aa27.ps

svm的分类和应用~~有详细的例子,非常实际和好用~~

73 83.022 /Times-Roman rf /Ft 134[42 1[60 2[28 32 37
2[42 46 69 23 2[23 46 1[28 37 3[42 12[55 46 2[51 1[60
78 55 1[42 5[60 60 14[42 42 42 42 2[21 28 42[46 2[{
TeXBase1Encoding ReEncodeFont}30 83.022 /Times-Bold rf
/Fu 138[80 48 56 64 2[72 80 1[40 2[40 1[72 48 64 1[64
1[72 19[135 96 4[112 2[104 104 1[104 62[80 2[{
TeXBase1Encoding ReEncodeFont}20 143.462 /Times-Bold
rf /Fv 32[37 54[25 17[37 27[33 37 37 54 37 37 21 29 25
37 37 37 37 58 21 37 1[21 37 37 25 33 37 33 37 33 3[25
1[25 46 54 1[71 54 54 46 42 50 1[42 54 54 66 46 54 29
25 54 54 42 46 54 50 50 54 6[21 37 37 37 37 37 37 37
37 37 37 21 19 25 19 2[25 25 2[62 34[42 2[{
TeXBase1Encoding ReEncodeFont}73 74.7198 /Times-Roman
rf end
%%EndProlog
%%BeginSetup
%%Feature: *Resolution 600dpi
TeXDict begin
%%PaperSize: A4

%%EndSetup
%%Page: 1 1
1 0 bop 500 -215 a Fv(to)19 b(appear)g(in)g(Adv)n(ances)i(in)d(Neural)h
(Information)h(Processing)g(Systems)e(12)500 -132 y(S.A.)f(Solla,)h(T)
-6 b(.K.)18 b(Leen)h(and)h(K.-R.)e(M)6 b(\250)-31 b(uller)19
b(\(eds.\),)f(547\226553,)j(MIT)e(Press)f(\(2000\))p
450 -6 3000 34 v 1213 243 a Fu(Lar)o(ge)34 b(Mar)o(gin)g(D)-5
b(A)d(Gs)35 b(f)l(or)1207 409 y(Multiclass)f(Classi\002cation)p
450 564 3000 9 v 936 848 a Ft(J)o(ohn)20 b(C.)g(Platt)843
939 y Fs(Microsoft)f(Research)889 1030 y(1)h(Microsoft)f(W)-7
b(ay)809 1121 y(Redmond,)18 b(W)-10 b(A)21 b(98052)809
1213 y Fr(jplatt@micr)l(osoft.com)2221 848 y Ft(Nello)f(Cristianini)
1938 939 y Fs(Dept.)25 b(of)20 b(Engineering)d(Mathematics)2173
1030 y(Uni)n(v)o(ersity)i(of)h(Bristol)2131 1121 y(Bristol,)g(BS8)h
(1TR)f(-)h(UK)2005 1213 y Fr([e-mail])1607
1448 y Ft(J)o(ohn)f(Shawe-T)-8 b(aylor)1393 1539 y Fs(Department)19
b(of)h(Computer)f(Science)1147 1630 y(Ro)o(yal)h(Hollo)n(w)o(ay)g
(Colle)o(ge)f(-)i(Uni)n(v)o(ersity)e(of)h(London)1362
1722 y(EGHAM,)g(Surre)o(y)-5 b(,)18 b(TW20)i(0EX)g(-)g(UK)1411
1813 y Fr([e-mail])1765 2097 y
Fq(Abstract)749 2291 y Fs(W)-7 b(e)27 b(present)f(a)h(ne)n(w)f
(learning)f(architecture:)37 b(the)26 b(Decision)g(Directed)g(Ac)o
(yclic)749 2382 y(Graph)32 b(\(DD)m(A)m(G\),)f(which)i(is)h(used)e(to)h
(combine)f(man)o(y)f(tw)o(o-class)j(classi\002ers)749
2473 y(into)d(a)h(multiclass)g(classi\002er)-5 b(.)60
b(F)o(or)31 b(an)h Fp(N)9 b Fs(-class)31 b(problem,)i(the)e(DD)m(A)m(G)
h(con-)749 2565 y(tains)22 b Fp(N)9 b Fo(\()p Fp(N)28
b Fn(\000)19 b Fo(1\))p Fp(=)p Fo(2)i Fs(classi\002ers,)h(one)f(for)g
(each)g(pair)g(of)g(classes.)30 b(W)-7 b(e)22 b(present)f(a)749
2656 y(VC)d(analysis)g(of)f(the)g(case)h(when)f(the)h(node)e
(classi\002ers)i(are)g(hyperplanes;)e(the)h(re-)749 2747
y(sulting)h(bound)e(on)i(the)h(test)g(error)f(depends)f(on)h
Fp(N)27 b Fs(and)18 b(on)g(the)h(mar)o(gin)d(achie)n(v)o(ed)749
2839 y(at)26 b(the)h(nodes,)f(b)n(ut)g(not)g(on)g(the)g(dimension)f(of)
g(the)h(space.)43 b(This)26 b(moti)n(v)n(ates)g(an)749
2930 y(algorithm,)c(D)m(A)m(GSVM,)h(which)g(operates)f(in)i(a)f(k)o
(ernel-induced)d(feature)j(space)749 3021 y(and)k(uses)h(tw)o(o-class)f
(maximal)g(mar)o(gin)f(hyperplanes)e(at)k(each)f(decision-node)749
3113 y(of)f(the)g(DD)m(A)m(G.)g(The)g(D)m(A)m(GSVM)h(is)g
(substantially)f(f)o(aster)g(to)h(train)f(and)g(e)n(v)n(alu-)749
3204 y(ate)h(than)f(either)g(the)h(standard)e(algorithm)g(or)h(Max)g(W)
m(ins,)j(while)d(maintaining)749 3295 y(comparable)18
b(accurac)o(y)g(to)j(both)e(of)h(these)g(algorithms.)450
3587 y Fq(1)99 b(Intr)n(oduction)450 3780 y Fs(The)17
b(problem)g(of)g(multiclass)h(classi\002cation,)g(especially)g(for)f
(systems)h(lik)o(e)g(SVMs,)h(doesn')o(t)d(present)450
3871 y(an)h(easy)g(solution.)22 b(It)c(is)f(generally)f(simpler)g(to)h
(construct)f(classi\002er)h(theory)e(and)i(algorithms)e(for)h(tw)o(o)
450 3963 y(mutually-e)o(xclusi)n(v)o(e)g(classes)k(than)f(for)f
Fp(N)29 b Fs(mutually-e)o(xclusi)n(v)o(e)15 b(classes.)26
b(W)-7 b(e)20 b(belie)n(v)o(e)f(constructing)450 4054
y Fp(N)9 b Fs(-class)21 b(SVMs)g(is)g(still)g(an)f(unsolv)o(ed)e
(research)i(problem.)450 4182 y(The)d(standard)e(method)h(for)g
Fp(N)9 b Fs(-class)17 b(SVMs)h([10)n(])f(is)h(to)f(construct)f
Fp(N)26 b Fs(SVMs.)f(The)16 b Fp(i)p Fs(th)h(SVM)g(will)h(be)450
4274 y(trained)h(with)h(all)h(of)e(the)h(e)o(xamples)f(in)h(the)g
Fp(i)p Fs(th)g(class)h(with)f(positi)n(v)o(e)f(labels,)h(and)f(all)i
(other)e(e)o(xamples)450 4365 y(with)k(ne)o(gati)n(v)o(e)d(labels.)32
b(W)-7 b(e)24 b(refer)e(to)h(SVMs)g(trained)f(in)g(this)i(w)o(ay)e(as)h
Fr(1-v-r)h Fs(SVMs)g(\(short)e(for)f(one-)450 4456 y(v)o(ersus-rest\).)
i(The)16 b(\002nal)i(output)d(of)i(the)g Fp(N)27 b Fs(1-v-r)16
b(SVMs)h(is)h(the)g(class)g(that)f(corresponds)e(to)i(the)g(SVM)450
4548 y(with)k(the)h(highest)e(output)g(v)n(alue.)28 b(Unfortunately)-5
b(,)18 b(there)j(is)h(no)f(bound)e(on)i(the)h(generalization)d(error)
450 4639 y(for)h(the)g(1-v-r)e(SVM,)j(and)f(the)g(training)f(time)h(of)
g(the)g(standard)f(method)g(scales)i(linearly)f(with)g
Fp(N)9 b Fs(.)450 4767 y(Another)22 b(method)f(for)i(constructing)e
Fp(N)9 b Fs(-class)23 b(classi\002ers)h(from)e(SVMs)i(is)g(deri)n(v)o
(ed)d(from)h(pre)n(vious)450 4859 y(research)17 b(into)h(combining)e
(tw)o(o-class)j(classi\002ers.)25 b(Knerr)18 b([5)o(])g(suggested)g
(constructing)e(all)j(possible)450 4950 y(tw)o(o-class)k(classi\002ers)
g(from)e(a)i(training)e(set)j(of)e Fp(N)32 b Fs(classes,)23
b(each)f(classi\002er)h(being)f(trained)f(on)h(only)p
eop
%%Page: 2 2
2 1 bop 450 83 a Fs(tw)o(o)20 b(out)g(of)f Fp(N)29 b
Fs(classes.)d(There)19 b(w)o(ould)g(thus)h(be)g Fp(K)28
b Fo(=)23 b Fp(N)9 b Fo(\()p Fp(N)26 b Fn(\000)16 b Fo(1\))p
Fp(=)p Fo(2)j Fs(classi\002ers.)26 b(When)20 b(applied)e(to)450
174 y(SVMs,)j(we)f(refer)g(to)g(this)h(as)g Fr(1-v-1)e
Fs(SVMs)i(\(short)e(for)h(one-v)o(ersus-one\).)450 296
y(Knerr)31 b(suggested)f(combining)g(these)i(tw)o(o-class)f
(classi\002ers)i(with)f(an)f(\223)-7 b(AND\224)32 b(gate)g([5)o(].)59
b(Fried-)450 387 y(man)23 b([4)o(])h(suggested)e(a)i(Max)f(W)m(ins)h
(algorithm:)30 b(each)23 b(1-v-1)f(classi\002er)i(casts)g(one)f(v)n
(ote)g(for)g(its)h(pre-)450 479 y(ferred)30 b(class,)35
b(and)30 b(the)h(\002nal)h(result)f(is)h(the)f(class)h(with)g(the)f
(most)g(v)n(otes.)58 b(Friedman)30 b(sho)n(ws)h(cir)n(-)450
570 y(cumstances)c(in)h(which)g(this)g(algorithm)e(is)j(Bayes)g
(optimal.)47 b(Kre\337el)27 b([6])h(applies)f(the)h(Max)g(W)m(ins)450
661 y(algorithm)19 b(to)h(Support)f(V)-9 b(ector)19 b(Machines)h(with)g
(e)o(xcellent)f(results.)450 783 y(A)28 b(signi\002cant)f(disadv)n
(antage)f(of)i(the)f(1-v-1)f(approach,)i(ho)n(we)n(v)o(er)m(,)f(is)h
(that,)i(unless)e(the)f(indi)n(vidual)450 874 y(classi\002ers)20
b(are)f(carefully)e(re)o(gularized)g(\(as)i(in)g(SVMs\),)g(the)g(o)o(v)
o(erall)e Fp(N)9 b Fs(-class)19 b(classi\002er)h(system)f(will)450
966 y(tend)24 b(to)g(o)o(v)o(er\002t.)35 b(The)24 b(\223)-7
b(AND\224)24 b(combination)e(method)g(and)i(the)g(Max)g(W)m(ins)g
(combination)e(method)450 1057 y(do)e(not)f(ha)n(v)o(e)h(bounds)f(on)g
(the)h(generalization)e(error)-5 b(.)25 b(Finally)-5
b(,)19 b(the)h(size)h(of)f(the)g(1-v-1)e(classi\002er)j(may)450
1148 y(gro)n(w)e(superlinearly)f(with)j Fp(N)9 b Fs(,)20
b(and)g(hence,)f(may)h(be)g(slo)n(w)g(to)h(e)n(v)n(aluate)e(on)h(lar)o
(ge)f(problems.)450 1270 y(In)k(Section)g(2,)g(we)h(introduce)d(a)i(ne)
n(w)g(multiclass)h(learning)d(architecture,)h(called)h(the)h(Decision)e
(Di-)450 1361 y(rected)29 b(Ac)o(yclic)g(Graph)g(\(DD)m(A)m(G\).)g(The)
g(DD)m(A)m(G)h(contains)f Fp(N)9 b Fo(\()p Fp(N)34 b
Fn(\000)25 b Fo(1\))p Fp(=)p Fo(2)k Fs(nodes,)i(each)f(with)g(an)450
1452 y(associated)22 b(1-v-1)e(classi\002er)-5 b(.)32
b(In)22 b(Section)g(3,)h(we)f(present)g(a)g(VC)h(analysis)f(of)g(DD)m
(A)m(Gs)g(whose)g(clas-)450 1544 y(si\002ers)28 b(are)f(hyperplanes,)f
(sho)n(wing)g(that)i(the)f(mar)o(gins)f(achie)n(v)o(ed)f(at)j(the)f
(decision)f(nodes)h(and)g(the)450 1635 y(size)20 b(of)f(the)g(graph)f
(both)h(af)n(fect)g(their)g(performance,)d(while)k(the)f
(dimensionality)f(of)h(the)g(input)g(space)450 1726 y(does)i(not.)27
b(The)20 b(VC)i(analysis)f(indicates)g(that)g(b)n(uilding)e(lar)o(ge)h
(mar)o(gin)g(D)m(A)m(Gs)h(in)g(high-dimensional)450 1818
y(feature)j(spaces)i(can)f(yield)g(good)f(generalization)f
(performance.)37 b(Using)26 b(such)f(bound)e(as)j(a)g(guide,)450
1909 y(in)c(Section)f(4,)h(we)g(introduce)d(a)j(no)o(v)o(el)f
(algorithm)f(for)h(multiclass)h(classi\002cation)f(based)g(on)h
(placing)450 2000 y(1-v-1)f(SVMs)i(into)f(nodes)f(of)h(a)h(DD)m(A)m(G.)
e(This)i(algorithm,)e(called)h(D)m(A)m(GSVM,)f(is)j(ef)n(\002cient)d
(to)i(train)450 2092 y(and)d(e)n(v)n(aluate.)k(Empirical)19
b(e)n(vidence)g(of)g(this)i(ef)n(\002cienc)o(y)e(is)i(sho)n(wn)f(in)g
(Section)g(5.)450 2314 y Fq(2)99 b(Decision)25 b(D)m(A)-5
b(Gs)450 2492 y Fs(A)17 b(Directed)f(Ac)o(yclic)g(Graph)g(\(D)m(A)m
(G\))f(is)j(a)f(graph)e(whose)h(edges)g(ha)n(v)o(e)g(an)h(orientation)e
(and)h(no)g(c)o(ycles.)450 2583 y(A)22 b(Rooted)f(D)m(A)m(G)g(has)h(a)g
(unique)e(node)g(such)h(that)h(it)g(is)g(the)g(only)e(node)h(which)g
(has)g(no)h(arcs)f(pointing)450 2675 y(into)31 b(it.)60
b(A)31 b(Rooted)g(Binary)g(D)m(A)m(G)g(has)h(nodes)f(which)g(ha)n(v)o
(e)g(either)g(0)g(or)g(2)h(arcs)f(lea)n(ving)g(them.)450
2766 y(W)-7 b(e)32 b(will)g(use)f(Rooted)g(Binary)f(D)m(A)m(Gs)h(in)g
(order)f(to)h(de\002ne)g(a)g(class)h(of)f(functions)f(to)h(be)g(used)f
(in)450 2857 y(classi\002cation)23 b(tasks.)33 b(The)22
b(class)h(of)g(functions)e(computed)f(by)j(Rooted)f(Binary)g(D)m(A)m
(Gs)h(is)g(formally)450 2949 y(de\002ned)c(as)i(follo)n(ws.)450
3112 y Ft(De\002nition)f(1)41 b Fs(Decision)24 b(D)m(A)m(Gs)g(\(DD)m(A)
m(Gs\).)35 b Fr(Given)23 b(a)h(space)g Fp(X)30 b Fr(and)23
b(a)h(set)h(of)f(boolean)e(functions)450 3204 y Fn(F)34
b Fo(=)26 b Fn(f)p Fm(f)44 b Fo(:)27 b Fp(X)33 b Fn(!)26
b(f)p Fo(0)p Fp(;)14 b Fo(1)p Fn(gg)p Fr(,)20 b(the)i(class)h
Fs(DD)m(A)m(G)o Fo(\()p Fn(F)8 b Fo(\))23 b Fr(of)f(Decision)g(D)m(A)m
(Gs)h(on)e Fp(N)32 b Fr(classes)23 b(o)o(ver)f Fn(F)30
b Fr(ar)m(e)450 3295 y(functions)21 b(whic)o(h)g(can)g(be)h
(implemented)e(using)h(a)h(r)l(ooted)f(binary)g(D)m(A)m(G)h(with)g
Fp(N)31 b Fr(leaves)22 b(labeled)f(by)450 3386 y(the)f(classes)h(wher)m
(e)g(eac)o(h)e(of)i(the)f Fp(K)29 b Fo(=)23 b Fp(N)9
b Fo(\()p Fp(N)27 b Fn(\000)18 b Fo(1\))p Fp(=)p Fo(2)i
Fr(internal)g(nodes)f(is)j(labeled)d(with)i(an)f(element)450
3477 y(of)h Fn(F)8 b Fr(.)29 b(The)21 b(nodes)g(ar)m(e)g(arr)o(ang)o
(ed)f(in)h(a)g(triangle)g(with)h(the)f(single)g(r)l(oot)h(node)e(at)h
(the)h(top,)f(two)g(nodes)450 3569 y(in)c(the)g(second)g(layer)g(and)f
(so)i(on)f(until)g(the)g(\002nal)f(layer)h(of)h Fp(N)26
b Fr(leaves.)e(The)17 b Fp(i)p Fr(-th)g(node)f(in)h(layer)h
Fp(j)28 b(<)22 b(N)450 3660 y Fr(is)f(connected)d(to)j(the)f
Fp(i)p Fr(-th)g(and)f Fo(\()p Fp(i)f Fo(+)g(1\))p Fr(-st)j(node)e(in)h
(the)h Fo(\()p Fp(j)i Fo(+)18 b(1\))p Fr(-st)j(layer)-9
b(.)450 3824 y Fs(T)i(o)28 b(e)n(v)n(aluate)e(a)i(particular)e(DD)m(A)m
(G)h Fp(G)h Fs(on)f(input)g Fp(x)37 b Fn(2)g Fp(X)7 b
Fs(,)28 b(starting)f(at)h(the)g(root)f(node,)g(the)h(binary)450
3915 y(function)f(at)j(a)f(node)g(is)h(e)n(v)n(aluated.)50
b(The)28 b(node)h(is)h(then)e(e)o(xited)g(via)i(the)f(left)g(edge,)h
(if)g(the)f(binary)450 4006 y(function)c(is)j(zero;)h(or)e(the)g(right)
f(edge,)h(if)g(the)g(binary)e(function)h(is)h(one.)44
b(The)27 b(ne)o(xt)f(node')-5 b(s)26 b(binary)450 4098
y(function)19 b(is)i(then)f(e)n(v)n(aluated.)25 b(The)20
b(v)n(alue)g(of)g(the)g(decision)g(function)f Fp(D)r
Fo(\()p Fp(x)p Fo(\))j Fs(is)f(the)g(v)n(alue)f(associated)450
4189 y(with)29 b(the)g(\002nal)g(leaf)f(node)g(\(see)h(Figure)f
(1\(a\)\).)50 b(The)28 b(path)g(tak)o(en)h(through)d(the)j(DD)m(A)m(G)f
(is)i(kno)n(wn)450 4280 y(as)g(the)f Fr(e)o(valuation)e(path)p
Fs(.)51 b(The)29 b(input)f Fp(x)j Fs(reaches)d(a)i(node)e(of)h(the)g
(graph,)h(if)f(that)h(node)e(is)i(on)f(the)450 4372 y(e)n(v)n(aluation)
23 b(path)i(for)f Fp(x)p Fs(.)40 b(W)-7 b(e)26 b(refer)e(to)h(the)g
(decision)f(node)g(distinguishing)f(classes)j Fp(i)f
Fs(and)g Fp(j)30 b Fs(as)c(the)450 4463 y Fp(ij)5 b Fs(-node.)37
b(Assuming)24 b(that)h(the)g(number)e(of)i(a)g(leaf)g(is)h(its)g
(class,)g(this)g(node)e(is)i(the)e Fp(i)p Fs(-th)h(node)f(in)h(the)450
4554 y Fo(\()p Fp(N)h Fn(\000)16 b Fp(j)22 b Fo(+)16
b Fp(i)p Fo(\))p Fs(-th)k(layer)f(pro)o(vided)e Fp(i)23
b(<)g(j)5 b Fs(.)25 b(Similarly)19 b(the)h Fp(j)5 b Fs(-nodes)19
b(are)g(those)h(nodes)f(in)m(v)n(olving)f(class)450 4646
y Fp(j)5 b Fs(,)20 b(that)h(is,)g(the)f(internal)f(nodes)h(on)f(the)i
(tw)o(o)f(diagonals)f(containing)f(the)j(leaf)f(labeled)f(by)h
Fp(j)5 b Fs(.)450 4767 y(The)20 b(DD)m(A)m(G)h(is)h(equi)n(v)n(alent)d
(to)i(operating)d(on)j(a)g(list,)h(where)e(each)g(node)g(eliminates)h
(one)f(class)i(from)450 4859 y(the)g(list.)30 b(The)22
b(list)h(is)f(initialized)g(with)f(a)i(list)f(of)g(all)g(classes.)31
b(A)22 b(test)h(point)e(is)h(e)n(v)n(aluated)e(against)i(the)450
4950 y(decision)f(node)g(that)h(corresponds)e(to)i(the)g(\002rst)h(and)
e(last)i(elements)f(of)f(the)h(list.)32 b(If)22 b(the)g(node)f(prefers)
p eop
%%Page: 3 3
3 2 bop 475 1344 a @beginspecial 93 @llx 300 @lly 469
@urx 721 @ury 1440 @rwi @setspecial
%%BeginDocument: dag.eps
%!PS-Adobe-3.0 EPSF-3.0
%%Title: Visio-dag.vsd
%%Creator: Windows NT 4.0
%%CreationDate: 17:56 5/10/1999
%%Pages: (atend)
%%BoundingBox: 93 300 469 721
%%LanguageLevel: 2
%%DocumentNeededFonts: (atend)
%%DocumentSuppliedFonts: (atend)
%%EndComments
%%BeginProlog

%%BeginResource: procset NTPSOct95
/NTPSOct95 100 dict dup begin/bd{bind def}bind def/ld{load def}bd/ed{exch def}
bd/a{currentpoint}bd/c/curveto ld/d/dup ld/e/eofill ld/f/fill ld/tr/translate
ld/gr/grestore ld/gs/gsave ld/j/setlinejoin ld/L/lineto ld/M/moveto ld/n
/newpath ld/cp/closepath ld/rm/rmoveto ld/sl/setlinewidth ld/sd/setdash ld/g
/setgray ld/r/setrgbcolor ld/s/stroke ld/t/show ld/aw/awidthshow ld/im
/imagemask ld/MS{moveto show}bd/SF{findfont exch scalefont setfont}bd/SM{cmtx
setmatrix}bd/MF{findfont exch makefont setfont}bd/CM{/cmtx matrix currentmatrix
def}bd/B{M exch dup 0 rlt exch 0 exch rlt neg 0 rlt}bd/CB{B cp eoclip}bd/EA{1
index 0/G0 put 4 string 1 1 4 -1 roll{3 copy neg exch cvs dup 0 71 put cvn 3 -1
roll exch put}for pop}bd/rlt/rlineto ld/L2?/languagelevel where{pop
languagelevel 2 ge}{false}ifelse def end def 
%%EndResource
%%EndProlog
%%BeginSetup
%%EndSetup
NTPSOct95 begin
%%Page: 1 1
NTPSOct95 /PageSV save put
13.238 780.059 translate 72 600 div dup neg scale
0 0 transform .25 add round .25 sub exch .25 add round .25 sub exch itransform translate
1 j
1 setlinecap
2 sl
n
1990 801 M
1992 767 L
1998 734 L
2007 702 L
2020 671 L
2036 641 L
2055 614 L
2078 589 L
2103 566 L
2130 547 L
2160 531 L
2191 518 L
2223 509 L
2256 503 L
2290 501 L
2324 503 L
2357 509 L
2389 518 L
2420 531 L
2450 547 L
2477 566 L
2502 589 L
2525 614 L
2544 641 L
2560 671 L
2573 702 L
2582 734 L
2588 767 L
2590 801 L
2588 835 L
2582 868 L
2573 900 L
2560 931 L
2544 961 L
2525 988 L
2502 1013 L
2477 1036 L
2450 1055 L
2420 1071 L
2389 1084 L
2357 1093 L
2324 1099 L
2290 1101 L
2256 1099 L
2223 1093 L
2191 1084 L
2160 1071 L
2130 1055 L
2103 1036 L
2078 1013 L
2055 988 L
2036 961 L
2020 931 L
2007 900 L
1998 868 L
1992 835 L
1990 801 L
cp
gs
1 g
e
gr
s
%%IncludeFont: Helvetica
[133.66 0 0 -133 0 0]/Helvetica MF
(1 vs 4)2112 841 MS
n
1390 2001 M
1392 1967 L
1398 1934 L
1407 1902 L
1420 1871 L
1436 1841 L