THE INSTITUTE OF ELECTRONICS, INFORMATION AND COMMUNICATION ENGINEERS TECHNICAL REPORT OF IEICE. y y y y 3-8656 7{3{ E-mal: ynamura@jsk.t.u-tokyo.ac.jp, yyftane,nakamurag@ynl.t.u-tokyo.ac.jp Proto-Symbol Development and Manpulaton n te Geometry of Stocastc Model for Moton Generaton and Recognton Tetsunar INAMURA y, Hroak TANIE y, and Yosko NAKAMURA y y Graduate Scool of Informaton Scence and Tecnology, Unv. of Tokyo Hongo 7{3{, Bunkyo-ku, Tokyo, 3-8656 Japan E-mal: ynamura@jsk.t.u-tokyo.ac.jp, yyftane,nakamurag@ynl.t.u-tokyo.ac.jp Abstract Humans' prmtve skll of mtatve learnng s regarded as an orgn of uman ntellgence because t s sad tat mtaton s fundamental functon for communcaton and symbol manpulaton. He ave proposed \mmess model" n order to approac to a symbol emergence framework from beavor recognton/generaton for umanod robots. In ts paper, we propose a matematcal model for moton recognton and generaton as combnaton of basc motons by proto-symbol manpulaton wc s abstract expresson of moton patterns. In order to descrbe te proto-symbol manpulaton as geometrc manpulaton, constructon of proto-symbol space and geometrc proto-symbol manpulaton metod are establsed. Key words Hdden Markov Model, Proto-Symbol, Symbol Emergence, Imtaton Learnng. [] [2] HMM HMM [3]
Walk Run Walk Run Conventonal Mmess Model [] (left sde) and proposed model (rgt sde) 2. 2. (Contnuous HMM: CHMM) CHMM CHMM [] 2. 2 HMM Kullback-Lebler HMM Kullback-Lebler. 2 p,p 2 Kullback-Lebler D(p p 2) () Z D(p p 2)= p p(x) (x)log dx () ; p 2(x) HMM 2 HMM, 2 [4] D( 2)= n y T T log p(y T j ) ; log p(y T j 2) (2) T n D( 2) j= D( 2 ), 2 HMM (2). D s ( 2)= (D( 2)+D(2 )) (3) 2 2. 3 [5] j f j f j n x d j d 2 j = jx ;x j j 2 f j d j S x S 2 = j (f j ; d j) 2 (4) (4) x T 2 = j ; f 2 j ; d 2 j 2 4f 2 j (5) x x P T f j ' d j T 2 (f = j ;d j ) 2 (f j +d j ) 2 j ' P 4f 2 j (fj + dj)2 = S 2 j S T S x [6] f j D s( j) 3. () (2) 3. n HMM HMM ^ ^ 2 n Kullback-Lebler ^ (5) 2
^ ^x x Kullback-Lebler D ;^ ^x x d(^x x ) ^x HMM HMM Kullback-Lebler D s(^ ) D(^ ) = n n log p(^y T n j^) ; log p(^y T n j ) T n ' T log p(^yt j^) ; T log p(^yt j ) (6) jont angle[rad].4.3.2. 0.9 0.8 0.7 n=, k= n=, k=50 n=00, k=50 orgnal 0.6 0 0.4 0.8.2.6 2.0 2.4 2.8 tme[s] T log p(^yt j ) T log p(^yt j^) Kullback- Lebler "dance","kck","squat","swng","walk" T log p(yt j ) T log p(yt j j) T log p(yt j j) -000 Result of T log p(yj) for eac moton and HMM y dance kck squat swng walk dance 5.00-3978 -450-547 -6736 kck -4526 3.4-290 -4985-432 squat -6624-3239 7.05-8278 -202 swng -880-7762 -9339 8.86-3469 walk -8573-4498 -02-0944 5.49 T log p(yt j ) 0 T log p(^yt j ^) 0 HMM D(^ ) 3. 2 HMM = fa () j b() ()g 2 = fa (2) j b(2) ()g :(; ) HMM ^ = fa^ j ^b ()g a^ j = a () j +(; )a (2) j (7) ^b (o) = M m= c () mn ( () m () m ) 2 Comaprson between eac generated moton wt several condtons + ( ; )c (2) mn ( (2) m (2) m ) (8) P M b (o) b (o) = cmn ( m= m m) ^ HMM step Q step2 step n Q,,Q n ^Q step3 ^Q O step4 step step3 k O,, O k ^O m k n = 00 k =50 [7] HMM 2 ( ) ( ) ( ) ( ) HMM^ ^ 3
Proto-Symbol Space Proto-Symbol Space proto-symbol space Walk Run Kck Walk Run Kck step2 step3 step Tspan step () (2) step2 () C (2) C 3 Observed Beavor Observed Beavor Procedure of projectng moton n proto-symbol space 3. 3 (t) 3 (t) dt o[] O[t] = o[] o[2] o[t ] T (t) [t] T span (Step) O = o[] o[2] o[t span] O x[] (Step2) T step k O k = o[ + (k ; ) T step] o[t span +(k ; ) T step] x k T ;Tspan T step + T ;Tspan n = T step + k = 2 n (9) [a] a (t) [t] = x[] x[2] x[n] (Step3) (0) (n) T Tstep 4 Tc step4 (n) C T Tstep Tc Procedure of moton generaton step3 3. 4 3.2 x [t] 4 k x[k] (t) (Step ) k (t) T T c (Step 2) c (t) = T t T c () Tc T T step Step3 c (t) (k = 0 n) 3 (Step 4
(a) (b) (c) (d) (e) 6 An novel moton: from walkng to kckng (f) 5 Sx motons performed by uman 4) (Step 5) 4. 20 20[ms] 20 5 walk, kck, squat, stoop, stretc, trow 6 0 4. 6 walk kck 7 7 3 [x[] x[n]] walk kck HMM [8] [9] [0] 4. 2 walk kck [t] 8 walk kck trd dmenson -0 7 0 5 0-5 -20-0 0 0 frst dmenson 20 30-20 0 20 second dmenson walk stretc kck squat trow stoop traject A result of moton recognton n te proto-symbol space 8 Generated moton by contnuous proto-symbol manpulaton 5
Sot Meta Proto-Symbol Abstract wt HMMs Walk Run Observe Beavor 9 Generaton wt HMMs Kck Generate Beavor Proto-Symbol Space θ (t) Outlne of a erarccal mmess model 5. x x (t) [t] = x[] x[2] x[n] [t] 9 walk kck M(sot) (t) M M(t) [t] M 0 6. [] Tetsunar Inamura, Iwak Tosma, and Yosko Nakamura. Acquston and embodment of moton elements n closed mmess loop. In te Proc. of IEEE Int'l Conf. on Robotcs & Automaton, pp. 539{544, 2002. [2] Merln Donald. Orgns of te Modern Mnd. Harvard Unversty Press, Cambrdge, 99. [3] Terrence W. Deacon. Te symbolc speces. W.W. Norton & Company. Inc., 997. [4] L.R.Rabner B.H.Juang. A probablstc dstance measure for dden markov models. In AT&T Tecncal Journal, Vol. 64, pp. 39{408, 985. [5].., 980. [6].., 986. [7],,.. '03, 2003. [8] Toskazu Wada and Takas Matsuyama. Appearance based beavor recognton by event drven selectve attenton. In IEEE Computer Socety Conference on Computer Vson and Pattern Recognton, pp. 759{764, 998. [9] J. Yamato, J. Oya, and K. Is. Recognzng uman acton n tme-sequental mages usng dden markov model. In IEEE Computer Socety Conference on Computer Vson and Pattern Recognton, pp. 379{385, 992. [0] P.K. Pook and D.H. Ballard. Recognzng teleoperated manpulatons. In IEEE Internatonal Conference onrobotcs and Automaton, pp. 578{585, 993. 6