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newpath 76.75 1.28 0.7 0 360 arc fill (immediately)f(incorporated)h(into)0 4154 y(the)j(tree,)h(and)g(the)f (of)244 4258 y(e)o(xamples)28 b(that)h(has)g(been)h(incorporated)f newpath 50.81 1.09 0.7 0 360 arc fill b(3.3)124 b(2.7)h(2.4)g(1.4)g(1.2)g(1.9)f(2.2)p 2917 b(0.0)g(0.0)g(0.0)g(0.0)1084 2201 y(breast-cancer)149 ( newpath 203.18 5.70 0.7 0 360 arc fill newpath 0.89 0.00 0.7 0 360 arc fill newpath 57.93 0.00 0.7 0 360 arc fill 2599 2190 V 126 w(10.9)1334 2230 y(b)o(upa)p 1478 2248 Fd(\()p Fs(log)p Fd(\()p Fk(i)p Fd(\))e(+)j Fs(log)o )31 b(In)23 b(such)h(a)f(case,)h 4427 y(e)o(xamples)18 b(online,)i(such)f(as)g(kno)n(wledge)f 2936 2596 V 150 w(18.3)851 2637 y(horse-dead)p 1117 2655 b(During)25 b(the)g(recursi)n(v)o(e)g(transposition,)f(it)i(may)f(be)h % set origin newpath 98.97 0.60 0.7 0 360 arc fill 4003 y(road)124 b(2.4)h(1.4)g(2.2)f(2.0)h(2.0)g(2.2)g(1.4)g(1.6)1187 newpath 211.20 0.22 0.7 0 360 arc fill newpath 221.01 0.20 0.7 0 360 arc fill (0.0)p 2892 4660 V 1006 4663 1888 4 v eop b(140.3)g(0.2)g(0.2)g(0.1)g(0.1)1150 4526 y(wa)o(v)o(eform)e(722.0)i newpath 160.11 31.63 0.7 0 360 arc fill newpath 33.61 1.24 0.7 0 360 arc fill 5767 y(is)29 b(incorporated)f(into)g(the)h(tree. 1156 y(842. A decision tree or a classification tree is a tree in which each internal (non-leaf) node is labeled with an input feature. newpath 110.36 1.39 0.7 0 360 arc fill psf$urx psf$llx sub div N/psf$sy psf$y psf$ury psf$lly sub div N psf$sx newpath 41.55 1.28 0.7 0 360 arc fill (20.0)p 2892 3207 V 1114 3247 a(lung-cancer)p 1398 3265 (xample)0 3722 y(to)g(the)g(tree)h(without)e(re)n(vising)g(the)i(tree,) (v)n(alues. newpath 144.23 8.83 0.7 0 360 arc fill (assessed)h(at)g(a)g(node)f(by)h(installing)e(it,)k(including)c )36 b(This)26 b(ef)n(fect)0 2900 y(of)33 )f Fk(Principles)g(and)g(pr)l newpath 143.70 5.59 0.7 0 360 arc fill newpath 0.26 0.00 0.7 0 360 arc fill , (attrib)n(ute)f(selection)g(metric)0 4459 y(can)f(be)g(selected)g(as)g 2885 2480 V 126 w(86.5)922 2521 y(glass-no-id)p 1191 b(4.5)125 b(2.9)f(3.4)h(3.3)g(3.6)g(4.3)g(4.0)118 b(1.6)1172 )195 2152 y(T)-8 b(o)25 b(decide)h(whether)f(to)g newpath 226.01 15.38 0.7 0 360 arc fill , which in physics is associated with the lack of information in out-of-equilibrium, non-extensive, dissipative and quantum systems. -7 b(ransposition)195 3688 y Fs(As)21 b(described)f(abo)o(v)o(e,)h(the) newpath 21.87 0.03 0.7 0 360 arc fill % Character code assignments were made as follows: (that)h(is)f(inde)o(x)o(ed)g(by)h(the)f(error)0 1791 3672 V 1189 3712 a(nettalk)p 1373 3730 V 99 w(110.6)100 newpath 189.50 0.38 0.7 0 360 arc fill newpath 260.94 30.30 0.7 0 360 arc fill )h newpath 161.43 37.33 0.7 0 360 arc fill newpath 251.94 17.51 0.7 0 360 arc fill {\displaystyle i} newpath 122.27 2.41 0.7 0 360 arc fill p using each feature to find which one will split the root node.

(set)g(of)h(a)g(symbolic)d(v)n(ariable)i(is)h(often)f(smaller)g(than)g newpath 156.14 6.55 0.7 0 360 arc fill (Ef)n(\002cient)f(T)m(ree)h(Restructuring)1305 b Fs(38)0 124 w(80.3)g(79.6)f(79.9)h(79.7)g(80.1)f(81.6)h(80.3)g(80.9)p newpath 181.02 12.48 0.7 0 360 arc fill newpath 190.55 22.54 0.7 0 360 arc fill )59 3044 y(led24)e(61.9)h(62.9)f(61.4)h(62.9)g(62.4)f(62.4)h(60.5)g(57.1)h newpath 116.71 4.53 0.7 0 360 arc fill % Standard Encoding + ISO Latin 1 + extra characters from Lucida. b(5.5)124 b(0.2)h(0.1)100 b(0.1)g(0.1)150 b(12.0)938 (leaf. (5.0)g(3.0)g(1494.0)1057 3741 y(pima)124 b(897.5)h(390.9)f(682.3)100 N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin 2599 2655 V 151 w(8.6)1225 2695 y(horse-sick)p 1478 2713 newpath 3.07 0.04 0.7 0 360 arc fill newpath 29.15 0.02 0.7 0 360 arc fill

newpath 75.42 8.31 0.7 0 360 arc fill b(In)29 b(the)g(incremental)g(case,)i(one)e(tak)o(es)g(the)g(current)g newpath 140.78 0.42 0.7 0 360 arc fill newpath 129.94 8.95 0.7 0 360 arc fill Ff(g)e Fs(then)h(the)g(possible)e(binary)i(tests)f(w)o(ould)g(be)h

newpath 198.48 7.46 0.7 0 360 arc fill (30.2)f(22.4)p 2936 3817 V 150 w(32.6)776 3858 y(primary-tumor)p

(21.0)f(17.6)p 2936 4282 V 150 w(20.9)1023 4322 y(v)o(a)p newpath 89.12 0.00 0.7 0 360 arc fill 1117 2945 V 199 w(9.8)174 b(5.3)h(9.2)f(9.4)150 b(8.8)g(8.3)f(8.3)h {\displaystyle t} Fs(,)44 b Fc(hungar)q(ian)p Fs(,)j Fc(s)m(witz)o(er)q(land)p 587 y(F)o(or)40 b(each)g(leaf,)k(the)c(number)f(of)h(bits)f(needed)h b(21.0)f(17.5)h(35.2)100 b(0.1)g(0.1)g(0.0)g(0.0)p 2892 (xample)0 5478 y(still)j(remaining)h(in)g(the)h(pool. newpath 13.04 0.03 0.7 0 360 arc fill newpath 25.14 0.82 0.7 0 360 arc fill newpath 186.43 0.38 0.7 0 360 arc fill (Mor)n(gan)f(Kaufmann. newpath 243.47 33.56 0.7 0 360 arc fill newpath 84.69 4.96 0.7 0 360 arc fill b Fc(I2)g Fs(is)f(ITI)h(in)g(batch)g(mode,)g(with)f(a)h(leaf)g(being)f b(of)h(which)f(are)i(presented)f(here. newpath 128.33 0.11 0.7 0 360 arc fill )48 b(Often,)32 )69 b(F)o(or)39 b(incremental)e(induction,)j (e-one-out)h(cross)g(v)n(alidation)e(is)i(practical)g(for)h(decision)e 2415 y(The)j Fc(hungar)q(ian)j Fs(data)d(\002le)g(w)o(as)f(compiled)g Information gain is used to decide which feature to split on at each step in building the tree. TR/showpage{}N/erasepage{}N/copypage{}N/p 3 def @MacSetUp}N/doclip{

b(0.1)p 2644 2451 V 1463 2492 a(fayyad)p 1646 2509 V )30 b(Mer)n(ging)22 b(of)g(symbolic)f(v)n(ariable)i(information) newpath 67.73 0.00 0.7 0 360 arc fill newpath 2.67 0.00 0.7 0 360 arc fill b(is)f(the)g(cost)h(of)g(adding)f(the)g(information)g(from)g(the)h(e)o b(tests)i(at)g(a)g(node)g(is)f(limited)g(in)g(size)h(to)g(the)g(number) newpath 94.74 3.53 0.7 0 360 arc fill (an)g(e)o(xisting)f(tree)i(and)f(a)h(ne)n(w)f(training)f(e)o(x-)0 Fk(e)n(xpected-misclassi\002cation-cost)e Fs(measures)i(the)h(penalty)e newpath 2.91 0.11 0.7 0 360 arc fill

Some examples are given below. (ensuring,)g(after)0 3481 y(each)k(training)d(e)o(xample,)h(that)h(the)

b(6.0)f(2.9)h(3.1)g(3.0)g(3.8)g(3.9)118 b(3.1)1236 4410 (mark)h(a)f(decision)g(node)g(as)h(pruned,)f(the)g(MDL)g(for)h(the)f %%BeginSetup newpath 193.99 20.88 0.7 0 360 arc fill b(\002gures)g(do)g(not)f(sho)n(w)g(the)h(cost)g(of)g(b)n(uilding)e(a)j newpath 6.24 0.00 0.7 0 360 arc fill b(1.2)h(1.2)f(1.2)h(3.7)100 b(0.0)g(0.0)g(0.0)g(0.0)1184 newpath 230.54 0.20 0.7 0 360 arc fill 2347 y(cle)o(v)o(eland)f(71.6)h(45.7)124 b(42.6)h(42.5)g(38.7)f(33.1)h newpath 253.98 1.24 0.7 0 360 arc fill , /Ff 4 104 df<007FB912E0BA12F0A26C18E03C04789A4D>0 D<18034E7E851803851801 1 (487.6)h(724.7)f(3.1)h(2.7)100 b(1.2)g(0.8)125 b(273.3)930 newpath 258.16 0.20 0.7 0 360 arc fill

w(best)p 2996 1848 V 35 w(test)p Fs(,)h(and)f(pseudo-code)0 y(primary-tumor)147 b(95.3)j(43.5)124 b(78.2)h(62.0)g(79.6)f(74.3)h newpath 75.16 4.08 0.7 0 360 arc fill (separate)g(pruning)e(set)h(are)0 3990 y(oxymoronic)24 (an)g(algebraic)f(approach)h(to)g(\002nding)f(irreducible)g(trees. %EndDVIPSBitmapFont newpath 187.90 20.91 0.7 0 360 arc fill (5.0)1200 3828 y(post-op)f(7.8)100 b(12.2)125 b(8.3)99 newpath 44.88 0.07 0.7 0 360 arc fill newpath 205.37 13.89 0.7 0 360 arc fill )37 %%Page: 10 10 V 124 w(2.8)g(2.6)g(2.1)g(2.7)f(2.2)h(2.2)p 2599 2713 (5.7)p 2936 4572 V 175 w(6.5)997 4613 y(zoo)p 1117 4630 newpath 167.63 0.70 0.7 0 360 arc fill b(1.0)f(1.3)h(1.3)g(1.9)g(0.6)g(0.4)118 b(0.5)1122 2899 newpath 123.33 2.09 0.7 0 360 arc fill b(0.0)g(0.0)g(0.0)g(0.0)p 2892 3962 V 1261 4003 a(road)p

newpath 176.52 10.12 0.7 0 360 arc fill

b(day)-6 b(,)22 b(and)g(reb)n(uild)f(the)h(embedded)g(decision)f(tree)i g(91.8)h(92.4)p 800 4634 V 1030 4674 a(Mean)f(79.5)g(78.1)f(77.9)h /Type /Page 12 11 bop 0 280 a Fl(Decision)24 b(T)m(ree)h(Induction)f(Based)h(on)g 55 55 55 55 55 55 55 55 55 1[55 9[55 6[55 1[55 13[55 % at 96 and 145 that we move the things normally found there down to here. newpath 137.09 5.87 0.7 0 360 arc fill -8 b(ables)25 b(16)f(and)h(17. newpath 49.10 0.64 0.7 0 360 arc fill

/eight /nine /colon /semicolon /less /equal /greater /question newpath 50.64 0.07 0.7 0 360 arc fill 3524 y(e)o(xamples. newpath 85.75 3.31 0.7 0 360 arc fill b(8.5)1161 2056 y(balance-scale)125 b(7.2)g(5.7)g(5.7)g(5.8)f(5.7)h 3730 V 1250 3770 a(pima)p 1398 3788 V 99 w(146.0)g(173.8)124 newpath 136.29 5.61 0.7 0 360 arc fill b(1.1)h(1.4)g(1.1)g(0.8)g(0.8)f(0.8)p 2917 2974 V 1183 /Parent 2 0 R newpath 183.36 0.42 0.7 0 360 arc fill (pattern)0 4876 y(recognition,)27 b(and)h(it)f(w)o(as)h(also)f newpath -4.0 58.40 moveto -8.0 58.40 lineto stroke 2885 2131 V 126 w(94.2)878 2172 y(breast-cancer)p 1191 {\displaystyle S_{f}} )31 b(Lea)n(v)o(es)24 b(\(pruning\))1479

)0 4668 y(F)o(or)38 newpath 47.23 0.00 0.7 0 360 arc fill Fs(and)g Fc(C2)g Fs(on)g(a)n(v)o(erage. newpath 161.17 10.05 0.7 0 360 arc fill

%%Page: 17 17 (also)e(pro)o(vided)g(to)g(UCI)i(by)e(generous)h(donors. newpath 232.08 0.21 0.7 0 360 arc fill b(6.3)1295 2463 y(fayyad)123 b(4.9)i(3.8)g(3.8)g(3.7)f(3.9)h(3.5)151 b(Kaufmann. newpath 230.77 13.25 0.7 0 360 arc fill

stream newpath 247.44 7.97 0.7 0 360 arc fill

(1.9)h(2.0)151 b(3.3)1225 2695 y(horse-sick)124 b(2.0)h(1.9)g(1.9)g newpath 194.49 0.36 0.7 0 360 arc fill newpath 222.30 9.33 0.7 0 360 arc fill %%Page: 12 12 newpath 104.27 3.51 0.7 0 360 arc fill (each)g(grandchild. (signi\002cance)g(test)f(that)h(is)f(designed)g(to)g(handle)h(multiple) )30 b(W)l(ith)22 b(no)g(additional)g(information,)f(there)i(can)g

(Ef)n(\002cient)f(T)m(ree)h(Restructuring)1305 b Fs(36)1453 (D.)g(\(1986\). newpath 219.80 0.53 0.7 0 360 arc fill

)h(San)g(Mateo,)g(CA:)h (be)h(a)g(decision)0 4739 y(node)23 b(with)f(a)i(speci\002ed)f(test,)g 99.6264 /Times-Italic rf /Fl 133[44 1[50 2[50 28 39 33 newpath 69.05 0.08 0.7 0 360 arc fill newpath 23.29 0.22 0.7 0 360 arc fill (as)f(one)g(can)h(see)0 3820 y(in)c(Figure)g(3,)h(there)f(are)h(only)f newpath 91.79 0.00 0.7 0 360 arc fill (tree)h(size)e(of)h(the)g(algorithms)e(when)i(pruning)f(is)g(turned)g newpath 243.97 0.26 0.7 0 360 arc fill 2277 V 1076 2317 a(chess-551x39)p 1398 2335 V 99 w(200.7)g(262.2)f newpath 37.32 0.83 0.7 0 360 arc fill % 0xE0 (Ef)n(\002cient)f(T)m(ree)h(Restructuring)1305 b Fs(34)1391 3885 y(the)32 b(tree)h(at)f(time)d Fk(t)7 b Fs(,)33 b(where)e

= % draw the y-axis with height 12 Fc(I1)p Fs(,)h Fc(I2)p Fs(,)g Fc(C1)p Fs(,)h(and)e Fc(C2)p 4219 y(P)o(azzani,)33 b(M.,)f(Merz,)h(C.,)g(Murphy)-6 /Parent 2 0 R b(a)g(set)g(of)g(e)o(xamples. newpath 45.45 0.00 0.7 0 360 arc fill Fs(and)f Fc(usama-m)o(ys)g Fs(tasks)f(come)h(from)g(Usama)f(F)o(ayyad.) Fk(i)p Fd(\))f Fs(bits)h(to)h(specify)f(the)h(e)o(xception,)f(and)0 2858 V 1106 2899 a(ionosphere)p 1373 2916 V 149 w(2.1)150

/.notdef /.notdef /.notdef /.notdef (limited)f(re-e)o(xamination)g(of)i(the)f(e)o(xample.

{\displaystyle x_{1},x_{2},x_{3}} %%Page: 20 20 newpath 159.19 0.43 0.7 0 360 arc fill newpath 151.11 40.97 0.7 0 360 arc fill )29 b(The)20 b )g newpath 232.09 12.81 0.7 0 360 arc fill b(2.2)h(2.2)g(4.5)g(6.2)g(4.0)118 b(3.0)1111 4177 y(switzerland)149 1398 2219 V 124 w(7.2)g(9.3)100 b(11.3)124 b(5.9)h(6.0)g(4.9)g(6.0)g b(the)g(number)g(of)h(possible)f(tests)f(at)i(the)g(node,)h newpath 77.49 0.18 0.7 0 360 arc fill

(lar)n(ger)g(set)244 4702 y(of)i(possible)e(outcomes)h(than)g(that)h newpath 72.51 11.06 0.7 0 360 arc fill )43 b(When)29 (ee)h(induction)p Fs(,)179 1746 y(\(T)-7 b(echnical)35

b(I1)f(I2)103 b(C1)h(C2)p 2892 1983 V 1006 1986 1888 newpath 157.99 33.07 0.7 0 360 arc fill newpath 182.34 8.56 0.7 0 360 arc fill 4410 y(a)k(deliberate)g(choice. )21 b(E.,)f(Berkman,)0 5745 y(N.)j(C.,)g(and)f(Clouse,)h(J.)g(A. f(returned)i(for)f(the)g(unlabelled)g(e)o(xample)f(is)h(that)g(of)g newpath 180.29 0.51 0.7 0 360 arc fill newpath 155.06 0.18 0.7 0 360 arc fill 25 24 bop 0 280 a Fl(Decision)24 b(T)m(ree)h(Induction)f(Based)h(on)g 50 33 1[55 55 55 83 22 50 1[22 55 55 28 55 55 50 55 55 i )42 b(Under)29 b(what)f(conditions,)g(if)g(an)o newpath 175.20 6.58 0.7 0 360 arc fill Fs(returns)h(the)f(number)g(of)h(leaf)g(nodes)g(in)f(the)g(tree. w(9.3)h(9.4)g(8.6)g(6.5)f(5.8)h(4.7)p 2599 4282 V 151 2892 4311 V 1304 4351 a(v)o(a)p 1398 4369 V 124 w(43.1)125 14 13 bop 0 280 a Fl(Decision)24 b(T)m(ree)h(Induction)f(Based)h(on)g (68.6)g(70.5)h(68.2)1022 3160 y(lenses)f(90.0)g(83.3)f(83.3)h(83.3)g b Fk(lazy)g(mode)p Fs(,)h(one)f(delays)g(ensuring)g(that)f(the)h(tree)h newpath 193.72 0.40 0.7 0 360 arc fill 5526 y(\002nal)f(size)g(early)g(in)f(the)h(training. % s The split with the highest information gain will be taken as the first split and the process will continue until all children nodes each have consistent data, or until the information gain is 0. (incorporated)h(and)g(therefore)g(has)g(no)g(ef)n(fect)g(on)0 newpath 196.10 7.27 0.7 0 360 arc fill /ModDate (D:20140816110100+02'00') / /Font 44 0 R 3962 V 1236 4003 a(road)p 1373 4020 V 149 w(9.1)150 b(5.8)124

)52 b(F)o(or)32 b(the)0 3439 V 99 w(0.2)c(0.1)g(0.1)k(0.0)118 b(0.0)104 b(0.0)p

1800 y(T)-8 b(able)25 b(17. (player)g(on-mo)o(v)o(e,)e(coded)i(as)f(`x'. )h Fk(Pr)l(oceedings)e(of)179 1199 y(Utgof)n(f,)43 b(P)-11 b(. /Parent 2 0 R b(0.6)125 b(0.3)f(1.0)h(1.0)g(0.6)g(0.9)g(1.0)118 b(0.8)1119 )p eop (26.0)h(22.6)g(20.0)150 b(28.6)838 2056 y(balance-scale)g(52.3)g(40.0) in 1984. newpath 161.70 10.38 0.7 0 360 arc fill b(166.1)149 b(94.0)125 b(133.0)g(160.3)f(0.6)h(0.5)100 2885 2190 V 126 w(66.2)1047 2230 y(b)o(upa)p 1191 2248 )36 b(\(1996\). 174 b(3.2)871 3218 y(lung-cancer)g(9.0)h(6.4)149 b(4.0)h(4.0)g(4.5)f %%Page: 37 37 (Ef)n(\002cient)f(T)m(ree)h(Restructuring)1305 b Fs(27)880

(3.1)h(2.7)p 2599 4630 V 151 w(3.2)p 1087 4634 1727 4 @start /Fa 133[22 25 25 36 25 25 14 19 17 1[25 25 25 1309 y Fs(to)0 1429 y(ha)n(v)o(e)g(a)g(higher)f(leaf)h(count)g(and)f(a) )p eop (e)o(xplicit)d(cost)i(matrix)g(that)g(speci\002es)0 3115 1 )0 . 45 45 71 25 2[25 45 1[30 40 45 40 45 40 9[86 1[66 56 (of)h(each)g(update)g(of)g(the)f(tree.

(of)g(v)n(alues,)h(nor)f(a)g(lar)n(ge)g(number)g(of)g(classes)g(is)f 3160 y(lenses)p 1205 3178 V 175 w(0.0)174 b(0.0)h(0.0)g(0.0)124 newpath 239.51 14.68 0.7 0 360 arc fill

26 36 translate (1.1)g(1.4)118 b(0.8)1122 2666 y(horse-dead)149 b(2.5)125 newpath 197.84 0.17 0.7 0 360 arc fill newpath 230.24 18.35 0.7 0 360 arc fill newpath 125.65 0.80 0.7 0 360 arc fill )195 h(incremental)0 4444 y(in)d(an)o(y)g(sense,)j(b)n(ut)d(it)g(pro)o