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(clustering\072) -485.017 (construction) -337.983 (of) ] TJ T* [ (the) -271.986 (af) 25.0081 <026e697479> -273.013 (matri) 1 (x) ] TJ /R38 9.9626 Tf 74.857 0 Td [ (A) -0.39944 ] TJ /R26 9.9626 Tf 8.66172 0 Td [ (\054) -277.99 (the) -271.984 (objecti) 25 (v) 14.9828 (e) -271.999 (function\054) -278.003 (and) -271.989 (optimiza\055) ] TJ -83.5187 -11.9559 Td [ (tion) -256.991 (method\056) -329.991 (W) 79.9866 (e) -256.982 <627269650379> -256.991 (re) 25.0056 (vie) 24.986 (w) -257.011 (the) -257.006 (related) -257.011 (w) 10.0032 (orks) -257.001 (re) 15.0073 (g) 4.98446 (arding) ] TJ T* [ (these) -249.988 (three) -249.997 (subjects\056) ] TJ /R32 9.9626 Tf 11.9551 -11.9551 Td (Notation\072) Tj /R26 9.9626 Tf 42.3609 0 Td [ (In) -303.986 (this) -304.003 (study) 64.999 (\054) -317.001 (bold) -304.003 (uppercase) -303.988 (letters) -304.013 (\050) ] TJ /R32 9.9626 Tf 149.642 0 Td [ (e) 15.0122 (\056g) ] TJ /R26 9.9626 Tf 11.7461 0 Td (\056) Tj /R38 9.9626 Tf 5.51875 0 Td [ (X) -0.39699 ] TJ /R36 9.9626 Tf 8.66211 0 Td [ (\051) -0.90181 ] TJ /R26 9.9626 Tf 3.87422 0 Td (\054) Tj -233.759 -11.9547 Td [ (bold) -336 (lo) 24.9885 (wercase) -335.015 (letters) -336.008 (\050) ] TJ /R32 9.9626 Tf 94.9898 0 Td [ (e) 15.0122 (\056g) ] TJ /R26 9.9626 Tf 11.7461 0 Td (\056) Tj /R38 9.9626 Tf 5.83281 0 Td [ (x) -0.89691 ] TJ /R26 9.9626 Tf 6.04727 0 Td [ (\051\054) -357 (and) -336.017 (plain) -334.983 (lo) 24.986 (wercase) -335.993 (letters) ] TJ -118.616 -11.9551 Td (\050) Tj /R32 9.9626 Tf 3.31797 0 Td [ (e) 15.0122 (\056g) ] TJ /R26 9.9626 Tf 11.7457 0 Td (\056) Tj /R34 9.9626 Tf 6.22813 0 Td [ (x) -0.49992 ] TJ /R26 9.9626 Tf 5.69414 0 Td [ (\051) -374.999 (denote) -374.982 (matrices\054) -407.01 (column) -375.006 (v) 14.9828 (ectors\054) -406 (and) -376.011 (scalars\054) -406.006 (re\055) ] TJ -26.9859 -11.9563 Td [ (specti) 24.9934 (v) 14.9828 (ely) 65.0161 (\056) ] TJ /R38 9.9626 Tf 45.4117 0 Td (0) Tj /R26 9.9626 Tf 5.72891 0 Td (\054) Tj /R38 9.9626 Tf 5.18203 0 Td (1) Tj /R26 9.9626 Tf 5.72813 0 Td [ (\054) -269.992 (and) ] TJ /R38 9.9626 Tf 22.2191 0 Td [ (I) -0.09802 ] TJ /R40 6.9738 Tf 4.34492 -1.49375 Td [ (n) -0.19955 ] TJ /R26 9.9626 Tf 8.07383 1.49375 Td [ (are) -266.005 (the) -265.985 (all\055zero) -265.995 (v) 14.9828 (ector) 39.9933 (\054) -269.989 (all\055one) -265.98 (v) 14.0026 (ec\055) ] TJ -96.6887 -11.9547 Td [ (tor) 40.0031 (\054) -380.993 (and) ] TJ /R34 9.9626 Tf 34.8719 0 Td [ (n) -0.1985 ] TJ /R48 9.9626 Tf 8.96602 0 Td [ <02> -0.79889 ] TJ /R34 9.9626 Tf 10.734 0 Td [ (n) -0.1985 ] TJ /R26 9.9626 Tf 9.51289 0 Td [ (identity) -355 (matrix\054) -379.991 (respecti) 24.986 (v) 14.9828 (ely) 65.0186 (\056) ] TJ /R38 9.9626 Tf 122.072 0 Td [ (X) -0.39699 ] TJ /R36 9.9626 Tf 8.66172 0 Td [ (\133) -0.80379 ] TJ /R34 9.9626 Tf 2.76719 0 Td [ (S) -2.19081 (\073) -167.791 (T) -0.39699 ] TJ /R36 9.9626 Tf 17.7629 0 Td [ (\135) -0.80379 ] TJ /R26 9.9626 Tf 6.3 0 Td [ (is) -354.985 (a) ] TJ -221.649 -11.9551 Td [ (submatrix) -249.997 (in) ] TJ /R38 9.9626 Tf 52.582 0 Td [ (X) -0.39944 ] TJ /R26 9.9626 Tf 11.1527 0 Td [ (with) -250.015 (ro) 25.0179 (w) -249.995 (subset) ] TJ /R34 9.9626 Tf 65.334 0 Td [ (S) -0.20095 ] TJ /R26 9.9626 Tf 9.17422 0 Td [ (and) -249.993 (column) -250.007 (subset) ] TJ /R34 9.9626 Tf 76.652 0 Td [ (T) -0.39699 ] TJ /R26 9.9626 Tf 7.20508 0 Td (\056) Tj /R24 10.9589 Tf -222.1 -18.3402 Td [ (1\0561\056) -250.004 (Related) -249.993 (W) 74.9894 (ork) ] TJ /R24 9.9626 Tf 11.9547 -17.9328 Td [ <4166026e697479> -273.016 (matrix\072) ] TJ /R26 9.9626 Tf 71.0191 0 Td [ (The) -273.008 (choice) -273.008 (of) -273.993 (an) -273.013 (af) 25.0056 <026e697479> -273.013 (matrix) -272.989 (is) -272.999 (im\055) ] TJ -82.9742 -11.9551 Td [ (portant) -445.982 (in) -447.011 (graph\055based) -445.992 (clustering\056) -898.992 (The) -447.019 (most) -446.014 (simple) -446.989 (ap\055) ] TJ T* [ (proaches) -428.982 (are) -429 (dista) 1.00228 (n) -1.01454 (c) 1.01454 (e\055based\054) -474 (such) -429.017 (as) ] TJ /R34 9.9626 Tf 157.075 0 Td [ (k) -0.59794 ] TJ /R26 9.9626 Tf 5.5 0 Td [ (\055NN) -428.987 (graph) -427.997 (or) -428.987 (the) ] TJ -162.575 -11.9559 Td [ (Gaussian) -450.998 (k) 10.0032 (ernel) -450.984 (of) -450.981 (Euclidean) -449.984 (distances) -450.998 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R26 9.9626 Tf 1 0 0 1 480.616 388.532 Tm (24) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R26 9.9626 Tf 1 0 0 1 490.579 388.532 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R26 9.9626 Tf 1 0 0 1 497.563 388.532 Tm (26) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R26 9.9626 Tf 1 0 0 1 507.525 388.532 Tm [ (\135\056) -912.985 (Other) ] TJ -198.664 -11.9551 Td [ (methods) -541.01 (are) -540 (learning) -540.991 (an) -541.008 (af) 25.0056 <026e697479> -541.008 (matrix) -540.003 (from) -540.998 (the) -540.998 (data\054) ] TJ 11.9547 TL T* [ (such) -340.009 (as) -341 (based) -340.014 (on) -340.992 (sparse) -340.017 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R26 9.9626 Tf 1 0 0 1 413.24 364.622 Tm (6) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R26 9.9626 Tf 1 0 0 1 418.221 364.622 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R26 9.9626 Tf 1 0 0 1 424.109 364.622 Tm (25) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R26 9.9626 Tf 1 0 0 1 434.072 364.622 Tm [ (\135) -339.987 (or) -339.982 (lo) 24.986 (w\055rank) -341.002 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R26 9.9626 Tf 1 0 0 1 494.893 364.622 Tm (13) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R26 9.9626 Tf 1 0 0 1 504.856 364.622 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R26 9.9626 Tf 1 0 0 1 510.734 364.622 Tm (23) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R26 9.9626 Tf 1 0 0 1 520.696 364.622 Tm [ (\135) -341.007 (self\055) ] TJ -211.835 -11.9551 Td [ (representation\056) -460.994 (In) -299.987 (these) -300.999 (methods\054) -311.987 (an) -301.009 (af) 25.0056 <026e697479> -299.989 (matrix) -300.004 (is) -300.994 (rep\055) ] TJ 11.9551 TL T* [ (resented) -350.013 (by) -350.01 (a) -349.986 (coef) 25.0081 <026369656e74> -349.015 (matrix) -349.996 (of) -350.02 (linear) -350.01 (combinations) -350.005 (of) ] TJ T* [ (data\056) -606.012 (Some) -349.013 (recent) -349.005 (studies) -349.005 (inte) 14.9926 (grated) -348.015 (the) -348.991 (tw) 10.0081 (o) -348.996 (problems) -349.005 (of) ] TJ 11.9559 TL T* [ (learning) -280.015 (af) 25.0081 <026e697479> -281.012 (and) -279.988 (clustering) -280.983 (into) -280.007 (one) -279.988 (optimization) -280.992 (prob\055) ] TJ 11.9551 TL T* [ (lem) -249.983 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R26 9.9626 Tf 1 0 0 1 329.614 304.846 Tm (17) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R26 9.9626 Tf 1 0 0 1 339.576 304.846 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R26 9.9626 Tf 1 0 0 1 344.557 304.846 Tm (12) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R26 9.9626 Tf 1 0 0 1 354.52 304.846 Tm (\135\056) Tj /R24 9.9626 Tf -33.7031 -11.9551 Td [ (Objecti) 10.0179 (v) 10.0032 (e) -285.996 (function\072) ] TJ /R26 9.9626 Tf 86.1602 0 Td (If) Tj /R34 9.9626 Tf 9.48789 0 Td [ (f) -0.59794 ] TJ /R40 6.9738 Tf 4.87812 -1.49375 Td [ (j) -0.70017 ] TJ /R36 9.9626 Tf 4.19805 1.49375 Td [ (\050) -0.90181 ] TJ /R38 9.9626 Tf 3.87383 0 Td [ (Z) -0.79889 ] TJ /R36 9.9626 Tf 7.00195 0 Td [ (\051) -0.90181 ] TJ /R26 9.9626 Tf 6.72813 0 Td [ (is) -286.016 (a) -287.016 (constant) -286.006 (and) ] TJ /R34 9.9626 Tf 70.075 0 Td [ (a) -0.59794 ] TJ /R40 6.9738 Tf 5.26602 -1.49375 Td [ (i) -0.19605 (j) -0.70017 ] TJ /R48 9.9626 Tf 10.4559 1.49375 Td [ <15> -0.80379 ] TJ /R36 9.9626 Tf 11.1891 0 Td (0) Tj /R26 9.9626 Tf -231.269 -11.9547 Td [ (for) -370.019 (all) ] TJ /R34 9.9626 Tf 28.9453 0 Td [ (i) -0.49992 (\073) -167.82 (j) -0.79889 ] TJ /R26 9.9626 Tf 12.534 0 Td [ (\054) -400.009 (we) -369 (can) -369.98 (easily) -370.002 <026e64> -369.012 (that) -370.002 (the) -370.007 (global) -369.992 (optimal) -368.997 (so\055) ] TJ -41.4793 -11.9551 Td [ (lution) -376.998 (is) -376.984 (obtained) -377.011 (by) -376.006 (assigning) -376.991 (all) -376.986 (data) -376.991 (points) -377 (to) -376.986 (a) -377 (single) ] TJ 11.9551 TL T* [ (cluster) 54.9859 (\056) ] TJ /R34 9.9626 Tf 32.932 0 Td [ (f) -0.60039 ] TJ /R40 6.9738 Tf 4.87734 -1.49492 Td [ (j) -0.70017 ] TJ /R36 9.9626 Tf 4.19766 1.49492 Td [ (\050) -0.90181 ] TJ /R38 9.9626 Tf 3.87422 0 Td [ (Z) -0.79889 ] TJ /R36 9.9626 Tf 7.00195 0 Td [ (\051) -0.90181 ] TJ /R26 9.9626 Tf 6.81211 0 Td [ (is) -294.997 (designed) -294.985 (to) -294.02 (a) 19.9918 (v) 20.0016 (oid) -294.99 (this) -294.985 (tri) 24.986 (vial) -294.995 (solution) -295 (and) ] TJ -59.6949 -11.9559 Td [ (encourage) -353 (the) -352.993 (cluster) -352.985 (size) -352.995 (not) -352 (to) -352.99 (be) -353 (too) -352.98 (lar) 17.997 (ge\056) -618.99 (F) 14.9926 (or) -353 (e) 15.0122 (xam\055) ] TJ (ple\054) ' /R34 9.9626 Tf 17.4539 0 Td [ (f) -0.60039 ] TJ /R40 6.9738 Tf 4.87773 -1.49414 Td [ (j) -0.70017 ] TJ /R36 9.9626 Tf 4.19727 1.49414 Td [ (\050) -0.90181 ] TJ /R38 9.9626 Tf 3.875 0 Td [ (Z) -0.79889 ] TJ /R36 9.9626 Tf 7.00078 0 Td [ (\051) -322.902 (\075) -0.79889 ] TJ /R38 9.9626 Tf 18.0422 0 Td (1) Tj /R46 6.9738 Tf 5.72891 3.95781 Td [ (\076) -0.89971 ] TJ /R38 9.9626 Tf 6.725 -3.95781 Td [ (z) -0.10047 ] TJ /R40 6.9738 Tf 5.09219 -1.49414 Td [ (j) -0.70017 ] TJ /R26 9.9626 Tf 6.92695 1.49414 Td [ (is) -274.02 (used) -273.984 (in) -273.984 (a) -273.998 (macro\055a) 19.9967 (v) 14.9828 (erage) -274.003 (association\054) ] TJ -79.9199 -11.9551 Td (while) Tj /R34 9.9626 Tf 25.782 0 Td [ (f) -0.60039 ] TJ /R40 6.9738 Tf 4.87695 -1.49414 Td [ (j) -0.70017 ] TJ /R36 9.9626 Tf 4.19805 1.49414 Td [ (\050) -0.90181 ] TJ /R38 9.9626 Tf 3.87383 0 Td [ (Z) -0.79889 ] TJ /R36 9.9626 Tf 7.00195 0 Td [ (\051) -492.913 (\075) -0.79889 ] TJ /R38 9.9626 Tf 21.4332 0 Td (1) Tj /R46 6.9738 Tf 5.72773 3.95703 Td [ (\076) -0.89971 ] TJ /R38 9.9626 Tf 6.725 -3.95703 Td [ (A) -0.39944 (z) -0.10047 ] TJ /R40 6.9738 Tf 13.7543 -1.49414 Td [ (j) -0.70017 ] TJ /R26 9.9626 Tf 7.84297 1.49414 Td [ (is) -366.003 (used) -366.008 (in) -366.008 (a) -365.003 (normalized) -365.993 (cut) -366.008 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R26 9.9626 Tf 1 0 0 1 529.341 221.16 Tm (19) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R26 9.9626 Tf 1 0 0 1 539.303 221.16 Tm (\135\056) Tj -230.441 -11.9551 Td [ (Please) -401.997 (refer) -401.992 (to) -402 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R26 9.9626 Tf 1 0 0 1 376.199 209.205 Tm (20) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R26 9.9626 Tf 1 0 0 1 386.162 209.205 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R26 9.9626 Tf 1 0 0 1 392.657 209.205 Tm (5) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R26 9.9626 Tf 1 0 0 1 397.639 209.205 Tm [ (\135) -402.014 (for) -402.011 (more) -402.002 (details\056) -766.005 (These) -402.006 (objecti) 25 (v) 14.9828 (e) ] TJ -88.7766 -11.9551 Td [ (functions) -266.982 (are) -268.007 (bas) 0.98758 (ed) -267.995 (on) -267.004 (macro) -267.009 (a) 19.9918 (v) 14.9828 (erage) -268.004 <28112e652e2c> ] TJ /R34 9.9626 Tf 174.078 0 Td [ (l) -0.40189 ] TJ /R26 9.9626 Tf 3.16914 0 Td [ (th) -267.004 (cluster\047) 54.981 (s) -267.009 (en\055) ] TJ -177.247 -11.9559 Td [ (er) 17.9896 (gy) ] TJ /R38 9.9626 Tf 20.3199 0 Td [ (z) -0.10047 ] TJ /R46 6.9738 Tf 5.09219 3.61602 Td [ (\076) -0.89971 ] TJ /R40 6.9738 Tf 6.20898 TL T* [ (j) -0.70017 ] TJ /R38 9.9626 Tf 6.725 2.59297 Td [ (A) -0.39944 (z) -0.10047 ] TJ /R40 6.9738 Tf 13.7539 -1.49414 Td [ (j) -0.70017 ] TJ /R26 9.9626 Tf 6.99297 1.49414 Td [ (is) -281 (di) 24.9885 (vided) -280.015 (by) -281.002 (the) ] TJ /R34 9.9626 Tf 69.6031 0 Td [ (l) -0.40189 ] TJ /R26 9.9626 Tf 3.16875 0 Td [ (th) -281.002 (cluster) -280.017 (size\051\056) -402.006 (Optimizing) ] TJ -125.656 -11.9551 Td [ (such) -259.003 (macro\055a) 19.9942 (v) 14.9828 (erage\055based) -258.001 (cost) -259 (functions) -258.001 (tends) -258.996 (to) -257.986 (yield) -258.996 (un\055) ] TJ 11.9547 TL T* [ (desirable) -249.983 (small) -250.007 (clusters\056) ] TJ 11.9551 -11.9551 Td [ (Accordingly) 64.999 (\054) -362.016 (Chen) ] TJ /R32 9.9626 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