AT THE GROUP LEVEL GROUP ANALYSIS Martn M. Mont UCLA Psychology NITP AGGREGATING MULTIPLE SUBJECTS When we conduct mult-subject analyss we are tryng to understand whether an effect s sgnfcant across a group of people. Whether

More information

Positive Semi-definite Programming Localization in Wireless Sensor Networks

Positive Semi-definite Programming Localization in Wireless Sensor Networks Postve Sem-defnte Programmng Localzaton n Wreless Sensor etworks Shengdong Xe 1,, Jn Wang, Aqun Hu 1, Yunl Gu, Jang Xu, 1 School of Informaton Scence and Engneerng, Southeast Unversty, 10096, anjng Computer

More information

APPLICATION OF MULTIVARIATE LOSS FUNCTION FOR ASSESSMENT OF THE QUALITY OF TECHNOLOGICAL PROCESS MANAGEMENT

APPLICATION OF MULTIVARIATE LOSS FUNCTION FOR ASSESSMENT OF THE QUALITY OF TECHNOLOGICAL PROCESS MANAGEMENT 3. - 5. 5., Brno, Czech Republc, EU APPLICATION OF MULTIVARIATE LOSS FUNCTION FOR ASSESSMENT OF THE QUALITY OF TECHNOLOGICAL PROCESS MANAGEMENT Abstract Josef TOŠENOVSKÝ ) Lenka MONSPORTOVÁ ) Flp TOŠENOVSKÝ

More information

Electrical analysis of light-weight, triangular weave reflector antennas

Electrical analysis of light-weight, triangular weave reflector antennas Electrcal analyss of lght-weght, trangular weave reflector antennas Knud Pontoppdan TICRA Laederstraede 34 DK-121 Copenhagen K Denmark Emal: kp@tcra.com INTRODUCTION The new lght-weght reflector antenna

More information

Joint Probabilistic Curve Clustering and Alignment

Joint Probabilistic Curve Clustering and Alignment Jont Probablstc Curve Clusterng and Algnment Scott Gaffney and Padhrac Smyth School of Informaton and Computer Scence Unversty of Calforna, Irvne, CA 9697-345 {sgaffney,smyth}@cs.uc.edu Abstract Clusterng

More information

Mixed Linear System Estimation and Identification

Mixed Linear System Estimation and Identification 48th IEEE Conference on Decson and Control, Shangha, Chna, December 2009 Mxed Lnear System Estmaton and Identfcaton A. Zymns S. Boyd D. Gornevsky Abstract We consder a mxed lnear system model, wth both

More information

A Fast Visual Tracking Algorithm Based on Circle Pixels Matching

A Fast Visual Tracking Algorithm Based on Circle Pixels Matching A Fast Vsual Trackng Algorthm Based on Crcle Pxels Matchng Zhqang Hou hou_zhq@sohu.com Chongzhao Han czhan@mal.xjtu.edu.cn Ln Zheng Abstract: A fast vsual trackng algorthm based on crcle pxels matchng

More information

A Statistical Model Selection Strategy Applied to Neural Networks

A Statistical Model Selection Strategy Applied to Neural Networks A Statstcal Model Selecton Strategy Appled to Neural Networks Joaquín Pzarro Elsa Guerrero Pedro L. Galndo joaqun.pzarro@uca.es elsa.guerrero@uca.es pedro.galndo@uca.es Dpto Lenguajes y Sstemas Informátcos

More information

TN348: Openlab Module - Colocalization

TN348: Openlab Module - Colocalization TN348: Openlab Module - Colocalzaton Topc The Colocalzaton module provdes the faclty to vsualze and quantfy colocalzaton between pars of mages. The Colocalzaton wndow contans a prevew of the two mages

More information

Fuzzy Filtering Algorithms for Image Processing: Performance Evaluation of Various Approaches

Fuzzy Filtering Algorithms for Image Processing: Performance Evaluation of Various Approaches Proceedngs of the Internatonal Conference on Cognton and Recognton Fuzzy Flterng Algorthms for Image Processng: Performance Evaluaton of Varous Approaches Rajoo Pandey and Umesh Ghanekar Department of

More information

Optimization Methods: Integer Programming Integer Linear Programming 1. Module 7 Lecture Notes 1. Integer Linear Programming

Optimization Methods: Integer Programming Integer Linear Programming 1. Module 7 Lecture Notes 1. Integer Linear Programming Optzaton Methods: Integer Prograng Integer Lnear Prograng Module Lecture Notes Integer Lnear Prograng Introducton In all the prevous lectures n lnear prograng dscussed so far, the desgn varables consdered

More information

6.854 Advanced Algorithms Petar Maymounkov Problem Set 11 (November 23, 2005) With: Benjamin Rossman, Oren Weimann, and Pouya Kheradpour

6.854 Advanced Algorithms Petar Maymounkov Problem Set 11 (November 23, 2005) With: Benjamin Rossman, Oren Weimann, and Pouya Kheradpour 6.854 Advanced Algorthms Petar Maymounkov Problem Set 11 (November 23, 2005) Wth: Benjamn Rossman, Oren Wemann, and Pouya Kheradpour Problem 1. We reduce vertex cover to MAX-SAT wth weghts, such that the

More information

We Two Seismic Interference Attenuation Methods Based on Automatic Detection of Seismic Interference Moveout

We Two Seismic Interference Attenuation Methods Based on Automatic Detection of Seismic Interference Moveout We 14 15 Two Sesmc Interference Attenuaton Methods Based on Automatc Detecton of Sesmc Interference Moveout S. Jansen* (Unversty of Oslo), T. Elboth (CGG) & C. Sanchs (CGG) SUMMARY The need for effcent

More information

A Post Randomization Framework for Privacy-Preserving Bayesian. Network Parameter Learning

A Post Randomization Framework for Privacy-Preserving Bayesian. Network Parameter Learning A Post Randomzaton Framework for Prvacy-Preservng Bayesan Network Parameter Learnng JIANJIE MA K.SIVAKUMAR School Electrcal Engneerng and Computer Scence, Washngton State Unversty Pullman, WA. 9964-75

More information

Related-Mode Attacks on CTR Encryption Mode

Related-Mode Attacks on CTR Encryption Mode Internatonal Journal of Network Securty, Vol.4, No.3, PP.282 287, May 2007 282 Related-Mode Attacks on CTR Encrypton Mode Dayn Wang, Dongda Ln, and Wenlng Wu (Correspondng author: Dayn Wang) Key Laboratory

More information

UB at GeoCLEF Department of Geography Abstract

UB at GeoCLEF Department of Geography   Abstract UB at GeoCLEF 2006 Mguel E. Ruz (1), Stuart Shapro (2), June Abbas (1), Slva B. Southwck (1) and Davd Mark (3) State Unversty of New York at Buffalo (1) Department of Lbrary and Informaton Studes (2) Department

More information

Wavefront Reconstructor

Wavefront Reconstructor A Dstrbuted Smplex B-Splne Based Wavefront Reconstructor Coen de Vsser and Mchel Verhaegen 14-12-201212 2012 Delft Unversty of Technology Contents Introducton Wavefront reconstructon usng Smplex B-Splnes

More information

BAYESIAN MULTI-SOURCE DOMAIN ADAPTATION

BAYESIAN MULTI-SOURCE DOMAIN ADAPTATION BAYESIAN MULTI-SOURCE DOMAIN ADAPTATION SHI-LIANG SUN, HONG-LEI SHI Department of Computer Scence and Technology, East Chna Normal Unversty 500 Dongchuan Road, Shangha 200241, P. R. Chna E-MAIL: slsun@cs.ecnu.edu.cn,

More information

Incremental MQDF Learning for Writer Adaptive Handwriting Recognition 1

Incremental MQDF Learning for Writer Adaptive Handwriting Recognition 1 200 2th Internatonal Conference on Fronters n Handwrtng Recognton Incremental MQDF Learnng for Wrter Adaptve Handwrtng Recognton Ka Dng, Lanwen Jn * School of Electronc and Informaton Engneerng, South

More information

Machine Learning. Topic 6: Clustering

Machine Learning. Topic 6: Clustering Machne Learnng Topc 6: lusterng lusterng Groupng data nto (hopefully useful) sets. Thngs on the left Thngs on the rght Applcatons of lusterng Hypothess Generaton lusters mght suggest natural groups. Hypothess

More information

Some Advanced SPC Tools 1. Cumulative Sum Control (Cusum) Chart For the data shown in Table 9-1, the x chart can be generated.

Some Advanced SPC Tools 1. Cumulative Sum Control (Cusum) Chart For the data shown in Table 9-1, the x chart can be generated. Some Advanced SP Tools 1. umulatve Sum ontrol (usum) hart For the data shown n Table 9-1, the x chart can be generated. However, the shft taken place at sample #21 s not apparent. 92 For ths set samples,

More information

A Hidden Markov Model Variant for Sequence Classification

A Hidden Markov Model Variant for Sequence Classification Proceedngs of the Twenty-Second Internatonal Jont Conference on Artfcal Intellgence A Hdden Markov Model Varant for Sequence Classfcaton Sam Blasak and Huzefa Rangwala Computer Scence, George Mason Unversty

More information

SENSITIVITY ANALYSIS IN LINEAR PROGRAMMING USING A CALCULATOR

SENSITIVITY ANALYSIS IN LINEAR PROGRAMMING USING A CALCULATOR SENSITIVITY ANALYSIS IN LINEAR PROGRAMMING USING A CALCULATOR Judth Aronow Rchard Jarvnen Independent Consultant Dept of Math/Stat 559 Frost Wnona State Unversty Beaumont, TX 7776 Wnona, MN 55987 aronowju@hal.lamar.edu

More information

Data Mining: Model Evaluation

Data Mining: Model Evaluation Data Mnng: Model Evaluaton Aprl 16, 2013 1 Issues: Evaluatng Classfcaton Methods Accurac classfer accurac: predctng class label predctor accurac: guessng value of predcted attrbutes Speed tme to construct

More information