By : Moataz Al-Haj. Vision Topics Seminar (University of Haifa) Supervised by Dr. Hagit Hel-Or

Transcription

1 By : Moataz Al-Haj Vson Topcs Semnar (Unversty of Hafa) Supervsed by Dr. Hagt Hel-Or

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3 -Introducton to SVM : Hstory and motvaton -Problem defnton -The SVM approach: The Lnear separable case -SVM: Non Lnear separable case: - VC Dmenson - The kernel Trck : dscusson on Kernel functons. -Soft margn: ntroducng the slack varables and dscussng the trade-off parameter C. -Procedure for choosng an SVM model that best fts our problem ( K-fold ). -Some Applcatons of SVM. -Concluson: The Advantages and Drawbacks of SVM. -Software : Popular mplementatons of SVM -References

4 Before Startng Before startng: 1- throughout the lecture f you see underlned red colored text then clck on ths text for farther nformaton. 2-let me ntroduce you to Nodnkt :She s an outstandng student. Although she asks many questons but sometmes these questons are key questons that help us understand the materal more n depth. Also the notes that she gves are very helpful. H!

5 Introducton to SVM : Hstory and motvaton -Support Vector Machne (SVM) s a supervsed learnng algorthm developed by Vladmr Vapnk and t was frst heard n 1992, ntroduced by Vapnk, Boser and Guyon n COLT-92.[3] -(t s sad that Vladmr Vapnk has mentoned ts dea n 1979 n one of hs paper but ts major development was n the 90 s) - For many years Neural Networks was the ultmate champon, t was the most effectve learnng algorthm. TILL SVM CAME!

6 Introducton to SVM : Hstory and motvaton cont -SVM became popular because of ts success n handwrtten dgt recognton (n NIST (1998)). t gave accuracy that s comparable to sophstcated and carefully constructed neural networks wth elaborated features n a handwrtng recognton task.[1] -Much more effectve off the shelf algorthm than Neural Networks : It generalze good on unseen data and s easer to tran and doesn t have any local optma n contrast to neural networks that may have many local optma and takes a lot of tme to converge.[4]

7 Introducton to SVM : Hstory and motvaton cont - SVM has successful applcatons n many complex, real-world problems such as text and mage classfcaton, hand-wrtng recognton, data mnng, bonformatcs, medcne and bosequence analyss and even stock market! - In many of these applcatons SVM s the best choce. - We wll further elaborate on some of these applcatons latter n ths lecture.

8 Problem defnton: -We are gven a set of n ponts (vectors) : x1, x2,... x n such that x s a vector of length m, and each belong to one of two classes we label them by +1 and -1. -So our tranng set s: ( x, y ),( x, y ),...( x, y ) m x R, y + { 1, 1} n n So the decson functon wll be f ( x) = sgn( w x + b) - We want to fnd a separatng hyperplane w x+ b= 0 that separates these ponts nto the two classes. The postves (class +1 ) and The negatves (class -1 ). (Assumng that they are lnearly separable)

9 Separatng Hyperplane y = + 1 y = 1 x 2 f ( x) = sgn( w x + b) A separatng hypreplane w x+ b= 0 x 1 But There are many possbltes for such hyperplanes!!

10 Separatng Hyperplanes y = + 1 y = 1 Whch one should we choose! Yes, There are many possble separatng hyperplanes It could be ths one or ths or ths or maybe.!

11 Choosng a separatng hyperplane: -Suppose we choose the hypreplane (seen below) that s close to some sample. x - Now suppose we have a new pont x ' that should be n class -1 and s close to x. Usng our classfcaton functon f( x) ths pont s msclassfed! f ( x) = sgn( w x + b) Poor generalzaton! (Poor performance on unseen data) x x '

12 Choosng a separatng hyperplane: -Hyperplane should be as far as possble from any sample pont. -Ths way a new data that s close to the old samples wll be classfed correctly. Good generalzaton! x x '

13 Choosng a separatng hyperplane. The SVM approach: Lnear separable case -The SVM dea s to maxmze the dstance between The hyperplane and the closest sample pont. In the optmal hyperplane: The dstance to the closest negatve pont = The dstance to the closest postve pont. Aha! I see!

14 Choosng a separatng hyperplane. The SVM approach: Lnear separable case SVM s goal s to maxmze the Margn whch s twce the dstance d between the separatng hyperplane and the closest sample. Why t s the best? -Robust to outlners as we saw and thus strong generalzaton ablty. -It proved tself to have better performance on test data n both practce and n theory. x

15 Choosng a separatng hyperplane. The SVM approach: Lnear separable case Support vectors are the samples closest to the separatng hyperplane. Oh! So ths s where the name came from! These are Support Vectors x We wll see latter that the Optmal hyperplane s completely defned by the support vectors.

16 SVM : Lnear separable case. Formula for the Margn Let us look at our decson boundary :Ths separatng hyperplane equaton s : Where m m w R, x R, b R w Note that s orthogonal to w the separatng hyperplane and ts length s 1. Let γ be the dstance between the hyperplane and Some tranng example x. So γ s the length of the segment from p to. x t wx + b= 0 w w p γ x

17 SVM : Lnear separable case. Formula for the Margn cont p s pont on the hypreplane t so wp+ b= 0. On the other w hand p = x γ. w t w w ( x γ ) + b= 0 w w w p γ x defne γ = t w x + b w d = mn γ = mn 1.. n 1.. n t wx w + b Note that f we changed w to αw and b to αbths t t αwx+ αb wx+ b wll not affect d snce. αw = w

18 SVM : Lnear separable case. Formula for the Margn cont -Let x ' be a sample pont closet to The boundary. Set (we can rescale w and b). t wx' + b = 1 x ' -For unqueness set t wx + b = 1 for any sample boundary. So now x t wx' + b 1 d = = w w closest to the The Margn m = 2 w

19 SVM : Lnear separable case. Fndng the optmal hyperplane: To fnd the optmal separatng hyperplane, SVM ams to maxmze the margn: -Maxmze such that: m = 2 w T For y =+ 1, wx+ b 1 T For y = 1, wx+ b 1 Mnmze such that: y 1 2 w T ( wx+ b) 1 We transformed the problem nto a form that can be effcently solved. We got an optmzaton problem wth a convex quadratc objectve wth only lnear constrans and always has a sngle global mnmum. 2

20 SVM : Lnear separable case. The optmzaton problem: -Our optmzaton problem so far: I do remember the Lagrange Multplers from Calculus! s.t. mnmze y T ( wx+ b) w -We wll solve ths problem by ntroducng Lagrange multplers assocated wth the constrans: α n 1 2 mnmze L ( wb,, α) = w α ( y( x w+ b) 1) p 2 = 1 st. α 0 2

21 SVM : Lnear separable case. The optmzaton problem cont : So our prmal optmzaton problem now: We start solvng ths problem: L p = 0 w = α y x w = 1 n 1 2 mnmze L ( wb,, α) = w α ( y( x w+ b) 1) L p b = 0 p 2 = 1 st. α 0 n = 1 n α y = 0

22 SVM : Lnear separable case. Inroducng The Lagrangan Dual Problem. By substtutng the above results n the prmal problem and dong some math manpulaton we get: Lagrangan Dual Problem: maxmaze L ( ) 1 n n n t D α = α αα jyyx j xj = 1 2 = 0 j= 0 s. t α 0 and α y = 0 = 1 n α = { α1, α2,..., α n } are now our varables, one for each sample pont. x

23 SVM : Lnear separable case. Fndng w and b for the boundary t : Usng the KKT (Karush-Kuhn-Tucker) condton: ( T y wx b ) α ( + ) 1 = 0 -We can calculate b by takng such that α > 0 : Must be t 1 t t y( wx + b) 1 = 0 b= wx = y wx ( y {1, 1}) y -Calculatng w wll be done usng what we have found above : w= αyx α -Usually,Many of the -s are zero so the calculaton of w has a low complexty. wx+ b

24 SVM : Lnear separable case. The mportance of the Support Vectors : -Samples wth α > 0 are the Support Vectors: the closest samples to the separatng hyperplane. n -So w α yx α yx. = = = 1 SV t -And b y wx such that x s a support vector. = t -We see that the separatng hyperplane wx completely defned by the support vectors. -Now our Decson Functon s: + b t f ( x) = sgn( w x + b) = sgn( αyx x + b) SV s

25 SVM : Lnear separable case. Some notes on the dual problem: maxmaze L ( ) 1 n n n t D α = α αα jyyx j xj = 1 2 = 0 j= 0 s. t α 0 and α y = 0 = 1 -Ths s a quadratc programmng (QP) problem. A global maxmum of L α can always be found D ( ) L ( ) D α Can be optmzed usng a QP software. Some examples are Loqo, cplex, etc. (see -But for SVM the most popular QP s Sequental Mnmal Optmzaton (SMO): It was ntroduced by John C. Platt n 1999.And t s wdely used because of ts effcency.[4] n

26 VC (Vapnk-Chervonenks) Dmenson What f the sample ponts are not lnearly separable?! Defnton: The VC dmenson of a class of functons {f} s the maxmum number of ponts that can be separated (shattered) nto two classes n all possble ways by {f}. [6] -f we look at any (non -collnear) three ponts n 2d plane they can be Lnearly separated: These mages above are taken from. 2 The VC dmenson for a set of orented lnes n R s 3.

27 VC Dmenson cont Four ponts not separable n R By a hypreplane 2 But can be separable n 3 R By a hypreplane - The VC dmenson of the set of orented n hyperplanes n R s n+1. [6] -Thus t s always possble, for a fnte set of ponts to fnd a dmenson where all possble separaton of the pont set can be acheved by a hyperplane.

28 Non-lnearty: Data Preprocessng Ths dataset s not (well) lnearly separable: Ths one s: In fact, both are the same dataset! Top: Cartesan coordnates. Bottom: polar coordnates

29 Non-lnearty: Data Preprocessng Non-lnear separaton Lnear separaton Lnear classfer n polar space; acts non-lnearly n Cartesan space.

30 Do hgh dmensons always work?

31 Is ths safe? Caveat: We can separate any set, not just one wth reasonable y : There s a fxed feature map ϕ : R 2 R such that no matter how we label them the mages of the dots are always separable by hyperplanes.

32 Non-lnear SVM : Mappng the data to hgher dmenson Key dea: map our ponts wth a mappng functon φ to a space of suffcently hgh dmenson so that they wll be separable by a hypreplane: -Input space: the space where the ponts x are located -Feature space: the space of φ(x ) after transformaton For example :a non lnearly separable n one dmenson: 0 x φ ( x) = ( xx, ) mappng data to two-dmensonal space wth 2 Wow!, now we can use the lnear SVM we learned n ths hgher dmensonal space! x 2 0 x ( x)

33 Non Lnear SVM: Mappng the data to hgher dmenson cont -To solve a non lnear classfcaton problem wth a lnear classfer all we have to do s to substtute φ( x) Instead of x everywhere where x appears n the optmzaton problem: 1 maxmze L ( α) = α αα y y x x st. α 0 yα = 0 Now t wll be: n n n n t D j j j = 1 2 = 1 j= 1 = 1 1 maxmze L ( α) = α αα y yφ( x ) φ( x ) st. α 0 yα = 0 n n n n t D j j j = 1 2 = 1 j= 1 = 1 t The decson functon wll be: g( x) = f ( φ( x)) = sgn( w φ( x) + b) Clck here to see a demonstraton of mappng the data to a hgher dmenson so that the can be lnearly sparable.

34 Non Lnear SVM : An llustraton of the algorthm:

35 The Kernel Trck: But Computatons n the feature space can be costly because t may be hgh dmensonal! That s rght!, workng n hgh dmensonal space s computatonally expensve. -But luckly the kernel trck comes to rescue: If we look agan at the optmzaton problem: n n n n 1 t L α α αα y yφ x φ x stα yα maxmze ( ) = ( ) ( ). 0 = 0 D j j j = 1 2 = 1 j= 1 = 1 And the decson functon: n t t f ( φ( x)) = sgn( w φ( x) + b) = sgn( αyφ( x ) φ( x) + b) = 1 No need to know ths mappng explctly nor do we need to know the dmenson of the new space, because we only use the dot product of feature vectors n both the tranng and test.

36 The Kernel Trck: A kernel functon s defned as a functon that corresponds to a dot product of two feature vectors n some expanded feature space: T K( x, x ) φ( x ) φ( x ) j j Now we only need to compute K( x, xj) and we don t need to perform computatons n hgh dmensonal space explctly. Ths s what s called the Kernel Trck.

37 Kernel Trck: Computatonal savng of the kernel trck Example Quadratc Bass functon: (Andrew Moore) The cost of computaton s: 2 Om ( ) (m s the dmenson of nput) Where as the correspondng Kernel s : Kab (, ) = ( a b+ 1) 2 The cost of computaton s: Om ( ) To beleve me that t s really the real Kernel :

38 The Kernel Trck The lnear classfer reles on dot product between vectors K(x,x j )=x T x j If every data pont s mapped nto hgh-dmensonal space va some transformaton Φ: x φ(x), the dot product becomes: K(x,x j )= φ(x ) T φ(x j ) A kernel functon s some functon that corresponds to an nner product n some expanded feature space. Example: 2-dmensonal vectors x=[x 1 x 2 ]; let K(x,x j )=(1 + x T x j ) 2, Need to show that K(x,x j )= φ(x ) T φ(x j ): K(x,x j )=(1 + x T x j ) 2, = 1+ x 12 x j x 1 x j1 x 2 x j2 + x 22 x j x 1 x j1 + 2x 2 x j2 = [1 x x 1 x 2 x 2 2 2x 1 2x 2 ] T [1 x j1 2 2 x j1 x j2 x j2 2 2x j1 2x j2 ] = φ(x ) T φ(x j ), where φ(x) = [1 x x 1 x 2 x 2 2 2x 1 2x 2 ]

39 Hgher Order Polynomals (From Andrew Moore) R s the number of samples, m s the dmenson of the sample ponts. Q = yyφ( x) φ( x) kl k l k l 1 kl, R

40 The Kernel Matrx (aka the Gram matrx): K= -The central structure n kernel machnes -Informaton bottleneck : contans all necessary nformaton for the learnng algorthm. -one of ts most nterestng propertes: Mercer s Theorem. based on notes from

41 Mercer s Theorem: -A functon K( x, xj) s a kernel (there exsts a φ( x) such that K( x, ) ( ) T x j φ x φ( x j) ) The Kernel matrx s Symmetrc Postve Sem-defnte. -Another verson of mercer s theorem that sn t related to the kernel matrx s: K( x, xj) functon s a kernel Great!, so know we can check f K s a kernel wthout the need to know φ( x) for any g( u) 2 du gu ( ) such that s fnte then Kuvg (, ) ( u) g( v) dudv 0

42 Examples of Kernels: -Some common choces (the frst two always satsfyng Mercer s condton): t p -Polynomal kernel Kx (, xj) = ( xx j + 1) -Gaussan Radal Bass Functon RBF (data s lfted 1 2 to nfnte dmenson): K( x, xj) = exp( x ) 2 xj 2σ -Sgmodal : K( x, x j) = tanh( kx x j δ ) kernel for every k and ). δ -In fact, SVM model usng a sgmod kernel functon s equvalent to a two-layer, feed-forward neural network -Why s RBF nfnte dmenson? (t s not a

43 Makng Kernels: Now we can make complex kernels from smple ones: Modularty! Taken from (CSI 5325) SVM lecture [7]

44 Important Kernel Issues: How to know whch Kernel to use? I have some questons on kernels. I wrote them on the board. -Ths s a good queston and actually stll an open queston, many researches have been workng to deal wth ths ssue but stll we don t have a frm answer. It s one of the weakness of SVM. We wll see an approach to ths ssue latter. How to verfy that rsng to hgher dmenson usng a specfc kernel wll map the data to a space n whch they are lnearly separable? For most of the kernel functon we don t know the correspondng mappng functon φ( x) so we don t know to whch dmenson we rose the data. So even though rsng to hgher dmenson ncreases the lkelhood that they wll be separable we can t guarantee that. We wll see a compromsng soluton for ths problem.

45 Infnte VC dmenson Two classfcaton systems wth nfnte VC dmenson: 1-NN why? SVM s wth (certan) Gaussan radal bass functons. Why?

46 Important Kernel Issues: The Gaussan Radal Bass Kernel lfts the data to nfnte dmenson so our data s always separable n ths space so why don t we always use ths kernel? Frst of all we should decde whch to use n ths kernel ( 1 2 exp( x 2 xj )). 2σ Secondly,A strong kernel,whch lfts the data to nfnte dmenson, sometmes may lead us the severe problem of Overfttng: Symptoms of overfttng: 1-Low margn poor classfcaton performance. 2-Large number of support vectors Slows down the computaton. σ

47 Important Kernel Issues: 3-If we look at the kernel matrx then t s almost dagonal for small σσ. Ths means that the ponts are orthogonal and only smlar to tself. All these thngs lead us to say that our kernel functon s not really adequate. Snce t does not generalze good over the data. -It s good to say that Gaussan radal bass functon (RBF) s wdely used, but wth care. Related: another problem s that sometmes the ponts are lnearly separable but the margn s Low

48 Important Kernel Issues: Lnearly separable But low margn! All these problems leads us to the compromsng soluton: Soft Margn!

49 Soft Margn: -We allow error ξ Varables ξ1, ξ2,... ξ n ξ Is the devaton error from deal place for sample : -If 0< ξ < 1 then sample s on the rght sde of the hyperplane but wthn the regon of the margn. -If ξ > 1 then sample s on the wrong sde of the hyperplane. n classfcaton. We use slack (one for each sample). ξ > 1 0< ξ < 1 0< ξ < 1

50 Soft Margn: Taken from [11]

51 Soft Margn: The prmal optmzaton problem -We change the constrans to nstead of y( wx t + b) 1. Our optmzaton problem now s: mnmze 1 2 t y( wx + b) 1 ξ ξ 0 w 2 n + C ξ = 1 Such that: y( t wx + b) 1 ξ ξ 0 C > 0n s a constant. It s a knd of penalty on the term ξ. It s a tradeoff between the margn and the = 1 tranng error. It s a way to control overfttng along wth the maxmum margn approach[1].

52 Soft Margn: The Dual Formulaton. Our dual optmzaton problem now s: Such that: maxmze -We can fnd w usng : -To compute b we take any 1 n n n T α αα jyy j j = 1 2 = 1 j= 1 n xx 0 α C and α y = 0 n = 1 w = α yx = 1 α [ y( wx t + b) 1] = 0 Whch value for C 0 < α < C T α = 0 y( wx+ b) > 1 T 0 < α < C y( wx+ b) = 1 and solve for b. should we choose. T α = C y ( w x + b) < 1 (ponts wth ξ > 0)

53 Soft Margn: The C Problem - C plays a major role n controllng overfttng. -Fndng the Rght value for C s one of the major problems of SVM: -Larger C less tranng samples that are not n deal poston (whch means less tranng error that affects postvely the Classfcaton Performance (CP) ) But smaller margn (affects negatvely the (CP) ).C large enough may lead us to overfftng (too much complcated classfer that fts only the tranng set) -Smaller C more tranng samples that are not n deal poston (whch means more tranng error that affects negatvely the Classfcaton Performance (CP)) But larger Margn (good for (CP)). C small enough may lead to underfttng (naïve classfer)

54 Based on [12] and [3] Soft Margn: The C Problem: Overfttng and Underfttng Under-Fttng Over-Fttng Too much smple! Too much complcated! Trade-Off

55 SVM :Nonlnear case Recpe and Model selecton procedure: -In most of the real-world applcatons of SVM we combne what we learned about the kernel trck and the soft margn and use them together : n n n 1 maxmze α αα yyk( x, x) j j j = 1 2 = 1 j= 1 constraned to 0 α C and α y = 0 = 1 -We solve for α usng a Quadratc Programmng software. n w = α jy jφ( x j)( No need to fnd " w" because we may not know φ( x)) j= 1 -To fnd b we take any n < < and solve α [ y( wx t + b) 1] = 0 0 α C n n t α j j φ j φ α j j j j= 1 j= 1 n y( y( ( x)) ( x) + b) = 1 b= y yk( x, x) -The Classfcaton functon wll be: g( x) = sgn( αyk ( x, x) + b) = 1

56 SVM:Nonlnear case Model selecton procedure -We have to decde whch Kernel functon and C value to use. - In practce a Gaussan radal bass or a low degree polynomal kernel s a good start. [Andrew.Moore] - We start checkng whch set of parameters (such as C or σ f we choose Gaussan radal bass) are the most approprate by Cross-Valdaton (K- fold) ( [ 8 ]) : 1) dvde randomly all the avalable tranng examples nto K equal-szed subsets. 2) use all but one subset to tran the SVM wth the chosen para. 3) use the held out subset to measure classfcaton error. 4) repeat Steps 2 and 3 for each subset. 5) average the results to get an estmate of the generalzaton error of the SVM classfer.

57 SVM:Nonlnear case Model selecton procedure cont -The SVM s tested usng ths procedure for varous parameter settngs. In the end, the model wth the smallest generalzaton error s adopted. Then we tran our SVM classfer usng these parameters over the whole tranng set. - For Gaussan RBF tryng exponentally growng sequences of C and σ s a practcal method to dentfy good parameters : - A good choce * s the followng grd: C = σ = 2,2,..., ,2,..., * Ths grd (~400 possbltes!) s suggested by LbSVM (An ntegrated and easy-to-use tool for SVM classfer )

58 SVM:Nonlnear case Model selecton procedure: example Ths example s provded n the lbsvm gude. In ths example they are searchng the best values for C and σ for an RBF Kernel for a gven tranng usng the model selecton procedure we saw above. C = 2, σ = s a good choce

59 SVM For Mult-class classfcaton: (more than two classes) There are two basc approaches to solve q-class problems ( q > 2) wth SVMs ([10],[11]): 1- One vs. Others: works by constructng a regular SVM ω for each class that separates that class from all the other classes (class postve and not negatve). Then we check the output of each of the q SVM classfers for our nput and choose the class that ts t correspondng SVM has the maxmum output. ( g( x) = wx+ b) 2-Parwse (one vs one): We construct Regular SVM for each par of classes (so we construct q(q-1)/2 SVMs). Then we use max-wns votng strategy: we test each SVM on the nput and each tme an SVM chooses a certan class we add vote to that class. Then we choose the class wth hghest number of votes.

60 SVM For Mult-class classfcaton cont : -Both mentoned methods above gve n average comparable accuracy results (where as the second method s relatvely slower than the frst ). -Sometmes for certan applcaton one method s preferable over the other. -More advanced method to mprove parwse method ncludes usng decson graphs to determne the class selected n a smlar manner to knockout tournaments: Example of advanced parwse SVM. The numbers 1-8 encode the classes. Taken from[10]

61 Applcatons of SVM: We wll see now some applcatons for SVM from dfferent felds and elaborate on one of them whch s facal expresson recognton. For more applcatons you can vst: 1- Handwrtten dgt recognton: The Success of SVM n Ths applcaton made t popular: 1.1% test error rate for SVM n NIST (1998). Ths s the same as the error rates of a carefully constructed neural network, LeNet 4 that was made by hand.[1]

62 Applcatons of SVM: contnued Today SVM s the best classfcaton method for handwrtten dgt recognton [10]: 2- Another feld that uses SVM s Medcne: t s used n detectng Mcrocalcfcatons n Mammograms whch s an ndcator for breast cancer, usng SVM. when compared to several other exstng methods, the proposed SVM framework offers the best performance [ 8 ]

63 Applcatons of SVM: contnued 3-SVM even has uses n Stock market feld s Stock Market: Wow! many applcatons for SVM!

64 Applcatons of SVM: Facal Expresson Recognton Facal Expresson Recognton: based on Facal Expresson Recognton Usng SVM by Phlpp Mchel et al [9]: -Human bengs naturally and ntutvely use facal expresson as an mportant and powerful modalty to communcate ther emotons and to nteract socally. -Facal expresson consttutes 55 percent of the effect of a communcated message. -In ths artcle facal expresson are dvded nto sx basc peak emoton classes : {anger, dsgust, fear, joy, sorrow, surprse} (The neutral state s not a peak emoton class)

65 Applcatons of SVM: Facal Expresson Recognton -Three basc problems a facal expresson analyss approach needs to deal wth: 1-face detecton n a stll mage or mage sequence : Many artcles has dealt wth ths problem such as Vola&Jones. We assume a full frontal vew of the face. 2-Facal expresson data extracton: -An Automatc tracker extracts the poston of 22 facal features from the vdeo stream (or an mage f we are workng wth stll mage). -For each expresson, a vector of feature dsplacements s calculated by takng the Eucldean dstance between feature locatons n a neutral state of the face and a peak frame representatve of the expresson.

66 Applcatons of SVM: Facal Expresson Recognton 3-Facal expresson classfcaton: We use The SVM method we saw to construct our classfer and the vectors of feature dsplacements for the prevous stage are our nput.

67 Applcatons of SVM: Facal Expresson Recognton vectors of feature dsplacements

68 Applcatons of SVM: Facal Expresson Recognton -A set of 10 examples for each basc emoton (n stll mages) was used for tranng, followed by classfcaton of 15 unseen examples per emoton. They used lbsvm as the underlyng SVM classfer. -At frst They used the standard SVM classfcaton usng lnear kernel and they got 78% accuracy. -Then wth subsequent mprovements ncludng selecton of a kernel functon (they chose RBF) and the rght C customzed to the tranng data, the recognton accuracy mproved to 87.9%! -The human celng n correctly classfyng facal expressons nto the sx basc emotons has been establshed at 91.7% by Ekman &Fresen

69 Applcatons of SVM: Facal Expresson Recognton We see some partcular combnatons such as (fear vs. dsgust) are harder to dstngush than others. -Then they moved to constructng ther classfer for streamng vdeo rather than stll mages: Clck here for a demo of facal expresson recognton (from another source but also used SVM)

70 The Advantages of SVM: Based on a strong and nce Theory[10]: -In contrast to prevous black box learnng approaches, SVMs allow for some ntuton and human understandng. Tranng s relatvely easy[1]: -No local optmal, unlke n neural network -Tranng tme does not depend on dmensonalty of feature space, only on fxed nput space thanks to the kernel trck. Generally avods over-fttng [1]: - Tradeoff between classfer complexty and error can be controlled explctly. SVMs have been demonstrated superor classfcaton Accuraces to neural networks and other methods n many Apllcatons.[10]: -generalze well even n hgh dmensonal spaces under small tranng set condtons. Also t s robust to nose[10]

71 The Drawbacks of SVM: It s not clear how to select a kernel functon n a prncpled manner[2]. What s the rght value for the Trade-off parameter C [1]: - We have to search manually for ths value, Snce we don t have a prncpled way for that. Tends to be expensve n both memory and computatonal tme, especally for multclass problems[2]: - Ths s why some applcatons use SVMs for verfcaton rather than classfcaton. Ths strategy s computatonally cheaper once SVMs are called just to solve dffcult cases.[10]

72 Software: Popular mplementatons SVMlght: By Joachms, s one of the most wdely used SVM classfcaton and regresson package. Dstrbuted as C++ source and bnares for Lnux, Wndows, Cygwn, and Solars. Kernels: polynomal, radal bass functon, and neural (tanh). LbSVM : LIBSVM (Lbrary for Support Vector Machnes), s developed by Chang and Ln; also wdely used. Developed n C++ and Java, t supports also mult-class classfcaton, weghted SVM for unbalanced data, cross-valdaton and automatc model selecton. It has nterfaces for Python, R, Splus, MATLAB, Perl, Ruby, and LabVIEW. Kernels: lnear, polynomal, radal bass functon, and neural (tanh).

73 That s all folks!! Check next Sldes for References

74 References: 1) Martn Law : SVM lecture for CSE 802 CS department MSU. 2) Andrew Moore: Support vector machnes CS school CMU. 3) Vkramadtya Jakkula : Tutoral on Support vector machnes school of EECS Washngton State Unversty. 4) Andrew Ng : Support vector machnes Stanford unversty. 5) Nello Crstann : Support Vector and Kernel BIOwulf Technologes.www. support-vectors.net 6) Carlos Thomaz : Support vector machnes Intellgent Data Analyss and Probablstc Inference

75 References: 7) Greg Hamerly: SVM lecture (CSI 5325) 8) SUPPORT VECTOR MACHINE LEARNING FOR DETECTION OF MICROCALCIFICATIONS IMAMMOGRAMS Issam El-Naqa et.al 9) Facal Expresson Recognton Usng Support Vector Machnes Phlpp Mchel and Rana El Kalouby Unversty of Cambrdge. 10) Support Vector Machnes for Handwrtten Numercal Strng Recognton Luz S. Olvera and Robert Sabourn. 11) A practcal gude to Support Vector Classfcatons Chh-We Hsu, Chh-Chung Chang, and Chh-Jen Ln