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/R43 9.96260 Tf 1 0 0 1 77.16020 181.58700 Tm (34) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 87.12270 181.58700 Tm [ (\135\054) -202.98600 (temporal) -191.00200 (video) -191.00900 (se) 15.01830 (gmentation) -192.00200 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 214.52400 181.58700 Tm (39) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 224.48700 181.58700 Tm [ (\135\054) -202.00600 (and) -192.00200 (f) 9.99588 (ace) -191 (clus\055) ] TJ -174.37500 -11.95470 Td [ (tering) -302.99200 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 79.69100 169.63200 Tm (18) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 89.65350 169.63200 Tm [ (\135\054) -315.98700 (high\055dimensional) -303.01700 (datasets) -302.99000 (can) -303.99100 (be) -303.00800 (well) -302.99600 (approx\055) ] TJ -39.54140 -11.95630 Td [ (imated) -365.01400 (by) -366.00800 (a) -365.00200 (union) -365.01000 (of) -364.99700 (lo) 24.98850 (w\055dimensional) -366.00500 (subspaces\056) -655.00600 (In) -366.01500 (this) ] TJ 11.95510 TL T* [ (case\054) -325.98900 (the) -310.01900 (problem) -311.01900 (of) -311.00600 (clustering) -309.99600 (a) -311.01200 (high\055dimensional) -311.01400 (dataset) ] TJ T* [ (into) -216.99800 (multiple) -217.01500 (classes) -217.99100 (or) -216.98200 (cate) 15.01100 (gories) -217.00700 (reduces) -216.98300 (to) -217.01000 (the) -217.99500 (pr) 0.98268 (o) -1.01454 (bl) 0.99248 (em) -217.99500 (of) ] TJ T* [ (assigning) -291.98700 (each) -292 (data) -291.98700 (point) -290.98100 (to) -292.01700 (its) -292.00900 (o) 24.98110 (wn) -291.98300 (subspace) -292.01500 (and) -291.98600 (reco) 15.00980 (v) 14.98280 (er) 19.98930 (\055) ] TJ T* [ (ing) -282.99400 (the) -281.98400 (underlying) -283.01400 (lo) 24.98850 (w\055dimensional) -283 (structure) -282.01700 (of) -283.00900 (the) -283.00400 (data\054) -291.00500 (a) ] TJ T* [ (problem) -206.99700 (kno) 24.99150 (wn) -207.99700 (in) -207.01200 (the) -207.01700 (literature) -207.99000 (as) ] TJ /R47 9.96260 Tf 136.65700 0 Td [ (subspace) -207 (clustering) ] TJ /R43 9.96260 Tf 80.50510 0 Td (\133) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 270.59200 97.90120 Tm (37) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 280.55400 97.90120 Tm (\135\056) Tj /R41 9.96260 Tf -230.44200 -16.90080 Td [ (Prior) -257.98900 (W) 75.01690 (ork\056) ] TJ /R43 9.96260 Tf 55.23590 0 Td [ (Ov) 14.98520 (er) -258.00400 (the) -257.98900 (past) -257.98300 (decade\054) -260 (the) -257.98900 (subspace) -257.98100 (clustering) ] TJ 203.51400 473.10000 Td [ (problem) -280.98500 (has) -281.98500 (recei) 25.00560 (v) 14.98280 (ed) -281.01200 (a) -281.01700 (lot) -282.01200 (of) -281.01200 (attention) -281.99700 (in) -281.00200 (the) -281.00200 (literature) -282.01700 (and) ] TJ 11.95510 TL T* [ (man) 14.99010 (y) -231.99600 (methods) -230.98400 (ha) 19.99670 (v) 14.98280 (e) -232.00500 (been) -231.01800 (de) 25.01540 (v) 14.98280 (eloped\056) -304.01300 (Among) -232.01000 (the) 0.99003 (m\054) -235.98500 (spectral) ] TJ T* [ (clustering) -349.98800 (based) -350.99300 (methods) -349.98600 (ha) 19.99670 (v) 14.98280 (e) -349.98600 (become) -350.01000 (e) 15.01220 (xtremely) -351.01500 (popular) ] TJ (\133) ' ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 312.18000 518.23500 Tm (4) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 317.16100 518.23500 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 322.32100 518.23500 Tm (48) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 332.28400 518.23500 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 337.44500 518.23500 Tm (9) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 342.42600 518.23500 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 347.58600 518.23500 Tm (10) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 357.54900 518.23500 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 362.70900 518.23500 Tm (26) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 372.67200 518.23500 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 377.84300 518.23500 Tm (25) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 387.80500 518.23500 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 392.96600 518.23500 Tm (13) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 402.92800 518.23500 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 408.08900 518.23500 Tm (38) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 418.05100 518.23500 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 423.21200 518.23500 Tm (28) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 433.17400 518.23500 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 438.33500 518.23500 Tm (7) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 443.31600 518.23500 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 448.47700 518.23500 Tm (17) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 458.43900 518.23500 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 463.60000 518.23500 Tm (32) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 473.56200 518.23500 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 478.72300 518.23500 Tm (23) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 488.68500 518.23500 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 493.84600 518.23500 Tm (36) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 503.80800 518.23500 Tm [ (\135) -269.01900 (\050see) -268 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 531.83300 518.23500 Tm (37) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 541.79600 518.23500 Tm (\135) Tj -232.93400 -11.95590 Td [ (for) -254 (details\051\056) -322.98300 (These) -253.98900 (methods) -254.00200 (usually) -254.00700 (di) 24.98600 (vide) -253.98200 (the) -255.00600 (problem) -254.01200 (into) ] TJ 11.95510 TL T* [ (tw) 10.00810 (o) -327 (steps\072) -464.01300 (a\051) -327.01200 (learning) -326.98700 (an) -327.98400 (af) 25.00560 <026e69> 1.00473 (ty) -328.01400 (matrix) -327.01900 (that) -326.99000 (characterizes) ] TJ T* [ (whether) -338.01500 (tw) 10.00810 (o) -336.99800 (points) -337.98800 (are) -337.01500 (lik) 10.01790 (ely) -338.01200 (to) -336.99300 (lie) -338.01200 (in) -338.01200 (the) -336.99300 (same) -338.01200 (subspace\054) ] TJ T* [ (and) -196.00200 (b\051) -196.98400 (applying) -196.01100 (spectral) -195.99700 (clustering) -196.99700 (to) -195.99700 (this) -197.00100 (af) 25.00560 <026e697479> 65.00880 (\056) -291.98600 (Ar) 17.99700 (guably) 64.99410 (\054) ] TJ T* [ (the) -213.01600 <02727374> -214.01800 (step) -213.00900 (is) -213.99100 (the) -213.01600 (most) -212.99400 (important\054) -221.01700 (as) -214.00400 (the) -213.01300 (success) -213.01300 (of) -214.00400 (spectral) ] TJ T* [ (clustering) -224.00900 (depends) -223.98500 (on) -223.99200 (ha) 19.99670 (ving) -224.01700 (an) -224.00200 (appropriate) -223.98700 (af) 25.00560 <026e697479> -224.00200 (matrix\056) ] TJ 11.95510 -12 Td [ (State\055of\055the\055art) -211.00400 (methods) -210.98900 (for) -210.00400 (constructing) -210.98400 (the) -211.01400 (af) 25.00560 <026e697479> -210.98400 (ma\055) ] TJ -11.95510 -11.95510 Td [ (trix) -312.98900 (are) -314 (based) -313 (on) -312.99700 (the) ] TJ /R47 9.96260 Tf 86.42890 0 Td [ (self\055e) 20.00650 (xpr) 36.97910 (essiveness) -312.98700 (model) ] TJ /R43 9.96260 Tf 105.83700 0 Td (\133) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 504.44600 422.54900 Tm (9) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R43 9.96260 Tf 1 0 0 1 509.42700 422.54900 Tm [ (\135\056) -499.99500 (Under) ] TJ -200.56500 -11.95510 Td [ (this) -244.01300 (model\054) -244.01100 (each) -244.00600 (data) -243.01600 (point) ] TJ /R53 9.96260 Tf 109.27000 0 Td (x) Tj /R55 6.97380 Tf 6.56602 -1.49492 Td [ (j) -0.70017 ] TJ /R43 9.96260 Tf 6.62383 1.49492 Td [ (is) -243.98400 (e) 15.01220 (xpressed) -243.00400 (as) -243.99900 (a) -242.98400 (linear) -243.98900 (com\055) ] TJ -122.46000 -11.95590 Td [ (bination) -210.00700 (of) -208.98200 (all) -209.99400 (other) -209.01400 (data) -210.00200 (points\054) -218.00300 (i\056e\056\054) ] TJ /R53 9.96260 Tf 144.28300 0 Td (x) Tj /R55 6.97380 Tf 6.56523 -1.49414 Td [ (j) -0.70017 ] TJ /R57 9.96260 Tf 6.96484 1.49414 Td [ (\075) -0.80379 ] TJ /R59 9.96260 Tf 10.51720 7.47187 Td [ (P) -0.59794 ] TJ /R55 6.97380 Tf 10.51600 -10.45980 Td [ (i) -0.19605 ] TJ /R61 6.97380 Tf 2.81797 0 Td (6) Tj /R51 6.97380 Tf 0 0 Td (\075) Tj /R55 6.97380 Tf 6.11602 0 Td [ (j) -0.70017 ] TJ /R53 9.96260 Tf 5.85898 2.98789 Td (x) Tj /R55 6.97380 Tf 6.56484 -1.49414 Td [ (i) -0.19605 ] TJ /R49 9.96260 Tf 3.31719 1.49414 Td [ (c) -0.79889 ] TJ /R55 6.97380 Tf 4.31094 -1.49414 Td [ (i) -0.19605 (j) -0.70017 ] TJ /R57 9.96260 Tf 7.74102 1.49414 Td [ (\053) -0.80379 ] TJ /R53 9.96260 Tf 8.47305 0 Td [ (e) -0.59794 ] TJ /R55 6.97380 Tf 5.51484 -1.49414 Td [ (j) -0.70017 ] TJ /R43 9.96260 Tf 4.19805 1.49414 Td (\054) Tj -233.75900 -11.95510 Td [ (where) -390.99800 (the) -390.98600 (coef) 25.00810 <026369656e74> ] TJ /R49 9.96260 Tf 89.99800 0 Td [ (c) -0.80134 ] TJ /R55 6.97380 Tf 4.31094 -1.49375 Td [ (i) -0.19955 (j) -0.70367 ] TJ /R43 9.96260 Tf 10.91090 1.49375 Td [ (is) -391.01800 (used) -390.98400 (to) -390.98400 <6465026e65> -389.99900 (an) -390.99400 (af) 25.00560 <026e697479> -390.99400 (be\055) ] TJ -105.22000 -11.95470 Td [ (tween) -281.98500 (points) ] TJ /R49 9.96260 Tf 53.77190 0 Td [ (i) -0.49992 ] TJ /R43 9.96260 Tf 6.24414 0 Td (and) Tj /R49 9.96260 Tf 17.19800 0 Td [ (j) -0.79889 ] TJ /R43 9.96260 Tf 4.67305 0 Td [ (\054) -289.98800 (and) -281.98700 (the) -283.00200 (v) 14.98280 (ector) ] TJ /R53 9.96260 Tf 65.12380 0 Td [ (e) -0.59794 ] TJ /R55 6.97380 Tf 5.51602 -1.49414 Td [ (j) -0.70017 ] TJ /R43 9.96260 Tf 7.00898 1.49414 Td [ (captures) -281.98700 (de) 25.01540 (viations) ] TJ -159.53600 -11.95510 Td [ (from) -338.01200 (the) -338.99500 (self\055e) 15.01470 (xpressi) 24.99830 (v) 14.98280 (e) -337.98800 (model\056) -575.01200 (The) -338.01700 (coef) 25.01050 <026369656e7473> -337.99300 (are) -339.01200 (typi\055) ] TJ 11.95510 TL T* [ (cally) -239.98900 (found) -239.98200 (by) -239.98900 (solving) -239.99700 (an) -240 (optimization) -240.01900 (problem) -240.01400 (of) -240 (the) -239.98900 (form) ] TJ /R57 9.96260 Tf 7.45977 -19.06290 Td [ (m) -0.29897 (i) -0.79889 (n) -0.60039 ] TJ /R63 6.97380 Tf -0.81797 -5.97695 Td [ (c) -0.29757 ] TJ /R65 4.98130 Tf 4.07422 -0.99727 Td [ (j) -0.20095 ] TJ /R55 6.97380 Tf 3.72187 0.99727 Td [ (\073) -0.30107 ] TJ /R63 6.97380 Tf 2.36602 0 Td [ (e) -0.70017 ] TJ /R65 4.98130 Tf 4.35703 -0.99727 Td [ (j) -0.20095 ] TJ /R49 9.96260 Tf 5.38203 6.97422 Td [ (r) -0.19850 ] TJ /R57 9.96260 Tf 4.77109 0 Td [ (\050) -0.90181 ] TJ /R53 9.96260 Tf 3.87500 0 Td [ (c) -0.39944 ] TJ /R55 6.97380 Tf 5.11484 -1.49414 Td [ (j) -0.70017 ] TJ /R57 9.96260 Tf 4.19805 1.49414 Td [ (\051) -214.92000 (\053) -0.79889 ] TJ /R49 9.96260 Tf 15.89490 0 Td [ <0d> -0.70086 ] TJ /R67 9.96260 Tf 7.84687 0 Td [ <01> -0.79889 ] TJ /R49 9.96260 Tf 4.90430 0 Td [ (h) -0.20095 ] TJ /R57 9.96260 Tf 5.73984 0 Td [ (\050) -0.90181 ] TJ /R53 9.96260 Tf 3.87383 0 Td [ (e) -0.59794 ] TJ /R55 6.97380 Tf 5.51523 -1.49414 Td [ (j) -0.70017 ] TJ /R57 9.96260 Tf 4.19805 1.49414 Td [ (\051) -0.90181 ] TJ /R43 9.96260 Tf 8.81406 0 Td (s\056t\056) Tj /R53 9.96260 Tf 16.56480 0 Td (x) Tj /R55 6.97380 Tf 6.56602 -1.49414 Td [ (j) -0.70017 ] TJ /R57 9.96260 Tf 6.96484 1.49414 Td [ (\075) -0.80379 ] TJ /R49 9.96260 Tf 10.51600 0 Td [ (X) -0.49992 ] TJ /R53 9.96260 Tf 9.03633 0 Td [ (c) -0.40189 ] TJ /R55 6.97380 Tf 5.11484 -1.49414 Td [ (j) -0.70017 ] TJ /R57 9.96260 Tf 6.33398 1.49414 Td [ (\053) -0.80379 ] TJ /R53 9.96260 Tf 9.88398 0 Td [ (e) -0.59794 ] TJ /R55 6.97380 Tf 5.51602 -1.49414 Td [ (j) -0.70017 ] TJ /R49 9.96260 Tf 4.19688 1.49414 Td [ (\073) -167.79100 (c) -0.79889 ] TJ /R55 6.97380 Tf 8.74023 -1.49414 Td [ (j) -58.72290 (j) -0.70017 ] TJ /R57 9.96260 Tf 10.66480 1.49414 Td [ (\075) -278.78700 (0) ] TJ /R49 9.96260 Tf 15.49690 0 Td [ (\073) -0.80379 ] TJ /R43 9.96260 Tf 7.74922 0 Td (\0501\051) Tj -224.63400 -23.51800 Td (where) Tj /R49 9.96260 Tf 29.91290 0 Td [ (X) -0.49992 ] TJ /R57 9.96260 Tf 17.51410 0 Td [ (\075) -851.78700 (\133) -0.79889 ] TJ /R53 9.96260 Tf 18.99490 0 Td (x) Tj /R51 6.97380 Tf 6.56602 -1.49414 Td [ (1) -0.50062 ] TJ /R49 9.96260 Tf 4.46914 1.49414 Td [ (\073) -0.79889 ] TJ /R67 9.96260 Tf 4.42773 0 Td [ <01> -167.78800 <01> -166.80800 <01> -0.79889 ] TJ /R49 9.96260 Tf 14.94410 0 Td [ (\073) -0.79889 ] TJ /R53 9.96260 Tf 4.42695 0 Td (x) Tj /R55 6.97380 Tf 6.56602 -1.49414 Td [ (N) -0.90321 ] TJ /R57 9.96260 Tf 7.55703 1.49414 Td [ (\135) -0.80379 ] TJ /R43 9.96260 Tf 8.34219 0 Td [ (is) -560.00900 (the) -558.99500 (data) -559.98000 (matrix\054) ] TJ /R53 9.96260 Tf 86.98910 0 Td [ (c) -0.40189 ] TJ /R55 6.97380 Tf 5.11484 -1.49414 Td [ (j) -0.70017 ] TJ /R57 9.96260 Tf 12.67620 1.49414 Td [ (\075) -0.80379 ] TJ -228.50100 -11.95510 Td [ (\133) -0.79889 ] TJ /R49 9.96260 Tf 2.76719 0 Td [ (c) -0.80134 ] TJ /R51 6.97380 Tf 4.31172 -1.49492 Td [ (1) -0.50062 ] TJ /R55 6.97380 Tf 3.97109 0 Td [ (j) -0.70017 ] TJ /R49 9.96260 Tf 4.19805 1.49492 Td [ (\073) -167.78800 (\072) -166.80800 (\072) -167.78800 (\072) -167.78800 (\073) -166.80800 (c) -0.80134 ] TJ /R55 6.97380 Tf 26.45000 -1.49492 Td [ (N) -107.87800 (j) -0.70017 ] TJ /R57 9.96260 Tf 11.25590 1.49492 Td [ (\135) -0.79889 ] TJ /R61 6.97380 Tf 2.76797 3.61484 Td [ (\076) -0.89971 ] TJ /R43 9.96260 Tf 9.58516 -3.61484 Td [ (is) -286.99900 (the) -287.00400 (v) 14.98280 (ector) 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