Mining Sensor Streams for Discovering Human Activity Patterns Over Time
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1 Mg S S Dg H Ay O T S Bl Rw A Ay y g ply p l w g ppl lg y ll. M h pph y y g ly p g l h. ly h p l h y h, l ppl h hlh g lg wll h g l hg gg p. I h pp, w pp h g ql y p g g lpl gly, h x ppl. B h q q ppl, w g lgh h l ql y p, h p xh y (p) h q. O lgh l h pl lg wh yg q p g phyl p. W l h l lgh g ll w p. Ix T Ay D Mg; S E; S D; S Sq Mg; I. ITRODUCTIO H y y g ply p l w g ppl lg y ll. O h ppl. I y, h g gg ppl h g -pl g, hlg h h h y h pl. A S whh qpp wh yp, h, wh, RFID g, pw-l ll,. Th lw ll lyz y p. Rgzg h ly gly hlp pg, y, ply hlh g lly, ppl wh l. F xpl, y g h ly p wh, h y k hw plly ly h ly p. I l wh h l. A y p h h ly pp h y g,.g. l wk [1], By [2], l l [3], [4], Mk l [5], y By wk [6]. I l wl, g p h y pl, q ll g. Ml llg h y g, l -p. B, lly ply h g ll ph ll. Ah p k h p h. Akg h p h p h h, lly wh y pl h wl q. I h pl, ly w p h h pp g h y. Th h l q g [7], g y p [8], g x q-p y p [9], g y g lw l gp [1], g p [11]. h g pph k h g, h ply h h p gh hg. I l wl, w h l wh plly lw. Al h y p hg. Mg h ly llw w gg p h, l llw hg h p. Dg hg h p l y ppl. F xpl g lk h p p y p hg ly. I h l, y g h h pp l gg ppl, h wk ly, W lk g, pw p. M h pp h y q [12] [15]. Al h h pp g q q [16] [18]. T h kwlg, g h h pp g h y p h x. I h pp, w x h l- ww pph pp y Gll l. [13], y p q. Th l- ww pph h q g l- ww, h h h qy h kp ll ll l. Sh l ww pph q l h y p y. F xpl g lly h hg h p ll, h l p (.g. h h g) ll.
2 D h pl q ppl, w ly h h pp y Gll l. [13]. F ll, h -l pph [13], wll h h l g h [16] [18] w g q. Th wh y w p. S, [11], h plx h y, w y p q. I h q, h p gh p y l (ll p). Al h h q gh hg (ll p). Fg gl p g h l p l y ppl. F xpl y, Hy, l. [19] h h ll y p h w l wh l g p. Th hghlgh h h p gz ll h h whh p glly y l ly. Th, w l h pl yg q p g h p. A p gh p h jy h/h h lg g h y, ly g h lpg. W ll h lp p hgh pp gh lly l h h pp h h lg. I h pp, w x h DSM h pp y [11] g g l- ww [13]. O pp h llw - p g. A h x [11], w l h pl yg q hl l l hgh pg h g p. Szg h h pp, w h g lgh g y q p -, g lpl pl gl. S g lgh l h y p p h q p. T h kwlg, h h g h g h y p. Th h pp gz llw. F w xpl h l g wk l II. x w h l- ww l III. O pp l xpl I. W h hw h l xp w p. Flly w h pp wh l wk. II. STREAM MIIG RELATED WORK Sql p g h h [2] y h h pp g ql p [2] [23]. Cp h l pl g ql p, g ql p hllgg. I, w l g ly lkg p p h. Dp g hllgg, wh h p g w ppl h p w y h g pl h l w g ppl. A w h ppl l wk ly,, W lk g, pw p lg [24]. F g p, ppx g lx pp hhl ky p [15], [25]. Th pph w y Mk l. [15] g lk l llg h h p h h. L L l [14] pp h pg h p px. Thy l g h g g lgh [26]. M pph h h gg h hy [13], [26]. Th h lly hg l, whl l hg p gly lg. Th l h l h g ql p, lg h SEED lgh [18], h g ppx ql p W g [17], g lgh [27] g ll ql p [28]. All h pph l. Hw, p lw. Fg 1 p h w. A Fg 1,, h gl wh y ID, kg lly p h x. Th h pg p h, j. Apph pp y g y [29], [3] y l g hq h Ap hq [2] gp q gh. Ah h ply x lk k [3]. I, g h pl hq llw l wh plx y p h,, y lgh. I, w x h DSM h [11] gp gh h -g - y p. I hl h h h q pg y h l pp h g p [7] [11].
3 S M1 M 2 M 3 M 4 M 5 T ID I 1 {A, B, D, F, G, H} 2 {D, F, G, H, X} 3 {A, B, C, X, Y } O O O () T O O O M 2 M 3 M1 M 5 M1 M 4... () Fg. 1: T.. 31 y 24 h 4 q Fg. 2: l l- ww. Hw h pph h g pl. T h kwlg h h wk g y p y. III. TILTED-TIME WIDOW I h, w xpl h l ww l [13] l. Fg 2 hw xpl l l- ww wh h qy h kp wh p q h, h ll gly h l 24 h h g h ll h l 31 y. A w, h hy wll h k h l- ww l h hg. Oh h lgh l- ww h l pp p g [13]. Th l- ww l lx hhl p g h llwg. D 1. L h pp y σ, h x pp y ɛ, h lx ρ = ɛ/σ. A I q pp l h σ. I pp I l h σ, l h ɛ, -q; hw q. Ug h ppx pph q llw h -q p q l, whl g q p. T h qy h l- ww, h l qy I p. L j (I) h p qy I T j, wh j h TABLE I: Expl. Tp () S ID () 7/17/29 9:52:25 M4 7/17/29 9:56:55 M3 7/17/29 14:12:2 M15 wh T j, 1 j τ. H τ h p. F, wh 1 τ, h qy 1 (I),..., (I) p Eq 1 Eq 2 hl [31]. τ,, 1, (I) < σ (1) l, 1 l, l j (I) < ɛ j=1 l (2) j=1 Eq 1 p,, h h h h p, h p qy h, I, l h h qy q wh y,.., T 1 T. Eq 2 p h, T, wh T 1 T, h h y T l wh T 1 T, h h p pp I T 1 T l lwy l h h lx pp hhl, ɛ. I h h qy I wh T 1 T pg p. Th yp pg l pg. I l, w wll x pg hq, p. I. MODEL I llwg, w g w, h w wll l l. A. D Th p l, h =,, wh ID h p wh h. Tl I hw xpl l h. W y q 1, 2,..,. h y q,. W h h p k h B B wh h B [.. ], h h y B τ h B B. wh p τ. Eh, y A w, w l- ww g h hy p. I g h qy, w h p, whh wll xpl l I-B. Al, l h qy h gl g, h h h lgh
4 Mh..... Mh Wk Fg. 3: O l- ww. Wk Wk Wk h p y l ply l, w wll h g p q p. Th -l ww l p Fg 3. Th l- ww kp h hy p g h p 4 wk h ll wk gly. Th hy l h 4 wk ly kp h h gly. Rgg ppl g, l -l ww p l p. lgh l- ww. F xpl wl g p h p g l p. S, w xp h y p hg lly y h p, w h y h h k p. F xpl, p k wk h hg lp h ly y p. Ug h h w ly 15 p l l l- ww kpg y h. T p h l- ww, wh w h, w wll pl h p l h ll gly h k h x ll gly. Dg hg, w hk h ww ll,, h ww h k ; hw h hg p. B. Mg Ay O gl lp h h lly y p g. E h p hw h h. Bh hpp q qly whl lg wh h y. F xpl, h l pp y. M ppl wll p h y xly h wy h, h h p h h p gh hg (). I h y gh p y l h wg h ph (). Th DSM h pp [11] h p. F xpl, h p, {, x,, }, {,, q}, {,, }, p h h h h. W h ql p h h B τ y g x DSM h l p g l l l wh yg q g phyl p. A g p h B τ, w wll p h l- ww, wll p y p h pg. T p, h B τ h h B τ. Th h ly q q, whh wll g lg p. A pp q y h q q. DSM gll pp, ly h q. H, w h x pp ɛ llw h q p l. W wll l lly lpl pp l pg g h p. I g l l y p, h qy y g h. I h q g h p k, h p h l qly h p gh g. F xpl, h p h/h h lg- g h y ly g h lpg, h h wll gg qly h lg- h h. Th wh lkg q p, h h gh g qly h lp p gh. Th pl hpp wh yp, lly h gg h qly h h yp h. Th pl kw pl k k ly lly y pg lpl pp l [32]. W wll lly lpl pp l. T h, w y g h p g l g l, pg h l h, h,. Al yp gh xh yg q. I xp, w gz h. Th h kg h p h,.g.. I-, w wll ll h ky, h - kg, h RFID g. B g lyzg q lpl h, w h gh h hgh h g gg h ky g. H w wll p pp g. F h B τ, w p h gl pp g Eq 3. H l p l. h gy, S h gy. Al T () h qy p T. σ T (l) = 1/ S l S l T ().. S l = { l S } (3) A ll xpl, Fg 4 hw h p
5 σ k =.2 σ k =.2 σ =.2 σ =.2 σ.3 σ =.6 σ k =.1 σ =.3 j h p lgh (MDL) [33]. Ug p j llw k h ly h p p wh p p lgh y. Th p l gl p p T Eq 4. Th p l gl p p T Eq 5. H L h p lgh y M Dp lgh ppl (MDL), Γ y [11]. Cy lly hw hw g h p p. I p -p, h h h y h g q pg h w h. F gl p y h g y. Fg. 4: Th q/q l h gl pp, gll pp. gl pp l h xp. Ug h gl q, q q llwg. D 2. L gy l l l. Th qy p T, y T (), h p T whh. Th pp l l p T T (S) y h l h gy g L g T. L ɛ h x pp. S q pp l h σt (l). I -q pp l h σt (l), l h ɛ ; hw q. Oly h h q q wll h h B τ, whh h g lg q. W p gwh h [9] whh gw p y px x. T h h p, h p gl p. A gl p ll h h h l pg, h [11]. Dg p gwh, ly h wly p, qy y wll p. I h wly p h h gl p, xly h y h, w. Ohw wll w gl p. A h h p gwh, q hghly p wll g p. I lly g p qy, w p α T () = L(B T ) Γ L() + L(B T ) β T ( ) = (L(B T ) + L()) Γ L(B T ) + L( ) p h ply p gl p p h h. Cp gl p hw h ll ply h gl p p h wh p lgh y. B g h p l y g x p, w g, -g g p. D 3. L h p gl p Eq 4 p T. Al L σ g ɛ g h p x p. Th gl p g p α l h σ g. I -g p l h σ g, l h ɛ g ; hw g. W l g l yg g/-g p. L h g p ll gl p p T Eq 6. H h gl p y. β T () = 1 =1 (L(B T ) + L()) Γ L(B T ) + L( ) D 4. L h p gl p Eq 5 p T. Al L ɛ h x p. A g p T p β T ( ) l h β() T. I g p l h β() T, l h ɛ ; hw g. Dg h p gwh, h, h g p p, (4) (5) (6)
6 .. h p h h hghly q (wh p h lgh). W l p -xl gl p;.., h p h lly h lg p. T ly h y l p, l l p g l [34] Eq 7. I llw h gl p. Fg h llw p h l p whh h. H (, ) h j ply gl p, whl () () h gl ply. A hgh l l h. MI(, ) = (, ) lg (, ) () () W xg h p y px x h l g p. A p-pg p h p, h. W h pg p p g h p gwh h h l pg. h h l pg p whh p h l- ww h pg p. I h llwg w wll hw h l ww p g p h. C. Upg h T-Tl Ww A g h p h h h p, h l- ww wll p. Eh gl p wh l- ww. Th l- ww kp k h gl p hy wll. Wh w h, g g gl p, w wll pl h p h ll gly wh h ly p p. I gl p h h, w wll p. I h gl p p h h, h h gl p p l. I h pg gl p, w pp h llwg l pg h x h gl l pg h [13]. L α j () h p p gl p T j wh 1 j τ. F, wh 1 τ, h p α 1 (),..., α () p Eq 8 9 hl. H τ h p. (7) τ,, 1, α () < σ g (8) l, 1 l, l α j () < l ɛ g (9) j=1 Eq 8 p,, h h h h p, h p p h gl p, l h h p q wh y,.., T 1 T. Eq 9 p h, T, wh T 1 T, h h y T l wh T 1 T, h h p pp I T 1 T l lwy l h h lx p hhl, ɛ g. I h h p wh T 1 T pg p. W l p pg h gl p. W p k h llwg Eq 1 11 hl. τ,, 1, β ( k ) < β () (1) l, 1 l, l β j ( k ) < l ɛ (11) j=1 Eq 1 p wh h p p l h h g p p ll h,.. T 1 T. Eq 11 p h, wh T 1 T, h h y T l wh T 1 T, h h p p T 1 T l lwy l h h lx pp hhl, ɛ. I h h p wh T 1 T pg p.. EXERIMETS Th p h y w l h ll w p. Th ly h p lg pl l g hw Fg 5. W wll p Fg 5 5 p 1 p 2. Th p w qpp wh ll lg, ll wll, wh p/l h. Th w ll g 17 wk p 1, g 19 wk p 2. Dg ll, h p 2 w wy ppxly 2 y, g wk 12 g wk 17. Al h l wk ll h p l ll yl. I xp, w h h ppxly wk. I xp, w h x ɛ, ɛ g ɛ.9 h pg pp p l, gg l. Al σ g w.75 l xp. T l l h l lgh g h, h h w wh. A l 11 w
7 D D D T (Wk) S Tl-T Ml DSM () Ap 1. () Ap 2. Fg. 5: S p l g h p. O h p, l hw whl gl hw wh. ) E S # ( z S D 1K 9K 8K 7K 6K 5K 4K 3K 1K R S E D () Ap 1 ( = wk). D D T (Wk) S Tl-T Ml DSM () Ap 2 ( = wk). Fg. 7: Tl p ) E S # ( z S D 1K 9K 8K 7K 6K 5K 4K 3K 1K T (Wk) () Ap 1. R S E T (Wk) () Ap 2. Fg. 6: Tl ( = wk). h p. Th l hg, l, g, l h, h, l pp(kg), pl hyg, lpg, lpg (lxg) kg. Ap 1 l 193, 592 3, 384 y. Ap 2 l 132, 55 2, 62 y. Fg 6 6 hw h. A w, p 2 w h g w p, h w h gp Fg 6. W lgh h p. Fg 7 7 hw h p g gll pp DSM. g lpl gl pp pp h. Th l hyph h pp h l hgh pg g p g lpl gl pp l. S h p h h q l p l l q. F xpl h hkpg y hpp y 2-4 wk wh y p. Al h l p g gh, hy h, h g lxg. I hl h h lpl p, h y gh p jy g. O l h h p h gg h j pg h p p h. Th p p p p h p h, wll h p p l- ww. Th, h p gh pp pp whh hw ly h p h. A ly, h p, lgh p w yp pg. Th yp pg ll l pg, p p whl pg h h. Th yp pg l pg pg p l ww. Fg 8 8 hw h l h yp pg h. Fg 8 8 hw h l h yp pg h. Fg 8 8 hw h l pg l -l ww. h h gp p 2 l h 2 y wh w wy. By pg h l l pg Fg 8 8 g h Fg
8 5 lly Tl- Tl- ly 3K 1K T (Wk) l T T (Wk) l-p W1 W2 W3 W4 M2 M3 M4 M5 T(lly Fg Bk) () Ap 1 ( = wk). () Ap 1 ( = wk). () Ap 1 ( = l- ) lly Tl- Tl- ly 3K 3K 1K T (Wk) l T T (Wk) l-p W1 W2 W3 W4 M2 M3 M4 M5 T(lly Fg Bk) () Ap 1 ( = wk). () Ap 2 ( = wk). () Ap 2 ( = l- ) Fg. 8: Tl l-p. F h h, W1-W4 h wk 1-4, M1-M5 h , h h l pg hw llw h p. I ll, p wl, l p wl p. F h l pg l, p Fg 8, 8, 8 8 h l p p h y pg p h gg. Th h l p p h lgh lz. T xpl p, l p hw 9. W h lp lz w h llw lz h p lg wh h. Fg 9 hw kg y p 1 h w p h wk lw p. Fg 9 hw w l h y p p 2. h w l g w, lpl h hw lly. Fg 9 hw l pp p p 2. T hw h gl p, w ll y g h xlly p ll. W h y Eq 12. H 11 h h h h ll h gl p, 1 1 h h h ll h h h gl p ll. 11 py( ) = (12) Fg 1 1 hw h g y p 1 2. A ly, h h h l g l h. Th l h h h y h gg, h qkly lz g l h h. T hw h hg p p, w hw h l lgh kg y. Fg 11 hw h kg y. Fg 11 hw h l h -l ww. W lly h h qkly p h l pg p. Th hw h p h h w g h ll, y y h g, pg l wll p, kg lgh p. W l hw hw h g h kg p hg Fg 11. g h g y l hg h p. Fg 11 hw h y h kg. Sl h l h g y ll p, w h h y h lz qkly. I y, h l xp h w ql p. I l hw h g w yp pg hq llw lg pg, g l p, h l h p.
9 () A lz h kg p 1. () Tw l h p p 1. Fg. 9: lz p. () Ml pp p p 2. Cy O T Cy O T y C y C T (Wk) T (Wk) () Ap 1 ( = l- ). () Ap 2 ( = wk). Fg. 1: Tl p h y [Tkg M Ay] T (Wk) [Tkg M Ay] W1 W2 W3 W4 M2 M3 M4 M5 T (Wk) () ( ( = wk). () ( = l- ). ) ( M D D [Tkg M Ay] W1 W2 W3 W4 M2 M3 M4 M5 T (Wk) y C Cy [Tkg M Ay] T (Wk) () D ( = wk). () y ( = wk). Fg. 11:, y kg y p.
10 I. COCLUSIOS AD FUTURE WORK I h pp w hw h g h y ql p. W p x h l- ww l y-, ql p g h pl q ppl. I h, w l lly l y ply l h h. W l g ly h l hg. REFERECES [1] M. C. Mz, R. H. D, M. A, L., R. F. C. I, D. Mll, Th l wk h: A w, g h A A Al Illg Spg Syp Illg E, 1998, pp [2] O. Bzk, J. M,. Rg, A gp, g h 7h l Mll, 25, pp [3] M. hlp, K. Fhk, M. kwz, D., D. Fx, H. Kz, D. Hhl, Ig wh j, IEEE Cpg, l. 3,. 4, pp. 5 57, O.-D. 24. [4] U. M, A. Slg, D.. Swk, M. Dh, Ay g g g lpl y p, BS 6: g h Il Wkhp Wl Ipll By S wk, 26, pp [5] L. L, D. Fx, H. Kz, L- y g g ll k wk, g h Il J C Al Illg, 25, pp [6] T. I, F. y,. Kwh, F. H, K. Kg, Ay g wh j g y y wk, C 9: g h 3 ACM Il Wkhp Cx-Aw Sl-Mgg Sy, 29, pp [7] T. G, Z. W, X. T, H. g,, J. L, p: A gg p pph ql, l y g. g h IEEE Il C Cpg C, 29. [8] J., J. H, W. Wg, C- ql p g: h p-gwh h, Jl Illg I Sy, l. 28,. 2, pp , 27. [9]. Rh D. J. Ck, h h lp: Apg h h h, IEEE T Sy, M, Cy jl, A, l. 39,. 5, pp , Sp 29. [1] B. Shl, Up y y g lpl gp, 2 Il Wkhp L Cx Aw. Spg, 26. [11]. Rh, D. J. Ck, L. Hl, M. Sh-Eg, Dg gz k, IEEE T Kwlg D Egg, 21. [12] J. R C. H, Mg l q lg ww, I Cpg I Cl, 28. ICICIC 8. 3 Il C, , pp [13] C. Gll, J. H, J., X. Y,. S. Y, Mg Fq D S Mlpl T Gl. MIT, 23, h. 3. [14] H. L, S. y L, M. kw Sh, A lgh g q h hy, I. F Il Wkhp Kwlg Dy D S, 24. [15] G. S. Mk R. Mw, Appx qy, LDB 2: g h 28h l y Lg D B. LDB Ew, 22, pp [16] G. Ch, X. W, X. Zh, Sql p g lpl, ICDM 5: g h Fh IEEE Il C D Mg. Whg, DC, USA: IEEE Cp Sy, 25, pp [17] A. M F. Mgl, Mg ql p : pph, Jl Illg I Sy, l. 27,. 3, pp , 26. [18] C. Rï,. l, M. T, p: Mg ql p, BDA5: A 21 J B D A, O 25. [19] T. L. Hy, M. l,. L, I. A. Ty, J., A. G. A, D hlh: Sl lpl l, IEEE Cpg, l. 6,. 1, pp , 27. [2] R. Agwl R. Sk, Mg ql p, ICDE 95: g h Elh Il C D Egg. Whg, DC, USA: IEEE Cp Sy, 1995, pp [21] J., J. H, B. Mz-Al, H., Q. Ch, U. Dyl, M. H, xp: Mg ql p y px-pj gwh, g h 17h Il C D Egg. Whg, DC, USA: IEEE Cp Sy, 21, pp [22] J. Wg J. H, B: E g q l q, ICDE 4: g h 2h Il C D Egg. Whg, DC, USA: IEEE Cp Sy, 24, p. 79. [23] F. Mgl, F. Chl,. l, Th pp pph g ql p, KDD 98: g h S Ep Syp pl D Mg Kwlg Dy. L, UK: Spg-lg, 1998, pp [24] M. Glk, J. Ghk, R. Rg, Qyg g : y ly g lk l, SIGMOD 2: g h 22 ACM SIGMOD l Mg. w Yk, Y, USA: ACM, 22, pp [25] J. H. Chg W. S. L, Fg q ply l, KDD 3: g h h ACM SIGKDD l Kwlg y g. w Yk, Y, USA: ACM, 23, pp [26] W.-G. Tg, M.-S. Ch,. S. Y, A g- pl p g h, LDB 23: g h 29h l y lg. LDB Ew, 23, pp [27] J. H, Y. Ch, G. Dg, J., B. W. Wh, J. Wg, Y. D. C, S : A h l-l ly, D. lll D, l. 18,. 2, pp , 25. [28] C. Rï M. l, Mg ll ql p, DWK 8: g h 1h l D Whg Kwlg Dy. Bl, Hlg: Spg-lg, 28, pp [29] S. p, A. Bkwll, C. Fl, Ap, h- g, LDB 23: g h 29h l y lg. LDB Ew, 23, pp [3] K. K. L, I. Tg, B. K, D. Chg, Ol lgh g - lg wk, AKDD, 25. [31] J. Chg, Y. K, W. g, A y lgh g q, Kwlg I Sy, l. 16,. 1, pp. 1 27, 28. [32] B. L, W. H, Y. M, Mg l wh lpl pp, KDD 99: g h h ACM SIGKDD l Kwlg y g. w Yk, Y, USA: ACM, 1999, pp [33] J. R, Mlg y h p, A, l. 14, pp , [34] I. Gy A. El, A l l, Mh Lg Rh, l. 3, pp , 23.
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