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TJ /R44 9.96260 Tf 76.33320 0 Td [ (B) -0.49992 ] TJ /R32 9.96260 Tf -228.19300 -11.95510 Td [ (constitute) -243.01600 (a) -242.98300 (basis) -244.01800 (for) -242.98000 (the) -243.01100 (column\055space) -242.99400 (of) ] TJ /R44 9.96260 Tf 167.47500 0 Td [ (X) -0.49992 ] TJ /R32 9.96260 Tf 9.03516 0 Td [ (\056) -307.98500 (The) -243.01300 (matrix) ] TJ /R44 9.96260 Tf 51.90660 0 Td [ (C) -0.69841 ] TJ /R32 9.96260 Tf -228.41700 -11.95510 Td [ (contains) -327.01700 (coef) 25.00810 <026369656e7473> -327.99300 (used) -326.99200 (to) -326.99200 (form) -328.01300 (t) 0.98758 (he) -327.98300 (columns) -327.00700 (of) ] TJ /R44 9.96260 Tf 204.58600 0 Td [ (X) -0.49992 ] TJ /R32 9.96260 Tf 12.29690 0 Td (from) Tj -216.88300 -11.95510 Td [ (the) -283.00400 (basis\056) -407.98800 (Alternati) 25 (v) 14.98280 (ely) -283.00400 (one) -281.98600 (may) -283 (think) -282.98200 (of) -283.00900 (the) -281.98500 (ro) 25.01790 (ws) -283.00200 (of) ] TJ /R44 9.96260 Tf 216.09900 0 Td [ (X) -0.49992 ] TJ /R32 9.96260 Tf 11.85230 0 Td (as) Tj ET Q 3.98000 w 0 G 501.12100 1096.08000 m 1446.11000 1096.08000 l S q 10 0 0 10 0 0 cm BT /R32 5.97760 Tf 1 0 0 1 60.97110 102.74200 Tm (1) Tj /R32 7.97010 Tf 3.48672 -2.81328 Td [ (This) -318.99800 (w) 10.01290 (ork) -319.02400 (has) -319.02400 (been) -318.97900 (funded) -318.99500 (by) -318.99200 (the) -319.01300 (Swedish) -319 (Research) -318.98100 (Council) -318.97800 (\050grant) ] TJ -14.34570 -9.46406 Td [ (no\056) -524.01400 (2012\0554213\051) -320.99900 (and) -320.99500 (the) -321.02300 (Swedish) -321.00900 (F) 15.01280 (oundation) -322.01300 (for) -321.00300 (Strate) 15.00970 (gic) -321.02400 (Research) -320.99000 (\050Se\055) ] TJ 9.46484 TL T* [ (mantic) -249.99700 (Mapping) -250.01300 (and) -249.97800 (V) 60.00360 (isual) -250 (Na) 20.01810 (vig) 4.98077 (ation) -250.01100 (for) -249.98500 (Smart) -250.01300 (Robots\051\056) ] TJ ET Q q 736.99000 0 0 795.72100 3148.40000 5169.27000 cm /R54 Do Q q 737.01600 0 0 795.90100 3913.75000 5169.27000 cm /R55 Do Q q 737.01200 0 0 793.70600 4679.10000 5169.27000 cm /R56 Do Q q 10 0 0 10 0 0 cm BT /R32 9.96260 Tf 1 0 0 1 346.16100 504.97200 Tm [ (\050a\051) -6544.02000 (\050b\051) -6544.99000 (\050c) 1.00964 (\051) ] TJ -37.29880 -17.70700 Td [ (Figure) -292.00500 (1\072) -392.98100 (3D) -291.98300 (illustration) -290.99300 (of) -291.99000 (subspace) -292.01500 (representations\056) -434.99100 (\050a\051) -292 (\055) ] TJ 11.95590 TL T* [ (A) -271.01100 (2D) -271.00600 (subspace) -270.99900 (is) -271.00100 <0274746564> -272.00400 (to) -271.00400 (all) -271.00400 (the) -271.00400 (data) -271.00900 (\050global) -270.99400 (model\051\056) -373.99200 (\050b\051) -271.01400 (\055) ] TJ 11.95510 TL T* [ (A) -295.98700 (union) -294.98300 (of) -295.98700 (independent) -295.99700 (1D) -295 (subspaces) -296.00900 (is) -294.99500 <0274746564> -296 (to) -296.01900 (clustered) ] TJ T* [ (data) -350.01800 (\050l) 0.98513 (o) -1.01454 (c) 1.01454 (al) -350.01800 (models\051\056) -609.00600 (\050c\051) -349.01000 (\055) -349.98600 (Our) -348.99600 <756e69026564> -349.98600 (approach\056) -608.01100 (1D) -350.01000 (sub\055) ] TJ T* [ (spaces) -328.01900 (are) -327.99700 <0274746564> -327.99400 (to) -328.01100 (clustered) -328.00900 (data) -327.98000 (and) -328.01900 (restricted) -328.00900 (to) -328.01400 (lie) -328.01400 (in) -328.01400 (a) ] TJ T* [ (2D) -293.00300 (subspace\056) -439.00800 (\050F) 14.99010 (or) -293.98800 (t) 0.98758 (his) -294.01200 (data) ] TJ /R44 9.96260 Tf 114.68600 0 Td (m) Tj /R48 9.96260 Tf 12.31090 0 Td [ (\075) -358.81300 (3) ] TJ /R32 9.96260 Tf 16.29220 0 Td (\054) Tj /R44 9.96260 Tf 5.51875 0 Td [ (n) -0.20095 ] TJ /R48 9.96260 Tf 9.54219 0 Td [ (\075) -358.81300 (100) ] TJ /R32 9.96260 Tf 26.25590 0 Td (\054) Tj /R44 9.96260 Tf 5.51797 0 Td [ (r) -0.20095 ] TJ /R50 6.97380 Tf 4.49492 -1.49492 Td [ (0) -0.49712 ] TJ /R48 9.96260 Tf 8.03203 1.49492 Td [ (\075) -358.81300 (2) ] TJ /R32 9.96260 Tf 19.21330 0 Td (and) Tj /R44 9.96260 Tf -221.86400 -11.95590 Td [ (r) -0.19850 ] TJ /R52 6.97380 Tf 4.49492 -1.49414 Td [ (k) -0.29757 ] TJ /R48 9.96260 Tf 7.66914 1.49414 Td [ (\075) -278.78400 (1) ] TJ /R32 9.96260 Tf 15.49690 0 Td [ (\054) -249.99500 (see) -250 (Section) ] TJ ET Q 1 0 0 rg q 10 0 0 10 0 0 cm BT /R32 9.96260 Tf 1 0 0 1 389.09600 415.53300 Tm (2) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R32 9.96260 Tf 1 0 0 1 396.56800 415.53300 Tm [ (for) -250 <6465026e6974696f6e732e29> ] TJ /R44 9.96260 Tf -87.70550 -34.34610 Td [ (n) -0.19850 ] TJ /R32 9.96260 Tf 5.98008 0 Td [ (\055dimensional) -213.01300 (data\054) ] TJ /R44 9.96260 Tf 75.43670 0 Td [ (C) -0.69841 ] TJ /R32 9.96260 Tf 9.95898 0 Td [ (as) -212.98200 (a) -214.00800 (basis) -213.00400 (for) -214.00400 (the) -213.01300 (ro) 25.01540 (w\055space) -212.98400 (and) ] TJ /R44 9.96260 Tf 126.39300 0 Td [ (B) -0.49992 ] TJ /R32 9.96260 Tf 10.18200 0 Td (as) Tj -227.95100 -11.95510 Td [ (the) -301.98100 (coef) 25.00810 <026369656e74732e> -466.00600 (In) -301.98600 (both) -302.00600 (cases) -301.98900 (the) -301.97900 (data) -301.98400 (is) -302.01300 (approximated) -301.99400 (by) ] TJ 11.95510 TL (an) ' /R44 9.96260 Tf 11.89490 0 Td [ (r) -0.19850 ] TJ /R50 6.97380 Tf 4.49492 -1.49492 Td [ (0) -0.50062 ] TJ /R32 9.96260 Tf 4.46914 1.49492 Td [ (\055dimensional) -249.98800 (subspace\054) -249.98300 (as) -249.99700 (illustrated) -249.99700 (in) -249.98800 (Figure) ] TJ ET Q 1 0 0 rg q 10 0 0 10 0 0 cm BT /R32 9.96260 Tf 1 0 0 1 517.05700 357.27700 Tm (1) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R32 9.96260 Tf 1 0 0 1 522.03900 357.27700 Tm (\050a\051\056) Tj -201.22100 -12.39100 Td [ (In) -285.00900 (a) -285.99600 (sense) -285.00400 (the) -285.00400 (f) 9.99588 (actorization) ] TJ /R44 9.96260 Tf 110.94100 0 Td [ (B) -50.49160 (C) -0.70086 ] TJ /R52 6.97380 Tf 15.88870 3.61523 Td [ (T) -0.79819 ] TJ /R32 9.96260 Tf 9.11914 -3.61523 Td [ (can) -285.01600 (be) -285.99100 (seen) -285.01100 (as) -285.01100 (a) -285.99600 (com\055) ] TJ -147.90400 -11.95590 Td [ (pressed) -322.99500 (representation) -324 (of) ] TJ /R44 9.96260 Tf 104.27700 0 Td [ (M) -0.09802 ] TJ /R32 9.96260 Tf 13.97190 0 Td [ (where) -323.01000 (the) ] TJ /R44 9.96260 Tf 42.95510 0 Td [ (mn) -0.20095 ] TJ /R32 9.96260 Tf 17.94800 0 Td [ (elements) -323.02000 (ha) 19.99670 (v) 14.98280 (e) ] TJ -179.15200 -11.95510 Td [ (been) -331.98100 (reduced) -331.98600 (to) ] TJ /R48 9.96260 Tf 68.01990 0 Td [ (\050) -0.90181 ] TJ /R44 9.96260 Tf 3.87422 0 Td (m) Tj /R48 9.96260 Tf 11.56800 0 Td [ (\053) -0.79889 ] TJ /R44 9.96260 Tf 10.56870 0 Td [ (n) -0.19850 ] TJ /R46 9.96260 Tf 8.80000 0 Td [ <00> -0.80379 ] TJ /R44 9.96260 Tf 10.56910 0 Td [ (r) -0.20095 ] TJ /R50 6.97380 Tf 4.49492 -1.49375 Td [ (0) -0.49712 ] TJ /R48 9.96260 Tf 4.46914 1.49375 Td [ (\051) -0.90181 ] TJ /R44 9.96260 Tf 3.87500 0 Td [ (r) -0.20095 ] TJ /R50 6.97380 Tf 4.49375 -1.49375 Td [ (0) -0.49712 ] TJ /R32 9.96260 Tf 7.77930 1.49375 Td [ (de) 15.01710 (grees) -331.98400 (of) -331.98400 (freedom) -332.99800 (\050s) 0.98513 (ee) ] TJ -138.51200 -11.95470 Td (Section) Tj ET Q 1 0 0 rg q 10 0 0 10 0 0 cm BT /R32 9.96260 Tf 1 0 0 1 342.52600 309.02000 Tm (3\0561) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R32 9.96260 Tf 1 0 0 1 354.97900 309.02000 Tm [ (\051\056) -696.98200 (It) -378.01000 (is) -378.98300 (therefore) -379 (possible) -378.99600 (to) -378.98600 (compute) -379.01000 (the) -378.98600 (f) 9.99343 (ac\055) ] TJ -46.11680 -11.95510 Td [ (torization) -359.98600 (e) 25.01050 (v) 14.98280 (en) -358.99900 (if) -360.01300 (only) -359.99600 (a) -359.00400 (subset) -359.99400 (of) -360.01800 (the) -358.98900 (elements) -359.99400 (of) ] TJ /R44 9.96260 Tf 209.75100 0 Td [ (M) -0.09802 ] TJ /R32 9.96260 Tf 14.33520 0 Td (are) Tj -224.08600 -11.95510 Td [ (kno) 24.99090 (wn\054) -217.99300 (by) -211.01400 (solving) ] TJ /R44 9.96260 Tf 75.02890 0 Td [ (W) -0.40189 ] TJ /R46 9.96260 Tf 11.54490 0 Td [ <0c> -0.79889 ] TJ /R44 9.96260 Tf 8.50000 0 Td [ (M) -0.09802 ] TJ /R46 9.96260 Tf 13.51910 0 Td [ (\031) -0.80379 ] TJ /R44 9.96260 Tf 10.51600 0 Td [ (W) -0.40189 ] TJ /R46 9.96260 Tf 11.54490 0 Td [ <0c> -0.80379 ] TJ /R48 9.96260 Tf 8.50117 0 Td [ (\050) -0.90181 ] TJ /R44 9.96260 Tf 3.87383 0 Td [ (B) -50.49160 (C) -0.70086 ] TJ /R52 6.97380 Tf 15.89020 3.61484 Td [ (T) -0.79819 ] TJ /R48 9.96260 Tf 6.27578 -3.61484 Td [ (\051) -0.90181 ] TJ /R32 9.96260 Tf 3.87422 0 Td [ (\056) -297.00400 (Here) ] TJ /R46 9.96260 Tf 26.90080 0 Td [ <0c> -0.80379 ] TJ /R32 9.96260 Tf 9.84492 0 Td (denotes) Tj -205.81500 -11.95510 Td [ (element\055wise) -216.99600 (multiplication) -218.00800 (and) -217.01800 (the) -217.01300 (matrix) ] TJ /R44 9.96260 Tf 172.42900 0 Td [ (W) -0.40189 ] TJ /R32 9.96260 Tf 12.95900 0 Td [ (has) -217.01800 (elements) ] TJ /R44 9.96260 Tf -185.38800 -11.95590 Td [ (w) -0.89936 ] TJ /R52 6.97380 Tf 7.13203 -1.49414 Td [ (i) -0.19955 (j) -0.70367 ] TJ /R48 9.96260 Tf 10.71210 1.49414 Td [ (\075) -371.78800 (1) ] TJ /R32 9.96260 Tf 19.41600 0 Td [ (for) -299.99200 (kno) 24.99090 (wn) -299.98200 (data) -301.00600 (and) ] TJ /R48 9.96260 Tf 81.43400 0 Td (0) Tj /R32 9.96260 Tf 7.97266 0 Td [ (for) -299.98900 (missing) -300.01900 (data\056) -461.01600 (Note) -300.01900 (that) ] TJ -126.66700 -11.95510 Td [ (once) -198.98400 (computed\054) ] TJ /R44 9.96260 Tf 64.65390 0 Td [ (B) -50.49160 (C) -0.69841 ] TJ /R52 6.97380 Tf 15.89020 3.61602 Td [ (T) -0.79819 ] TJ /R32 9.96260 Tf 8.25469 -3.61602 Td [ (contains) -199.00100 (estimates) -198.01100 (of) -198.98600 (both) -199.00100 (kno) 24.99090 (wn) -197.99600 (and) ] TJ -88.79880 -11.95510 Td [ (missing) -235.01000 (data\056) -305.00300 (In) -235.01700 (this) -234.99500 (w) 10 (ay) -235.02000 (it) -235.00500 (is) -235.00500 (theoretically) -234.99000 (possible) -234.98000 (to) -235.01000 (\224pre\055) ] TJ 11.95510 TL T* [ (dict\224) -249.98800 (at) -249.99500 (most) ] TJ /R44 9.96260 Tf 53.40900 0 Td [ (mn) -0.19850 ] TJ /R46 9.96260 Tf 16.94100 0 Td [ <00> -0.79889 ] TJ /R48 9.96260 Tf 9.96289 0 Td [ (\050) -0.90181 ] TJ /R44 9.96260 Tf 3.87422 0 Td (m) Tj /R48 9.96260 Tf 10.96090 0 Td [ (\053) -0.80379 ] TJ /R44 9.96260 Tf 9.96289 0 Td [ (n) -0.20095 ] TJ /R46 9.96260 Tf 8.19414 0 Td [ <00> -0.80379 ] TJ /R44 9.96260 Tf 9.96211 0 Td [ (r) -0.20095 ] TJ /R50 6.97380 Tf 4.49492 -1.49492 Td [ (0) -0.49712 ] TJ /R48 9.96260 Tf 4.46875 1.49492 Td [ (\051) -0.90181 ] TJ /R44 9.96260 Tf 3.87500 0 Td [ (r) -0.20095 ] TJ /R50 6.97380 Tf 4.49414 -1.49492 Td [ (0) -0.49712 ] TJ /R32 9.96260 Tf 6.96016 1.49492 Td [ (missing) -249.98800 (elements\056) ] TJ -135.60500 -12.39100 Td [ (In) -251.99500 (the) -251.99000 (presence) -250.98300 (of) -251.99500 (missing) -251.98700 (data) -251.01200 (the) -251.98700 (lo) 24.98600 (w) -251.99200 (rank) -251.99700 (approxima\055) ] TJ -11.95510 -11.95470 Td [ (tion) -260.99100 (problem) -260.00800 (becomes) -261 (v) 14.98280 (ery) -260 (dif) 24.98600 <0263756c742c> -262.98100 (some) -260.99600 (v) 24.98110 (ariations) -260.01100 (of) -261.01500 (the) ] TJ 11.95630 TL T* [ (problem) -323.01700 (e) 25.01050 (v) 14.98280 (en) -323.00500 (NP\055hard) -322.98800 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R32 9.96260 Tf 1 0 0 1 407.20300 189.03200 Tm (17) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R32 9.96260 Tf 1 0 0 1 417.16600 189.03200 Tm [ (\135\056) -529.01000 (Ho) 24.98600 (we) 25.01540 (v) 14.98280 (er) 39.98350 (\054) -342.01600 (due) -323 (to) -322.99500 (its) -322.98500 (practical) ] TJ -108.30400 -11.95470 Td [ (importance) -337.01700 (a) -337.00700 (lot) -336.98300 (of) -337 (research) -337.01700 (ha) 19.99670 (v) 14.98280 (e) -337.00700 (been) -337.00300 (directed) -336.99300 (at) -336.99800 <026e64696e67> ] TJ 11.95510 TL T* [ (good) -308.98800 (algorithms\056) -487.00700 (In) -309.00500 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R32 9.96260 Tf 1 0 0 1 396.52300 165.12200 Tm (2) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R32 9.96260 Tf 1 0 0 1 401.50400 165.12200 Tm [ (\135) -309.01000 (it) 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0 0 1 491.86400 129.25600 Tm (8) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R32 9.96260 Tf 1 0 0 1 496.84600 129.25600 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R32 9.96260 Tf 1 0 0 1 502.32500 129.25600 Tm (30) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R32 9.96260 Tf 1 0 0 1 512.28800 129.25600 Tm [ (\135\056) -460.00200 (Ho) 24.98600 (w\055) ] TJ -203.42500 -11.95510 Td [ (e) 25.01050 (v) 14.98280 (er) 39.98600 (\054) -372.99400 (in) -348.00800 (man) 14.99010 (y) -348.99600 (applications) -348.01500 (such) -348.99100 (as) -348.02000 (structure) -348.00600 (from) -348.99100 (motion\054) ] TJ 11.95510 TL T* [ (where) -333.98800 (missing) -334.01300 (entries) -332.98900 (are) -333.99300 (highly) -333.98800 (correlated\054) -354.99500 (this) -333.99800 (approach) ] TJ T* [ (has) -249.99000 (been) -249.99500 (sho) 24.99340 (wn) -249.99000 (to) -249.98500 (perform) -249.98800 (poorly) -250.01200 (\050e\056g\056) -309.98700 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R32 9.96260 Tf 1 0 0 1 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