(original) (raw)

%!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: wabi2002.dvi %%Pages: 11 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips wabi2002.dvi -o wabi2002.ps %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2002.07.08:1222 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 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y Fx(,)g(and)f(I.S.)h(Mian)3095 859 y Fw(1)527 1032 y Fv(1)600 1063 y Fu(Life)f(Sciences)f(Division,)g (La)n(wrence)h(Berk)n(eley)e(National)i(Lab)r(oratory)-6 b(,)26 b(Berk)n(eley)g(CA)g(94720)653 1123 y Fv(2)726 1155 y Fu(Departmen)n(t)e(of)i(EECS,)h(Univ)n(ersit)n(y)d(of)j (California)h(Berk)n(eley)-6 b(,)26 b(Berk)n(eley)g(CA)f(94720)600 1214 y Fv(3)673 1246 y Fu(Departmen)n(t)f(of)i(Statistics,)h(Univ)n (ersit)n(y)e(of)h(California)j(Berk)n(eley)-6 b(,)26 b(Berk)n(eley)f(CA)h(94720)523 1620 y Ft(1)112 b(Abstract)523 1835 y Fx(Molecular)17 b(pro\014ling)h(tec)n(hnologies)e(monitor)i (thousands)g(of)g(transcripts,)f(proteins,)h(metab)r(o-)523 1934 y(lites)32 b(or)e(other)h(sp)r(ecies)h(concurren)n(tly)e(in)h (biological)f(samples)h(of)h(in)n(terest.)f(Giv)n(en)g(t)n(w)n(o-)523 2034 y(class,)i(high-dimensional)g(pro\014ling)g(data,)h(nominal)g Fs(Liknon)f Fx([4])h(is)g(a)g(sp)r(eci\014c)g(imple-)523 2134 y(men)n(tation)28 b(of)h(a)f(metho)r(dology)f(for)i(p)r(erforming) e(sim)n(ultaneous)h(relev)-5 b(an)n(t)28 b(feature)g(iden-)523 2233 y(ti\014cation)d(and)f(classi\014cation.)g(It)h(exploits)f(the)h (w)n(ell-kno)n(wn)e(prop)r(ert)n(y)h(that)h(minimising)523 2333 y(an)h Fr(l)662 2345 y Fw(1)726 2333 y Fx(norm)f(\(via)h(linear)g (programming\))e(yields)j(a)e(sparse)g(h)n(yp)r(erplane)h([15,)13 b(26,)g(2,)g(8,)h(17].)523 2433 y(This)26 b(w)n(ork)f(\(i\))h(examines) f(computational,)h(soft)n(w)n(are)e(and)i(practical)f(issues)g (required)g(to)523 2532 y(realise)h(nominal)h Fs(Liknon)p Fx(,)f(\(ii\))i(summarises)e(results)g(from)h(its)g(application)f(to)h (\014v)n(e)g(real)523 2632 y(w)n(orld)k(data)h(sets,)g(\(iii\))h (outlines)f(heuristic)g(solutions)f(to)h(problems)g(p)r(osed)g(b)n(y)f (domain)523 2731 y(exp)r(erts)e(when)g(in)n(terpreting)g(the)g(results) g(and)g(\(iv\))h(de\014nes)f(some)g(future)h(directions)e(of)523 2831 y(the)g(researc)n(h.)523 3112 y Ft(2)112 b(In)m(tro)s(duction)523 3327 y Fx(Biologists)19 b(and)h(clinicians)g(are)f(adopting)h (high-throughput)g(genomics,)f(proteomics)g(and)523 3427 y(related)h(tec)n(hnologies)e(to)i(assist)f(in)i(in)n(terrogating)c (normal)i(and)h(p)r(erturb)r(ed)h(systems)e(suc)n(h)523 3526 y(as)f(una\013ected)h(and)g(tumour)g(tissue)g(sp)r(ecimens.)g(Suc) n(h)f(in)n(v)n(estigations)f(can)i(generate)e(data)523 3626 y(ha)n(ving)h(the)i(form)f Fq(D)26 b Fx(=)c Fq(f)p Fx(\()p Fp(x)1406 3638 y Fo(n)1452 3626 y Fr(;)14 b(y)1530 3638 y Fo(n)1574 3626 y Fx(\))p Fr(;)g(n)24 b Fq(2)f Fx(\(1)p Fr(;)14 b(:)g(:)g(:)f(;)h(N)9 b Fx(\))p Fq(g)19 b Fx(where)g Fp(x)2504 3638 y Fo(n)2573 3626 y Fq(2)k Fn(R)2705 3596 y Fo(P)2786 3626 y Fx(and,)c(for)g(t)n(w)n(o-class)523 3726 y(data,)25 b Fr(y)774 3738 y Fo(n)842 3726 y Fq(2)e(f)p Fx(+1)p Fr(;)14 b Fq(\000)p Fx(1)p Fq(g)p Fx(.)23 b(Eac)n(h)h(elemen)n (t)h(of)g(a)g(data)g(p)r(oin)n(t)g Fp(x)2419 3738 y Fo(n)2490 3726 y Fx(is)h(the)f(absolute)g(or)f(relativ)n(e)523 3825 y(abundance)e(of)g(a)h(molecular)e(sp)r(ecies)h(monitored.)g(In)h (transcript)e(pro\014ling,)h(a)g(data)g(p)r(oin)n(t)523 3925 y(represen)n(ts)30 b(transcript)g(\(gene\))i(lev)n(els)e(measured) h(in)g(a)g(sample)g(using)g(cDNA,)i(oligon)n(u-)523 4025 y(cleotide)i(or)f(similar)g(microarra)n(y)e(tec)n(hnology)-7 b(.)33 b(A)i(data)g(p)r(oin)n(t)g(from)f(protein)h(pro\014ling)523 4124 y(can)i(represen)n(t)f(Mass/Charge)f(\(M/Z\))i(v)-5 b(alues)37 b(for)g(lo)n(w)g(molecular)f(w)n(eigh)n(t)h(molecules)523 4224 y(\(proteins\))28 b(measured)e(in)i(a)f(sample)g(using)h(mass)f (sp)r(ectro)r(cop)n(y)-7 b(.)648 4327 y(In)36 b(cancer)g(biology)-7 b(,)35 b(pro\014ling)h(studies)h(of)f(di\013eren)n(t)h(t)n(yp)r(es)f (of)h(\(tissue\))g(sp)r(ecimens)523 4426 y(are)i(motiv)-5 b(ated)40 b(largely)e(b)n(y)h(a)h(desire)f(to)g(create)g(clinical)h (decision)f(supp)r(ort)g(systems)523 4526 y(for)d(accurate)g(tumour)h (classi\014cation)e(and)i(to)g(iden)n(tify)g(robust)f(and)h(reliable)f (targets,)523 4625 y(\\biomark)n(ers",)18 b(for)j(imaging,)f (diagnosis,)g(prognosis)f(and)i(therap)r(eutic)h(in)n(terv)n(en)n(tion) e([14,)523 4725 y(3,)13 b(13,)g(27,)g(18,)g(23,)g(9,)h(25,)e(28,)h(19,) g(21,)g(24].)32 b(Meeting)h(these)g(biological)e(c)n(hallenges)g (includes)523 4825 y(addressing)d(the)j(general)d(statistical)h (problems)h(of)f(classi\014cation)g(and)h(prediction,)f(and)523 4924 y(relev)-5 b(an)n(t)27 b(feature)g(iden)n(ti\014cation.)p eop %%Page: 2 2 2 1 bop 648 448 a Fx(Supp)r(ort)24 b(V)-7 b(ector)23 b(Mac)n(hines)g(\(SVMs\))i([30,)13 b(8])23 b(ha)n(v)n(e)g(b)r(een)h (emplo)n(y)n(ed)f(successfully)h(for)523 548 y(cancer)j (classi\014cation)f(based)h(on)g(transcript)g(pro\014les)g([5,)13 b(22,)g(25,)g(28].)27 b(Although)h(mec)n(ha-)523 648 y(nisms)e(for)f(reducing)g(the)h(n)n(um)n(b)r(er)g(of)f(features)h(to)f (more)g(manageable)f(n)n(um)n(b)r(ers)i(include)523 747 y(discarding)c(those)i(b)r(elo)n(w)f(a)g(user-de\014ned)g(threshold,)g (relev)-5 b(an)n(t)23 b(feature)g(iden)n(ti\014cation)g(is)523 847 y(usually)32 b(addressed)f(via)g(a)h(\014lter-wrapp)r(er)f (strategy)g([12,)13 b(22,)g(32].)31 b(The)h(\014lter)h(generates)523 946 y(candidate)k(feature)h(subsets)f(whilst)i(the)f(wrapp)r(er)e(runs) i(an)f(induction)i(algorithm)d(to)523 1046 y(determine)27 b(the)g(discriminativ)n(e)f(abilit)n(y)g(of)h(a)f(subset.)h(Although)f (SVMs)h(and)g(the)g(newly)523 1146 y(form)n(ulated)35 b(Minimax)h(Probabilit)n(y)f(Mac)n(hine)g(\(MPM\))i([20])e(are)g(go)r (o)r(d)g(wrapp)r(ers)g([4],)523 1245 y(the)28 b(c)n(hoice)f(of)g (\014ltering)h(statistic)f(remains)g(an)g(op)r(en)h(question.)648 1345 y(Nominal)33 b Fs(Liknon)g Fx(is)h(a)g(sp)r(eci\014c)g(implemen)n (tation)g(of)f(a)h(strategy)e(for)i(p)r(erforming)523 1445 y(sim)n(ultaneous)26 b(relev)-5 b(an)n(t)26 b(feature)h(iden)n (ti\014cation)g(and)g(classi\014cation)e([4].)i(It)g(exploits)g(the)523 1544 y(w)n(ell-kno)n(wn)20 b(prop)r(ert)n(y)g(that)h(minimising)g(an)g Fr(l)2006 1556 y Fw(1)2064 1544 y Fx(norm)g(\(via)g(linear)f (programming\))f(yields)523 1644 y(a)39 b(sparse)f(h)n(yp)r(erplane)g ([15,)13 b(26,)g(2,)g(8,)h(17].)38 b(The)h(h)n(yp)r(erplane)g (constitutes)g(the)g(classi\014er)523 1743 y(whilst)32 b(its)f(sparsit)n(y)-7 b(,)30 b(a)h(w)n(eigh)n(t)f(v)n(ector)g(with)i (few)g(non-zero)d(elemen)n(ts,)i(de\014nes)h(a)e(small)523 1843 y(n)n(um)n(b)r(er)f(of)h(relev)-5 b(an)n(t)29 b(features.)g (Nominal)h Fs(Liknon)f Fx(is)g(computationally)g(less)g(demand-)523 1943 y(ing)k(than)g(the)h(prev)-5 b(ailing)33 b(\014lter{\(SVM/MPM\))g (wrapp)r(er)f(strategy)g(whic)n(h)h(treats)g(the)523 2042 y(problems)27 b(of)g(feature)g(selection)g(and)g(classi\014cation) f(as)h(t)n(w)n(o)g(indep)r(enden)n(t)h(tasks)e([4,)14 b(16].)523 2142 y(Biologically)-7 b(,)36 b(nominal)i Fs(Liknon)g Fx(p)r(erforms)f(w)n(ell)h(when)h(applied)f(to)g(real)f(w)n (orld)g(data)523 2242 y(generated)23 b(not)g(only)h(b)n(y)f(the)h (ubiquitous)g(transcript)f(pro\014ling)g(tec)n(hnology)-7 b(,)22 b(but)j(also)d(b)n(y)523 2341 y(the)28 b(emergen)n(t)f(protein)g (pro\014ling)g(tec)n(hnology)-7 b(.)523 2589 y Ft(3)112 b(Sim)m(ultaneous)44 b(relev)-6 b(an)m(t)43 b(feature)i(iden)m (ti\014cation)e(and)691 2705 y(classi\014cation)523 2886 y Fx(Consider)29 b(a)h(data)f(set)h Fq(D)g Fx(=)d Fq(f)p Fx(\()p Fp(x)1577 2898 y Fo(n)1622 2886 y Fr(;)14 b(y)1700 2898 y Fo(n)1745 2886 y Fx(\))p Fr(;)g(n)27 b Fq(2)g Fx(\(1)p Fr(;)14 b(:)g(:)g(:)g(;)g(N)9 b Fx(\))p Fq(g)p Fx(.)29 b(Eac)n(h)g(of)h(the)h Fr(N)39 b Fx(data)29 b(p)r(oin)n(ts)523 2986 y(\(pro\014ling)36 b(exp)r(erimen)n(ts\))g(is)g(a)f Fr(P)12 b Fx(-dimensional)36 b(v)n(ector)e(of)j(features)e(\(gene)h(or) f(protein)523 3085 y(abundances\))e Fp(x)1059 3097 y Fo(n)1138 3085 y Fq(2)g Fn(R)1280 3055 y Fo(P)1375 3085 y Fx(\(usually)g Fr(N)42 b Fq(\030)33 b Fx(10)1988 3055 y Fw(1)2046 3085 y Fq(\000)22 b Fx(10)2217 3055 y Fw(2)2254 3085 y Fx(;)14 b Fr(P)44 b Fq(\030)33 b Fx(10)2570 3055 y Fw(3)2629 3085 y Fq(\000)22 b Fx(10)2800 3055 y Fw(4)2836 3085 y Fx(\).)34 b(A)g(data)f(p)r(oin)n(t)523 3185 y Fr(n)38 b Fx(is)g(assigned)e(to)i(one)g(of)g(t)n(w)n(o)f(classes)f Fr(y)1905 3197 y Fo(n)1990 3185 y Fq(2)41 b(f)p Fx(+1)p Fr(;)14 b Fq(\000)p Fx(1)p Fq(g)35 b Fx(suc)n(h)j(a)f(normal)g(or)g (tumour)523 3284 y(tissue)c(sample.)f(Giv)n(en)h(suc)n(h)f(t)n(w)n (o-class)f(high-dimensional)g(data,)i(the)g(analytical)e(goal)523 3384 y(is)37 b(to)f(estimate)h(a)f(sparse)f(classi\014er,)g(a)i(mo)r (del)g(whic)n(h)f(distinguishes)g(the)h(t)n(w)n(o)f(classes)523 3484 y(of)28 b(data)f(p)r(oin)n(ts)g(\(classi\014cation\))g Fm(and)h Fx(sp)r(eci\014es)f(a)g(small)g(subset)h(of)f(discriminatory)f (fea-)523 3583 y(tures)e(\(relev)-5 b(an)n(t)24 b(feature)h(iden)n (ti\014cation\).)f(Assume)h(that)g(the)g(data)f Fq(D)j Fx(can)d(b)r(e)h(separated)523 3683 y(b)n(y)31 b(a)g(linear)g(h)n(yp)r (erplane)g(in)h(the)g Fr(P)12 b Fx(-dimensional)30 b(input)i(feature)g (space.)f(The)g(learning)523 3783 y(task)e(can)f(b)r(e)i(form)n(ulated) f(as)f(an)h(attempt)h(to)f(estimate)g(a)g(h)n(yp)r(erplane,)f (parameterized)523 3882 y(in)39 b(terms)f(of)g(a)g(w)n(eigh)n(t)f(v)n (ector)g Fp(w)j Fx(and)e(bias)g Fr(b)p Fx(,)g(via)g(a)f(solution)h(to)g (the)h(follo)n(wing)e Fr(N)523 3982 y Fx(inequalities)27 b([30]:)1495 4142 y Fr(y)1536 4154 y Fo(n)1581 4142 y Fr(z)1620 4154 y Fo(n)1688 4142 y Fx(=)22 b Fr(y)1816 4154 y Fo(n)1861 4142 y Fx(\()p Fp(w)1963 4108 y Fo(T)2016 4142 y Fp(x)2066 4154 y Fo(n)2130 4142 y Fq(\000)c Fr(b)p Fx(\))23 b Fq(\025)g Fx(0)1775 4266 y Fq(8)p Fr(n)f Fx(=)h Fq(f)p Fx(1)p Fr(;)14 b(:)g(:)g(:)f(;)h(N)9 b Fq(g)40 b Fr(:)868 b Fx(\(1\))523 4426 y(The)27 b(h)n(yp)r(erplane)g (satisfying)g Fp(w)1560 4396 y Fo(T)1612 4426 y Fp(x)18 b Fq(\000)g Fr(b)k Fx(=)h(0)k(is)g(termed)g(a)g(classi\014er.)f(A)i (new)f(data)g(p)r(oin)n(t)523 4526 y Fp(x)34 b Fx(\(abundances)g(of)g Fr(P)45 b Fx(features)34 b(in)g(a)f(new)h(sample\))g(is)g(classi\014ed) f(b)n(y)h(computing)g Fr(z)i Fx(=)523 4625 y Fp(w)593 4595 y Fo(T)646 4625 y Fp(x)14 b Fq(\000)f Fr(b)p Fx(.)26 b(If)f Fr(z)i(>)22 b Fx(0,)j(the)h(data)f(p)r(oin)n(t)g(is)h(assigned)e (to)h(one)g(class)f(otherwise)h(it)g(b)r(elongs)g(to)523 4725 y(the)j(other)f(class.)648 4825 y(En)n(umerating)35 b(relev)-5 b(an)n(t)35 b(features)h(at)h(the)f(same)g(time)h(as)f (disco)n(v)n(ering)e(a)i(classi\014er)523 4924 y(can)e(b)r(e)h (addressed)e(b)n(y)i(\014nding)f(a)g(sparse)f(h)n(yp)r(erplane,)h(a)g (w)n(eigh)n(t)g(v)n(ector)f Fp(w)j Fx(in)f(whic)n(h)p eop %%Page: 3 3 3 2 bop 523 448 a Fx(most)30 b(comp)r(onen)n(ts)g(are)f(equal)g(to)h (zero.)g(The)g(rationale)f(is)h(that)g(zero)f(elemen)n(ts)h(do)g(not) 523 548 y(con)n(tribute)d(to)h(determining)f(the)h(v)-5 b(alue)28 b(of)f Fr(z)t Fx(:)1628 783 y Fr(z)f Fx(=)1815 679 y Fo(P)1781 704 y Fl(X)1782 880 y Fo(p)p Fw(=1)1915 783 y Fr(w)1974 795 y Fo(p)2013 783 y Fr(x)2060 795 y Fo(p)2117 783 y Fq(\000)18 b Fr(b)41 b(:)523 1024 y Fx(If)d Fr(w)675 1036 y Fo(p)754 1024 y Fx(=)h(0,)e(feature)h Fr(p)f Fx(is)h(\\irrelev)-5 b(an)n(t")35 b(with)j(regards)e(to)i (deciding)f(the)h(class.)f(Since)523 1124 y(only)26 b(non-zero)f (elemen)n(ts)i Fr(w)1438 1136 y Fo(p)1499 1124 y Fq(6)p Fx(=)c(0)j(in\015uence)h(the)g(v)-5 b(alue)27 b(of)f Fr(z)t Fx(,)g(they)h(can)f(b)r(e)h(regarded)e(as)523 1223 y(\\relev)-5 b(an)n(t")26 b(features.)648 1323 y(The)39 b(task)g(of)g(de\014ning)h(a)f(small)g(n)n(um)n(b)r(er)g(of)h(relev)-5 b(an)n(t)38 b(features)h(can)g(b)r(e)h(equated)523 1423 y(with)27 b(that)g(of)f(\014nding)g(a)g(small)g(set)h(of)f(non-zero)f (elemen)n(ts.)h(This)g(can)g(b)r(e)h(form)n(ulated)f(as)523 1522 y(an)32 b(optimisation)f(problem;)h(namely)g(that)g(of)g (minimising)h(the)f Fr(l)2656 1534 y Fw(0)2725 1522 y Fx(norm)g Fq(k)p Fp(w)q Fq(k)3101 1534 y Fw(0)3137 1522 y Fx(,)h(where)523 1622 y Fq(k)p Fp(w)q Fq(k)677 1634 y Fw(0)737 1622 y Fx(=)22 b(n)n(um)n(b)r(er)28 b(of)o Fq(f)p Fr(p)23 b Fx(:)g Fr(w)1405 1634 y Fo(p)1467 1622 y Fq(6)p Fx(=)f(0)p Fq(g)p Fx(,)j(the)h(n)n(um)n(b)r(er)f(of)g (non-zero)f(elemen)n(ts)h(of)g Fp(w)q Fx(.)h(Th)n(us)f(w)n(e)523 1721 y(obtain:)1655 1880 y(min)1672 1934 y Fk(w)q Fo(;b)2050 1880 y Fq(k)p Fp(w)q Fq(k)2204 1892 y Fw(0)1431 2057 y Fx(sub)5 b(ject)27 b(to)c Fr(y)1857 2069 y Fo(n)1902 2057 y Fx(\()p Fp(w)2004 2027 y Fo(T)2057 2057 y Fp(x)2107 2069 y Fo(n)2171 2057 y Fq(\000)18 b Fr(b)p Fx(\))23 b Fq(\025)g Fx(0)1817 2181 y Fq(8)p Fr(n)f Fx(=)h Fq(f)p Fx(1)p Fr(;)14 b(:)g(:)g(:)f(;)h(N)9 b Fq(g)40 b Fr(:)826 b Fx(\(2\))648 2340 y(Unfortunately)-7 b(,)27 b(problem)g(\(2\))g(is)g (NP-hard)f([10].)g(A)i(tractable,)e(con)n(v)n(ex)g(appro)n(xima-)523 2439 y(tion)h(to)f(this)h(problem)g(can)f(b)r(e)h(obtained)f(b)n(y)h (replacing)e(the)j Fr(l)2517 2451 y Fw(0)2580 2439 y Fx(norm)e(with)i(the)f Fr(l)3152 2451 y Fw(1)3216 2439 y Fx(norm)523 2539 y Fq(k)p Fp(w)q Fq(k)677 2551 y Fw(1)714 2539 y Fx(,)38 b(where)g Fq(k)p Fp(w)q Fq(k)1180 2551 y Fw(1)1257 2539 y Fx(=)1363 2477 y Fl(P)1451 2497 y Fo(P)1451 2564 y(p)p Fw(=1)1587 2539 y Fq(j)p Fr(w)1669 2551 y Fo(p)1708 2539 y Fq(j)p Fx(,)g(the)h(sum)g(of)f(the)h(absolute)e (magnitudes)h(of)h(the)523 2638 y(elemen)n(ts)28 b(of)f(a)g(v)n(ector)g ([10]:)1649 2808 y(min)1666 2862 y Fk(w)q Fo(;b)1811 2808 y Fq(k)p Fp(w)q Fq(k)1965 2820 y Fw(1)2024 2808 y Fx(=)2112 2745 y Fl(P)2200 2766 y Fo(P)2200 2833 y(p)p Fw(=1)2336 2808 y Fq(j)p Fr(w)2418 2820 y Fo(p)2457 2808 y Fq(j)1425 2984 y Fx(sub)5 b(ject)28 b(to)g Fr(y)1857 2996 y Fo(n)1902 2984 y Fx(\()p Fp(w)2004 2954 y Fo(T)2057 2984 y Fp(x)2107 2996 y Fo(n)2171 2984 y Fq(\000)18 b Fr(b)p Fx(\))23 b Fq(\025)g Fx(0)1817 3109 y Fq(8)p Fr(n)f Fx(=)h Fq(f)p Fx(1)p Fr(;)14 b(:)g(:)g(:)f(;)h(N)9 b Fq(g)40 b Fr(:)826 b Fx(\(3\))523 3267 y(A)28 b(solution)f(to)h(\(3\))f (yields)h(the)g(desired)f(sparse)f(w)n(eigh)n(t)h(v)n(ector)f Fp(w)q Fx(.)648 3367 y(Optimisation)35 b(problem)g(\(3\))h(can)f(b)r(e) h(solv)n(ed)f(via)g(linear)g(programming)e([11].)i(The)523 3467 y(ensuing)24 b(form)n(ulation)f(requires)g(the)i(imp)r(osition)g (of)f(constrain)n(ts)f(on)h(the)h(allo)n(w)n(ed)e(ranges)523 3566 y(of)36 b(v)-5 b(ariables.)34 b(The)i(in)n(tro)r(duction)f(of)g (new)h(v)-5 b(ariables)34 b Fr(u)2344 3578 y Fo(p)2382 3566 y Fr(;)14 b(v)2459 3578 y Fo(p)2534 3566 y Fq(2)37 b Fn(R)2680 3536 y Fo(P)2777 3566 y Fx(suc)n(h)e(that)h Fq(j)p Fr(w)3242 3578 y Fo(p)3281 3566 y Fq(j)g Fx(=)523 3666 y Fr(u)571 3678 y Fo(p)628 3666 y Fx(+)19 b Fr(v)752 3678 y Fo(p)819 3666 y Fx(and)28 b Fr(w)1040 3678 y Fo(p)1103 3666 y Fx(=)c Fr(u)1240 3678 y Fo(p)1297 3666 y Fq(\000)19 b Fr(v)1421 3678 y Fo(p)1488 3666 y Fx(ensures)27 b(non-negativit)n(y) -7 b(.)27 b(The)i(range)e(of)h Fr(w)2901 3678 y Fo(p)2965 3666 y Fx(=)c Fr(u)3102 3678 y Fo(p)3158 3666 y Fq(\000)19 b Fr(v)3282 3678 y Fo(p)3349 3666 y Fx(is)523 3765 y(unconstrained)31 b(\(p)r(ositiv)n(e)h(or)f(negativ)n(e\))g(whilst)i Fr(u)2175 3777 y Fo(p)2245 3765 y Fx(and)f Fr(v)2451 3777 y Fo(p)2521 3765 y Fx(remain)g(non-negativ)n(e.)e Fr(u)3367 3777 y Fo(p)523 3865 y Fx(and)21 b Fr(v)718 3877 y Fo(p)778 3865 y Fx(are)f(designated)h(the)g(\\p)r(ositiv)n(e")f(and)h(\\negativ) n(e")e(parts)i(resp)r(ectiv)n(ely)-7 b(.)20 b(Similarly)-7 b(,)523 3965 y(the)31 b(bias)f Fr(b)h Fx(is)f(split)h(in)n(to)g(p)r (ositiv)n(e)f(and)h(negativ)n(e)e(comp)r(onen)n(ts)h Fr(b)e Fx(=)g Fr(b)2814 3977 y Fw(+)2889 3965 y Fq(\000)20 b Fr(b)3010 3977 y Fj(\000)3066 3965 y Fx(.)31 b(Giv)n(en)f(a)523 4064 y(solution)d(to)h(problem)f(\(3\),)h(either)f Fr(u)1702 4076 y Fo(p)1768 4064 y Fx(or)f Fr(v)1909 4076 y Fo(p)1976 4064 y Fx(will)h(b)r(e)h(non-zero)e(for)h(feature)h Fr(p)f Fx([11]:)1272 4237 y(min)1193 4291 y Fk(u)p Fo(;)p Fk(v)q Fo(;b)1345 4299 y Fi(+)1391 4291 y Fo(;b)1440 4299 y Fh(\000)1875 4174 y Fl(P)1963 4195 y Fo(P)1963 4261 y(p)p Fw(=1)2085 4237 y Fx(\()p Fr(u)2165 4249 y Fo(p)2222 4237 y Fx(+)18 b Fr(v)2345 4249 y Fo(p)2383 4237 y Fx(\))1127 4417 y(sub)5 b(ject)28 b(to)70 b Fr(y)1601 4429 y Fo(n)1645 4417 y Fx(\(\()p Fp(u)20 b Fq(\000)e Fp(v)q Fx(\))1948 4387 y Fo(T)2001 4417 y Fp(x)2051 4429 y Fo(n)2115 4417 y Fq(\000)g Fx(\()p Fr(b)2266 4429 y Fw(+)2339 4417 y Fq(\000)g Fr(b)2458 4429 y Fj(\000)2514 4417 y Fx(\)\))24 b Fq(\025)e Fx(1)1612 4542 y Fr(u)1660 4554 y Fo(p)1721 4542 y Fq(\025)h Fx(0;)14 b Fr(v)1928 4554 y Fo(p)1989 4542 y Fq(\025)22 b Fx(0;)14 b Fr(b)2191 4554 y Fw(+)2269 4542 y Fq(\025)22 b Fx(0;)14 b Fr(b)2471 4554 y Fj(\000)2549 4542 y Fq(\025)23 b Fx(0)1513 4666 y Fq(8)p Fr(n)f Fx(=)g Fq(f)p Fx(1)p Fr(;)14 b(:)g(:)g(:)f(;)h(N)9 b Fq(g)p Fx(;)14 b Fq(8)p Fr(p)21 b Fx(=)h Fq(f)p Fx(1)p Fr(;)14 b(:)g(:)g(:)f(;)h(P)e Fq(g)41 b Fr(:)521 b Fx(\(4\))523 4825 y(A)22 b(detailed)g(description)f(of)g(the)h(origins)f(of)g(the)h Fq(\025)h Fx(1)e(constrain)n(t)g(can)g(b)r(e)h(found)g(elsewhere)523 4924 y([30].)p eop %%Page: 4 4 4 3 bop 648 448 a Fx(If)24 b(the)h(data)e Fq(D)k Fx(are)c(not)h (linearly)f(separable,)g(misclassi\014cations)f(\(errors)g(in)j(the)f (class)523 548 y(lab)r(els)c Fr(y)790 560 y Fo(n)835 548 y Fx(\))h(can)f(b)r(e)h(accoun)n(ted)e(for)h(b)n(y)g(the)h(in)n (tro)r(duction)f(of)h(slac)n(k)e(v)-5 b(ariables)19 b Fr(\030)3010 560 y Fo(n)3056 548 y Fx(.)h(Problem)523 648 y(\(4\))28 b(can)f(b)r(e)h(recast)f(yielding)g(the)h(\014nal)f (optimisation)g(problem,)1228 844 y(min)1149 898 y Fk(u)p Fo(;)p Fk(v)q Fo(;b)1301 906 y Fi(+)1347 898 y Fo(;b)1396 906 y Fh(\000)1629 781 y Fl(P)1716 802 y Fo(P)1716 868 y(p)p Fw(=1)1839 844 y Fx(\()p Fr(u)1919 856 y Fo(p)1975 844 y Fx(+)18 b Fr(v)2098 856 y Fo(p)2137 844 y Fx(\))h(+)f Fr(C)2350 781 y Fl(P)2437 802 y Fo(N)2437 868 y(n)p Fw(=1)2580 844 y Fr(\030)2616 856 y Fo(n)1082 1024 y Fx(sub)5 b(ject)28 b(to)23 b Fr(y)1509 1036 y Fo(n)1554 1024 y Fx(\(\()p Fp(u)c Fq(\000)f Fp(v)q Fx(\))1856 994 y Fo(T)1909 1024 y Fp(x)1959 1036 y Fo(n)2023 1024 y Fq(\000)g Fx(\()p Fr(b)2174 1036 y Fw(+)2248 1024 y Fq(\000)g Fr(b)2367 1036 y Fj(\000)2423 1024 y Fx(\)\))23 b Fq(\025)g Fx(1)18 b Fq(\000)g Fr(\030)2777 1036 y Fo(n)1477 1149 y Fr(u)1525 1161 y Fo(p)1586 1149 y Fq(\025)k Fx(0;)14 b Fr(v)1792 1161 y Fo(p)1853 1149 y Fq(\025)23 b Fx(0;)14 b Fr(b)2056 1161 y Fw(+)2133 1149 y Fq(\025)23 b Fx(0;)14 b Fr(b)2336 1161 y Fj(\000)2414 1149 y Fq(\025)23 b Fx(0;)14 b Fr(\030)2617 1161 y Fo(n)2685 1149 y Fq(\025)22 b Fx(0)1513 1273 y Fq(8)p Fr(n)g Fx(=)g Fq(f)p Fx(1)p Fr(;)14 b(:)g(:)g(:)f(;)h(N)9 b Fq(g)p Fx(;)14 b Fq(8)p Fr(p)21 b Fx(=)h Fq(f)p Fx(1)p Fr(;)14 b(:)g(:)g(:)f(;)h(P)e Fq(g)41 b Fr(:)521 b Fx(\(5\))523 1458 y Fr(C)45 b Fx(is)38 b(an)g(adjustable)g(parameter)e(w)n(eighing)i (the)g(con)n(tribution)g(of)g(misclassi\014ed)f(data)523 1558 y(p)r(oin)n(ts.)30 b(Larger)e(v)-5 b(alues)30 b(lead)g(to)g(few)n (er)g(misclassi\014cations)e(b)r(eing)j(ignored:)e Fr(C)34 b Fx(=)27 b(0)i(cor-)523 1658 y(resp)r(onds)d(to)g(no)g(outliers)g(b)r (eing)g(ignored)f(whereas)g Fr(C)30 b Fq(!)23 b(1)j Fx(leads)g(to)g (the)h(hard)f(margin)523 1757 y(limit.)523 2029 y Ft(4)112 b(Computational,)36 b(soft)m(w)m(are)i(and)g(practical)e(issues)523 2234 y Fx(Learning)26 b(the)h(sparse)e(classi\014er)h(de\014ned)h(b)n (y)f(optimisation)h(problem)f(\(5\))h(in)n(v)n(olv)n(es)e(min-)523 2334 y(imising)34 b(a)g(linear)f(function)i(sub)5 b(ject)34 b(to)h(linear)e(constrain)n(ts.)g(E\016cien)n(t)h(algorithms)f(for)523 2434 y(solving)26 b(suc)n(h)g(linear)g(programming)e(problems)i(in)n(v) n(olving)g Fq(\030)p Fx(10,000)e(v)-5 b(ariables)25 b(\()p Fr(N)9 b Fx(\))27 b(and)523 2533 y Fq(\030)p Fx(10,000)g(constrain)n (ts)h(\()p Fr(P)12 b Fx(\))31 b(are)d(w)n(ell-kno)n(wn.)h(Standalone)g (op)r(en)h(source)e(co)r(des)i(include)523 2633 y Fg(lp)p 616 2633 27 4 v 31 w(solve)862 2603 y Fw(4)924 2633 y Fx(and)e Fg(PCx)1218 2603 y Fw(5)1254 2633 y Fx(.)648 2734 y(Nominal)j Fs(Liknon)f Fx(is)h(an)g(implemen)n(tation)g(of)g(the) h(sparse)d(classi\014er)h(\(5\).)i(It)f(incor-)523 2833 y(p)r(orates)24 b(routines)g(written)i(in)f(Matlab)1774 2803 y Fw(6)1836 2833 y Fx(and)f(a)h(system)g(utilising)g Fg(perl)2826 2803 y Fw(7)2887 2833 y Fx(and)f Fg(lp)p 3138 2833 V 31 w(solve)p Fx(.)523 2933 y(The)h(co)r(de)g(is)g(a)n(v)-5 b(ailable)24 b(from)h(the)g(authors)g(up)r(on)g(request.)f(The)i(input) g(consists)e(of)h(a)g(\014le)523 3032 y(con)n(taining)33 b(an)g Fr(N)e Fq(\002)22 b Fx(\()p Fr(P)35 b Fx(+)22 b(1\))33 b(data)g(matrix)h(in)f(whic)n(h)h(eac)n(h)f(ro)n(w)f(represen) n(ts)g(a)i(single)523 3132 y(pro\014ling)26 b(exp)r(erimen)n(t.)i(The)f (\014rst)g Fr(P)39 b Fx(columns)27 b(are)f(the)i(feature)f(v)-5 b(alues,)27 b(abundances)f(of)523 3232 y(molecular)33 b(sp)r(ecies,)h(whilst)h(column)f Fr(P)h Fx(+)23 b(1)34 b(is)g(the)h(class)e(lab)r(el)h Fr(y)2703 3244 y Fo(n)2783 3232 y Fq(2)g(f)p Fx(+1)p Fr(;)14 b Fq(\000)p Fx(1)p Fq(g)p Fx(.)32 b(The)523 3331 y(output)25 b(comprises)f(the)h(non-zero) e(v)-5 b(alues)25 b(of)g(the)g(w)n(eigh)n(t)f(v)n(ector)g Fp(w)i Fx(\(relev)-5 b(an)n(t)24 b(features\),)523 3431 y(the)k(bias)f Fr(b)g Fx(and)h(the)g(n)n(um)n(b)r(er)f(of)h(non-zero)e (slac)n(k)g(v)-5 b(ariables)26 b Fr(\030)2522 3443 y Fo(n)2568 3431 y Fx(.)648 3532 y(The)f(adjustable)g(parameter)e Fr(C)32 b Fx(in)25 b(problem)g(\(5\))g(can)g(b)r(e)g(set)g(using)g (cross)e(v)-5 b(alidation)523 3631 y(tec)n(hniques.)35 b(The)g(results)g(describ)r(ed)g(here)g(w)n(ere)f(obtained)h(b)n(y)g(c) n(ho)r(osing)e Fr(C)42 b Fx(=)36 b(0)p Fr(:)p Fx(5)e(or)523 3731 y Fr(C)29 b Fx(=)23 b(1.)523 4003 y Ft(5)112 b(Application)35 b(of)j(nominal)e(Liknon)i(to)f(real)f(w)m(orld)h(data)523 4208 y Fx(Nominal)30 b Fs(Liknon)e Fx(w)n(as)h(applied)h(to)f(\014v)n (e)h(data)f(sets)g(in)h(the)g(size)g(range)e(\()p Fr(N)39 b Fx(=)29 b(19,)g Fr(P)41 b Fx(=)523 4308 y(1,987\))22 b(to)i(\()p Fr(N)33 b Fx(=)23 b(200,)g Fr(P)36 b Fx(=)23 b(15,154\).)f(A)i(data)g(set)f Fq(D)k Fx(yielded)d(a)f(sparse)f (classi\014er,)h Fp(w)i Fx(and)523 4407 y Fr(b)p Fx(,)20 b(and)g(a)f(sp)r(eci\014cation)h(of)g(the)g Fr(l)i Fx(relev)-5 b(an)n(t)19 b(features)g(\()p Fr(P)35 b Fq(\035)23 b Fr(l)r Fx(\).)d(Since)g(the)h(pro\014ling)e(studies)523 4507 y(pro)r(duced)26 b(only)g(a)g(small)f(n)n(um)n(b)r(er)h(of)h(data) e(p)r(oin)n(ts)i(\()p Fr(N)32 b Fq(\034)23 b Fr(P)12 b Fx(\),)26 b(the)h(generalisation)d(error)p 523 4565 473 4 v 546 4619 a Fv(4)606 4650 y Ff(http://www.netlib.org/ampl/so)q (lver)q(s/lps)q(olve)q(/)546 4710 y Fv(5)606 4742 y Ff(http://www-)t (fp.mcs.anl.gov/ot)q(c/Too)q(ls/P)q(Cx/)546 4801 y Fv(6)606 4833 y Ff(http://www.mathworks.com)546 4893 y Fv(7)606 4924 y Ff(http://www.perl.org/)p eop %%Page: 5 5 5 4 bop 523 448 a Fx(of)29 b(a)f(nominal)g Fs(Liknon)g Fx(classi\014er)f(w)n(as)h(determined)h(b)n(y)f(computing)h(the)g(lea)n (v)n(e-one-out)523 548 y(error)c(for)i Fr(l)r Fx(-dimensional)f(data)h (p)r(oin)n(ts.)g(A)g(classi\014er)f(trained)h(using)g Fr(N)f Fq(\000)18 b Fx(1)26 b(data)h(p)r(oin)n(ts)523 648 y(w)n(as)d(used)h(to)f(predict)h(the)g(class)f(of)h(the)g(withheld) h(data)e(p)r(oin)n(t;)h(the)h(pro)r(cedure)d(rep)r(eated)523 747 y Fr(N)36 b Fx(times.)28 b(The)g(results)f(are)g(sho)n(wn)g(in)g(T) -7 b(able)28 b(1.)648 847 y(Nominal)39 b Fs(Liknon)f Fx(p)r(erforms)h(w)n(ell)g(in)h(terms)f(of)g(sim)n(ultaneous)g(relev)-5 b(an)n(t)38 b(feature)523 947 y(iden)n(ti\014cation)29 b(and)h(classi\014cation.)e(In)i(all)f(\014v)n(e)g(transcript)g(and)h (protein)f(pro\014ling)f(data)523 1047 y(sets)e(a)g(h)n(yp)r(erplane)f (w)n(as)g(found,)i(the)g(w)n(eigh)n(t)e(v)n(ector)g(w)n(as)g(sparse)g (\()p Fr(<)e Fx(100)i(or)g Fr(<)e Fx(2\045)i(non-)523 1146 y(zero)30 b(comp)r(onen)n(ts\))i(and)f(the)h(relev)-5 b(an)n(t)30 b(features)h(w)n(ere)g(of)g(in)n(terest)g(to)g(domain)g (exp)r(erts)523 1246 y(\(they)26 b(generated)e(no)n(v)n(el)g (biological)f(h)n(yp)r(otheses)i(amenable)g(to)g(subsequen)n(t)f(exp)r (erimen-)523 1346 y(tal)30 b(or)g(clinical)g(v)-5 b(alidation\).)30 b(F)-7 b(or)30 b(the)g(protein)g(pro\014les,)g(b)r(etter)g(results)g(w) n(ere)f(obtained)523 1445 y(using)f(normalised)g(as)g(opp)r(osed)g(to)h (ra)n(w)e(v)-5 b(alues:)29 b(when)g(emplo)n(y)n(ed)e(to)i(predict)g (the)g(class)523 1545 y(of)f(16)f(indep)r(enden)n(t)i(non-cancer)d (samples,)i(the)g(51)f(relev)-5 b(an)n(t)28 b(features)f(had)h(a)g (test)g(error)523 1644 y(of)g(0)f(out)g(of)h(16.)648 1745 y(On)35 b(a)f(p)r(o)n(w)n(erful)h(desktop)g(computer,)g(a)g Fr(>)g Fx(1)g(GHz)g(In)n(tel-lik)n(e)g(mac)n(hine,)g(the)g(time)523 1844 y(required)e(to)g(create)f(a)h(sparse)f(classi\014er)h(v)-5 b(aried)32 b(from)h(2)g(seconds)g(to)g(20)g(min)n(utes.)h(F)-7 b(or)523 1944 y(the)24 b(larger)e(problems,)h(the)h(main)f(memory)g (RAM)h(requiremen)n(t)f(exceeded)g(500)f(MBytes.)523 2213 y Ft(6)112 b(Heuristic)41 b(solutions)h(to)h(problems)f(p)s(osed)i (b)m(y)f(domain)691 2329 y(exp)s(erts)523 2531 y Fx(Domain)37 b(exp)r(erts)g(wish)h(to)f(p)r(ostpro)r(cess)f(nominal)h Fs(Liknon)g Fx(results)f(to)i(assist)e(in)i(the)523 2631 y(design)31 b(of)g(subsequen)n(t)g(exp)r(erimen)n(ts)g(aimed)g(at)h(v) -5 b(alidating,)31 b(v)n(erifying)f(and)h(extending)523 2731 y(an)n(y)25 b(biological)f(predictions.)i(In)g(lieu)g(of)g(a)f (theoretically)g(sound)g(statistical)h(framew)n(ork,)523 2830 y(heuristics)34 b(ha)n(v)n(e)f(b)r(een)h(dev)n(elop)r(ed)g(to)g (prioritise,)f(reduce)h(or)f(increase)g(the)h(n)n(um)n(b)r(er)g(of)523 2930 y(relev)-5 b(an)n(t)27 b(features.)648 3030 y(In)34 b(order)f(to)h(prioritise)f(features,)g(assume)g(that)i(all)f Fr(P)46 b Fx(features)33 b(are)g(on)h(the)h(same)523 3130 y(scale.)26 b(The)i Fr(l)g Fx(relev)-5 b(an)n(t)26 b(features)h(can)g(b)r(e)g(rank)n(ed)f(according)f(to)i(the)h (magnitude)f(and/or)523 3229 y(sign)32 b(of)h(the)g(non-zero)e(elemen)n (ts)i(of)f(the)h(w)n(eigh)n(t)f(v)n(ector)g Fp(w)i Fx(\()p Fr(w)2598 3241 y Fo(p)2668 3229 y Fq(6)p Fx(=)d(0\).)i(T)-7 b(o)32 b(reduce)h(the)523 3329 y(n)n(um)n(b)r(er)28 b(of)g(relev)-5 b(an)n(t)27 b(features)h(to)g(a)g(\\smaller,)f(most)g(in)n(teresting")g (set,)i(a)e(histogram)g(of)523 3429 y Fr(w)582 3441 y Fo(p)644 3429 y Fq(6)p Fx(=)c(0)g(v)-5 b(alues)24 b(can)g(b)r(e)h(used) f(to)g(determine)h(a)e(threshold)h(for)g(pruning)g(the)h(set.)f(In)g (order)523 3528 y(to)31 b(increase)f(the)h(n)n(um)n(b)r(er)g(of)g (features)g(to)g(a)f(\\larger,)f(more)h(in)n(teresting")g(set,)h (nominal)523 3628 y Fs(Liknon)c Fx(can)g(b)r(e)i(run)e(in)h(an)g (iterativ)n(e)f(manner.)g(The)h Fr(l)h Fx(relev)-5 b(an)n(t)27 b(features)g(iden)n(ti\014ed)i(in)523 3728 y(one)24 b(pass)g(through)g (the)h(data)g(are)e(remo)n(v)n(ed)g(from)i(the)g(data)f(p)r(oin)n(ts)h (to)f(b)r(e)h(used)g(as)f(input)523 3827 y(for)f(the)g(next)g(pass.)f (Eac)n(h)g(successiv)n(e)g(round)g(generates)g(a)g(new)h(set)g(of)g (relev)-5 b(an)n(t)23 b(features.)523 3927 y(The)29 b(pro)r(cedure)e (is)i(terminated)g(either)f(b)n(y)h(the)g(domain)f(exp)r(ert)h(or)f(b)n (y)g(monitoring)g(the)523 4026 y(lea)n(v)n(e-one-out)c(error)g(of)i (the)h(classi\014er)e(asso)r(ciated)g(with)i(eac)n(h)e(set)i(of)f (relev)-5 b(an)n(t)26 b(features.)648 4127 y(Preliminary)16 b(results)i(from)g(analysis)f(of)h(the)h(gastroin)n(testinal)e(stromal) g(tumour/spindle)523 4226 y(cell)25 b(tumour)g(transcript)f (pro\014ling)h(data)f(set)h(indicate)g(that)h(these)f(extensions)f(are) h(lik)n(ely)523 4326 y(to)20 b(b)r(e)g(of)f(utilit)n(y)i(to)e(domain)h (exp)r(erts.)f(The)h(lea)n(v)n(e-one-out)d(error)h(of)h(the)i(relev)-5 b(an)n(t)19 b(features)523 4426 y(iden)n(ti\014ed)24 b(b)n(y)f(\014v)n(e)g(iterations)f(of)i(nominal)f Fs(Liknon)f Fx(w)n(as)h(at)g(most)g(one.)g(The)h(details)f(are:)523 4525 y(iteration)k(0)g(\(n)n(um)n(b)r(er)h(of)g(relev)-5 b(an)n(t)27 b(features)g(=)g(6,)h(lea)n(v)n(e-one-out)d(error)h(=)h (0\),)h(iteration)523 4625 y(1)g(\(5,)g(0\),)g(iteration)g(2)g(\(5,)g (1\),)g(iteration)g(3)g(\(9,)g(0\),)g(iteration)g(4)g(\(13,)g(1\),)g (iteration)g(5)g(\(11,)523 4724 y(1\).)648 4825 y(Iterativ)n(e)18 b Fs(Liknon)g Fx(ma)n(y)h(pro)n(v)n(e)e(useful)i(during)g(explorations) f(of)h(the)g(\(qualitativ)n(e\))g(as-)523 4924 y(so)r(ciation)f(b)r(et) 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y(tion)i(b)n(y)g(high-throughput)f(exp)r(erimen)n(tal)g(tec)n (hnologies.)g(\(ii\))h(Systematic)g(form)n(ulation)523 3764 y(and)22 b(extraction)g(of)h(large)e(n)n(um)n(b)r(ers)h(of)h (features)f(from)g(data)g(that)h(ma)n(y)f(b)r(e)h(in)g(the)g(form)f(of) 523 3864 y(strings,)j(images,)g(and)h(so)f(on)h(\()p Fm(a)j(priori)p Fx(,)e(features)f(\\relev)-5 b(an)n(t")24 b(for)h(one)h(problem)f(ma)n(y)h(b)r(e)523 3964 y(\\irrelev)-5 b(an)n(t")23 b(for)h(another\).)h(B.)g(En)n(unciate)f(sparse)g (solutions)g(for)g(classi\014cation)g(and)h(re-)523 4063 y(gression)d(problems)g(in)i(high-dimensions.)e(C.)i(Construct)f(and)g (assess)f(mo)r(dels.)h(\(i\))h(Learn)523 4163 y(a)g(v)-5 b(ariet)n(y)24 b(of)g(mo)r(dels)g(b)n(y)g(a)g(grid)g(searc)n(h)f (through)h(the)g(space)g(of)g(adjustable)h(parameters.)523 4263 y(\(ii\))i(Ev)-5 b(aluate)25 b(the)h(generalisation)e(error)g(of)i (eac)n(h)f(mo)r(del.)i(D.)f(Com)n(bine)g(b)r(est)g(mo)r(dels)g(to)523 4362 y(create)h(a)g(\014nal)g(decision)h(function.)g(E.)f(Prop)r(ose)f (h)n(yp)r(otheses)h(for)g(domain)g(exp)r(ert.)523 4627 y Ft(9)112 b(Ac)m(kno)m(wledgemen)m(ts)523 4825 y Fx(This)41 b(w)n(ork)e(w)n(as)g(supp)r(orted)h(b)n(y)h(NSF)g(gran)n(t)e(I)r (IS-9988642,)e(the)k(Director,)f(O\016ce)g(of)523 4924 y(Energy)h(Researc)n(h,)h(O\016ce)g(of)h(Health)g(and)f(En)n(vironmen)n (tal)f(Researc)n(h,)g(Division)i(of)p eop %%Page: 8 8 8 7 bop 523 448 a Fx(the)38 b(U.S.)h(Departmen)n(t)e(of)h(Energy)e (under)i(Con)n(tract)f(No.)g(DE-A)n(C03-76F00098)c(and)523 548 y(an)c(LBNL/LDRD)g(through)g(U.S.)g(Departmen)n(t)g(of)g(Energy)f (Con)n(tract)g(No.)h(DE-A)n(C03-)523 648 y(76SF00098.)p eop %%Page: 9 9 9 8 bop 523 448 a Ft(References)561 612 y Fu(1.)43 b(S.V.)25 b(Allander,)i(N.N.)e(Nupp)r(onen,)g(M.)h(Ringner,)g(G.)g(Hostetter,)h (G.W.)f(Maher,)h(N.)f(Gold-)663 703 y(b)r(erger,)j(Y.)f(Chen,)g (Carpten)g(J.,)h(A.G.)g(Elk)l(ahloun,)f(and)g(P)-6 b(.S.)28 b(Meltzer.)43 b(Gastroin)n(testinal)663 795 y(Stromal)25 b(T)-6 b(umors)25 b(with)h(KIT)f(m)n(utations)g(exhibit)g(a)h(remark)l (ably)e(homogeneous)i(gene)g(ex-)663 886 y(pression)g(pro\014le.)35 b Fa(Canc)l(er)28 b(R)l(ese)l(ar)l(ch)p Fu(,)g(61:8624{8628,)j(2001.) 561 972 y(2.)43 b(K.)26 b(Bennett)h(and)f(A.)g(Demiriz.)37 b(Semi-sup)r(ervised)25 b(supp)r(ort)h(v)n(ector)h(mac)n(hines.)36 b(In)26 b Fa(Neur)l(al)663 1063 y(and)c(Information)h(Pr)l(o)l(c)l (essing)h(Systems)p Fu(,)e(v)n(olume)d(11.)i(MIT)f(Press,)i(Cam)n (bridge)e(MA,)g(1999.)561 1149 y(3.)43 b(A.)24 b(Bhattac)n(harjee,)j (W.G.)e(Ric)n(hards,)g(J.)g(Staun)n(ton,)f(C.)h(Li,)h(S.)e(Mon)n(ti,)i (P)-6 b(.)24 b(V)-6 b(asa,)26 b(C.)f(Ladd,)663 1240 y(J.)k(Behesh)n (ti,)f(R.)g(Bueno,)h(M.)g(Gillette,)g(M.)g(Lo)r(da,)g(G.)g(W)-6 b(eb)r(er,)28 b(E.J.)h(Mark,)g(E.S.)g(Lander,)663 1332 y(W.)g(W)-6 b(ong,)30 b(B.E.)g(Johnson,)h(T.R.)f(Golub,)f(D.J.)i (Sugarbak)n(er,)e(and)g(M.)h(Mey)n(erson.)46 b(Clas-)663 1423 y(si\014cation)29 b(of)f(h)n(uman)f(lung)h(carcinomas)g(b)n(y)f (mrna)g(expression)i(pro\014ling)f(rev)n(eals)h(distinct)663 1514 y(adeno)r(carcinoma)d(sub)r(classes.)36 b Fa(Pr)l(o)l(c.)28 b(Natl.)f(A)l(c)l(ad.)h(Sci.)p Fu(,)e(98:13790{13795,)31 b(2001.)561 1600 y(4.)43 b(C.)38 b(Bhattac)n(haryy)n(a,)g(L.R.)f (Grate,)i(A.)e(Rizki,)h(D.C.)g(Radisky)-6 b(,)37 b(F.J.)i(Molina,)g (M.I.)f(Jor-)663 1691 y(dan,)26 b(M.J.)i(Bissell,)h(and)d(I.S.)h(Mian.) 37 b(Sim)n(ultaneous)26 b(relev)l(an)n(t)g(feature)h(iden)n (ti\014cation)g(and)663 1783 y(classi\014cation)32 b(in)f (high-dimensional)f(spaces:)i(application)g(to)e(molecular)h (pro\014ling)g(data.)663 1874 y Fa(Submitte)l(d,)d(Signal)f(Pr)l(o)l(c) l(essing)p Fu(,)h(2002.)561 1960 y(5.)43 b(M.P)-6 b(.)41 b(Bro)n(wn,)h(W.N.)f(Grundy)-6 b(,)39 b(D.)i(Lin,)f(N.)h(Cristianini,)i (C.W.)e(Sugnet,)g(T.S.)g(F)-6 b(urey)g(,)663 2051 y(M.)20 b(Ares,)g(Jr,)h(and)f(D.)f(Haussler.)26 b(Kno)n(wledge-based)21 b(analysis)g(of)f(microarra)n(y)g(gene)g(expres-)663 2143 y(sion)30 b(data)h(b)n(y)e(using)h(supp)r(ort)g(v)n(ector)g(mac)n (hines.)47 b Fa(Pr)l(o)l(c.)33 b(Natl.)e(A)l(c)l(ad.)h(Sci.)p Fu(,)e(97:262{267,)663 2234 y(2000.)561 2320 y(6.)43 b(P)-6 b(.)26 b(Cheeseman)f(and)h(J.)h(Stutz.)34 b(Ba)n(y)n(esian)27 b(Classi\014cation)h(\(AutoClass\):)f(Theory)f(and)g(Re-)663 2411 y(sults.)42 b(In)28 b(U.M.)g(F)-6 b(a)n(yy)n(ad,)28 b(G.)g(Piatetsky-Shapiro,)h(P)-6 b(.)28 b(Sm)n(yth,)e(and)i(R.)g(Uth)n (urusam)n(y)-6 b(,)26 b(ed-)663 2502 y(itors,)k Fa(A)l(dvanc)l(es)i(in) f(Know)t(le)l(dge)g(Disc)l(overy)h(and)f(Data)h(Mining)p Fu(,)c(pages)i(153{180.)i(AAAI)663 2594 y(Press/MIT)g(Press,)g(1995.)51 b(The)31 b(soft)n(w)n(are)i(is)e(a)n(v)l(ailable)h(at)e(the)h(URL)f Ff(http://www.gnu.)663 2685 y(org/directory/autoclass.html)p Fu(.)561 2771 y(7.)43 b(M.L.)28 b(Cho)n(w,)h(E.J.)g(Moler,)g(and)f (I.S.)f(Mian.)41 b(Iden)n(tifying)28 b(mark)n(er)e(genes)j(in)e (transcription)663 2862 y(pro\014le)e(data)h(using)g(a)g(mixture)e(of)i (feature)g(relev)l(ance)g(exp)r(erts.)34 b Fa(Physiolo)l(gic)l(al)28 b(Genomics)p Fu(,)663 2954 y(5:99{111,)h(2001.)561 3039 y(8.)43 b(N.)31 b(Cristianini)j(and)d(J.)i(Sha)n(w)n(e-T)-6 b(a)n(ylor.)53 b Fa(Supp)l(ort)35 b(V)-6 b(e)l(ctor)34 b(Machines)g(and)g(other)h(kernel-)663 3131 y(b)l(ase)l(d)29 b(le)l(arning)f(metho)l(ds)p Fu(.)36 b(Cam)n(bridge)25 b(Univ)n(ersit)n(y)g(Press,)i(Cam)n(bridge,)f(England,)g(2000.)561 3217 y(9.)43 b(S.M.)35 b(Dhanasek)l(aran,)h(T.R.)f(Barrette,)h(R.)f (Ghosh,)h(D.)e(Shah,)h(S.)g(V)-6 b(aram)n(bally)g(,)34 b(K.)h(Ku-)663 3308 y(rac)n(hi,)30 b(K.J.)f(Pien)n(ta,)h(M.J.)h(Rubin,) d(and)h(A.M.)h(Chinnaiy)n(an.)45 b(Delineation)30 b(of)g(prognostic)663 3399 y(biomark)n(ers)25 b(in)h(prostate)g(cancer.)35 b Fa(Natur)l(e)p Fu(,)27 b(432,)g(2001.)523 3485 y(10.)43 b(D.L.)26 b(Donoho)g(and)f(X.)h(Huo.)34 b(Uncertain)n(t)n(y)24 b(principles)j(and)e(idea)h(atomic)g(decomp)r(osition.)663 3576 y(T)-6 b(ec)n(hnical)26 b(Rep)r(ort,)g(Statistics)g(Departmen)n (t,)f(Stanford)g(Univ)n(ersit)n(y)-6 b(,)25 b(1999.)523 3662 y(11.)43 b(R.)29 b(Fletc)n(her.)44 b Fa(Pr)l(actic)l(al)32 b(Metho)l(ds)g(in)e(Optimization)p Fu(.)45 b(John)29 b(Wiley)g(&)g(Sons,)g(New)g(Y)-6 b(ork,)663 3754 y(2000.)523 3839 y(12.)43 b(T.)27 b(F)-6 b(urey)g(,)25 b(N.)h(Cristianini,)j(N.)d (Du\013y)-6 b(,)25 b(D.)h(Bednarski,)h(M.)g(Sc)n(h)n(ummer,)d(and)i(D.) g(Haussler.)663 3931 y(Supp)r(ort)20 b(v)n(ector)h(mac)n(hine)g (classi\014cation)i(and)e(v)l(alidation)h(of)g(cancer)g(tissue)g (samples)g(using)663 4022 y(microarra)n(y)j(expression)i(data.)34 b Fa(Bioinformatics)p Fu(,)26 b(16:906{914,)k(2000.)523 4108 y(13.)43 b(M.E.)66 b(Garb)r(er,)f(O.G.)h(T)-6 b(ro)n(y)n(ansk)l(a) n(y)n(a,)64 b(K.)h(Sc)n(hluens,)f(S.)h(P)n(etersen,)g(Z.)g(Thaesler,) 663 4199 y(M.)32 b(P)n(acy)n(ana-Gengelbac)n(h,)g(M.)g(v)l(an)e(de)h (Rijn,)h(G.D.)f(Rosen,)h(C.M.)h(P)n(erou,)f(R.I.)f(Wh)n(yte,)663 4291 y(R.B.)k(Altman,)g(P)-6 b(.O.)35 b(Bro)n(wn,)h(D.)g(Botstein,)g (and)f(I.)g(P)n(etersen.)63 b(Div)n(ersit)n(y)35 b(of)h(gene)g(ex-)663 4382 y(pression)30 b(in)g(adeno)r(carcinoma)h(of)f(the)g(lung.)47 b Fa(Pr)l(o)l(c.)32 b(Natl.)f(A)l(c)l(ad.)h(Sci.)p Fu(,)d (98:13784{13789,)663 4473 y(2001.)523 4559 y(14.)43 b(T.R.)d(Golub,)f (D.K.)h(Slonim,)f(P)-6 b(.)39 b(T)-6 b(ama)n(y)n(o,)39 b(C.)h(Huard,)f(M.)h(Gaasen)n(b)r(eek,)h(J.)f(Mesiro)n(v,)663 4650 y(H.)d(Coller,)j(M.L.)e(Loh,)g(J.R.)g(Do)n(wning,)g(M.A.)h (Caligiuri,)h(C.D.)e(Blo)r(omfeld,)h(and)e(E.S.)663 4742 y(Lander.)32 b(Molecular)27 b(classi\014cation)g(of)e(cancer:)h(Class)g (disco)n(v)n(ery)f(and)f(class)i(prediction)f(b)n(y)663 4833 y(gene)e(expression)h(monitoring.)31 b Fa(Scienc)l(e)p Fu(,)25 b(286:531{537,)j(1999.)k(The)24 b(data)f(are)h(a)n(v)l(ailable) h(at)663 4924 y(the)g(URL)g Ff(waldo.wi.mit.edu/MPR/data_sets.)q(html)q Fu(.)p eop %%Page: 10 10 10 9 bop 523 448 a Fu(15.)43 b(T.)20 b(Graep)r(el,)h(B.)f(Herbric)n(h,) g(R.)f(Sc)n(h\177)-38 b(olk)n(opf,)20 b(A.J.)g(Smola,)g(P)-6 b(.)20 b(Bartlett,)h(K.)e(M)r(\177)-41 b(uller,)22 b(K.)e(Ob)r(er-)663 540 y(ma)n(y)n(er,)e(and)i(R.C.)g(Williamson.)25 b(Classi\014cation)e (on)c(pro)n(ximit)n(y)f(data)i(with)g(lp-mac)n(hines.)k(In)663 631 y Fa(Ninth)29 b(International)i(Confer)l(enc)l(e)g(on)e(A)n (rti\014cial)h(Neur)l(al)g(Networks)p Fu(,)f(v)n(olume)e(470,)i(pages) 663 722 y(304{309.)f(IEE,)f(London,)e(1999.)523 821 y(16.)43 b(L.R.)26 b(Grate,)h(C.)f(Bhattac)n(haryy)n(a,)g(M.I.)h(Jordan,)g(and)e (I.S.)h(Mian.)36 b(In)n(tegrated)26 b(analysis)h(of)663 912 y(transcript)33 b(pro\014ling)g(and)f(protein)h(sequence)f(data.)55 b Fa(In)34 b(pr)l(ess,)h(Me)l(chanisms)g(of)e(A)l(geing)663 1003 y(and)28 b(Development)p Fu(,)f(2002.)523 1102 y(17.)43 b(T.)26 b(Hastie,)h(R.)e(Tibshirani,)j(,)e(and)f(F)-6 b(riedman)25 b(J.)35 b Fa(The)28 b(Elements)g(of)f(Statistic)l(al)i(L)l (e)l(arning:)663 1193 y(Data)f(Mining,)e(Infer)l(enc)l(e,)i(and)g(Pr)l (e)l(diction)p Fu(.)36 b(Springer-V)-6 b(erlag,)26 b(New)g(Y)-6 b(ork,)25 b(2000.)523 1292 y(18.)43 b(I.)49 b(Hedenfalk,)h(D.)g (Duggan,)g(Y.)f(Chen,)h(M.)h(Radmac)n(her,)d(M.)j(Bittner,)f(R.)g (Simon,)663 1383 y(P)-6 b(.)47 b(Meltzer,)h(B.)f(Gusterson,)h(M.)g (Esteller,)g(M.)g(Ra\013eld,)f(Z.)g(Y)-6 b(akhini,)46 b(A.)h(Ben-Dor,)663 1474 y(E.)26 b(Doughert)n(y)-6 b(,)24 b(J.)j(Kononen,)e(L.)h(Bub)r(endorf,)g(W.)f(F)-6 b(ehrle,)26 b(S.)g(Pittaluga,)h(S.)f(Gruvb)r(erger,)663 1566 y(N.)k(Loman,)g(O.)g (Johannsson,)i(H.)e(Olsson,)i(B.)f(Wilfond,)g(G.)g(Sauter,)f(O.-P)-6 b(.)31 b(Kallioniemi,)663 1657 y(A.)c(Borg,)h(and)f(J.)h(T)-6 b(ren)n(t.)38 b(Gene-expression)27 b(pro\014les)h(in)e(hereditary)h (breast)h(cancer.)39 b Fa(New)663 1748 y(England)28 b(Journal)g(of)f (Me)l(dicine)p Fu(,)f(344:539{548,)k(2001.)523 1847 y(19.)43 b(J.)18 b(Khan,)g(J.S.)h(W)-6 b(ei,)18 b(M.)h(Ringner,)f(L.H.)g(Saal,)h (M.)f(Ladan)n(yi,)g(F.)h(W)-6 b(estermann,)17 b(F.)h(Berthold,)663 1938 y(M.)35 b(Sc)n(h)n(w)n(ab,)f(An)n(tonescu)f(C.R.,)i(P)n(eterson)g (C.,)g(and)f(P)-6 b(.S.)35 b(Meltzer.)60 b(Classi\014cation)37 b(and)663 2029 y(diagnostic)22 b(prediction)e(of)i(cancers)f(using)g (gene)g(expression)g(pro\014ling)g(and)f(arti\014cial)i(neural)663 2121 y(net)n(w)n(orks.)34 b Fa(Natur)l(e)29 b(Me)l(dicine)p Fu(,)d(7:673{679,)k(2001.)523 2219 y(20.)43 b(G.)26 b(Lanc)n(k)n(erit,) g(L.)g(El)g(Ghaoui,)h(C.)f(Bhattac)n(haryy)n(a,)g(and)f(M.I.)i(Jordan.) 35 b(Minimax)25 b(proba-)663 2310 y(bilit)n(y)g(mac)n(hine.)34 b Fa(A)l(dvanc)l(es)29 b(in)e(Neur)l(al)h(Pr)l(o)l(c)l(essing)i (systems)p Fu(,)e(14,)e(2001.)523 2409 y(21.)43 b(L.A.)37 b(Liotta,)i(E.C.)f(Kohn,)f(and)g(E.F.)h(P)n(erticoin.)71 b(Clinical)39 b(proteomics.)f(p)r(ersonalized)663 2500 y(molecular)26 b(medicine.)34 b Fa(JAMA)p Fu(,)26 b(14:2211{2214,)k (2001.)523 2599 y(22.)43 b(E.J.)32 b(Moler,)g(M.L.)g(Cho)n(w,)g(and)e (I.S.)h(Mian.)50 b(Analysis)31 b(of)h(molecular)f(pro\014le)g(data)g (using)663 2690 y(generativ)n(e)26 b(and)f(discriminativ)n(e)h(metho)r (ds.)33 b Fa(Physiolo)l(gic)l(al)28 b(Genomics)p Fu(,)f(4:109{126,)i (2000.)523 2788 y(23.)43 b(D.A.)18 b(Notterman,)f(U.)h(Alon,)h(A.J.)g (Sierk,)f(and)g(A.J.)h(Levine.)j(T)-6 b(ranscriptional)20 b(gene)e(expres-)663 2880 y(sion)27 b(pro\014les)h(of)f(colorectal)i (adenoma,)e(adeno)r(carcinoma,)h(and)f(normal)g(tissue)g(examined)663 2971 y(b)n(y)d(oligon)n(ucleotide)k(arra)n(ys.)35 b Fa(Canc)l(er)29 b(R)l(ese)l(ar)l(ch)p Fu(,)f(61:3124{3130,)i(2001.)523 3069 y(24.)43 b(E.F.)22 b(P)n(etricoin)g(I)r(I)r(I,)e(A.M.)i(Ardek)l (ani,)f(B.A.)g(Hitt,)g(P)-6 b(.J.)22 b(Levine,)f(V.A.)g(F)-6 b(usaro,)22 b(S.M.)g(Stein-)663 3161 y(b)r(erg,)30 b(G.B)h(Mills,)g(C.) g(Simone,)e(D.A.)h(Fishman,)f(E.C.)i(Kohn,)f(and)f(L.A.)h(Liotta.)47 b(Use)30 b(of)663 3252 y(proteomic)c(patterns)f(in)h(serum)f(to)h(iden) n(tify)g(o)n(v)l(arian)h(cancer.)35 b Fa(The)28 b(L)l(anc)l(et)p Fu(,)g(359:572{577,)663 3343 y(2002.)523 3442 y(25.)43 b(S.)35 b(Ramasw)n(am)n(y)-6 b(,)35 b(P)-6 b(.)36 b(T)-6 b(ama)n(y)n(o,)35 b(R.)h(Rifkin,)g(S.)f(Mukherjee,)i(C.-H.)f(Y)-6 b(eang,)36 b(M.)g(Angelo,)663 3533 y(C.)18 b(Ladd,)g(M.)h(Reic)n(h,)f (E.)g(Latulipp)r(e,)h(J.P)-6 b(.)19 b(Mesiro)n(v,)g(T.)f(P)n(oggio,)j (W.)d(Gerald,)h(M.)g(Lo)r(da,)f(E.S.)663 3624 y(Lander,)24 b(and)g(T.R.)h(Golub.)32 b(Multiclass)26 b(cancer)f(diagnosis)g(using)g (tumor)e(gene)h(expression)663 3716 y(signatures.)44 b Fa(Pr)l(o)l(c.)31 b(Natl.)f(A)l(c)l(ad.)g(Sci.)p Fu(,)f (98:15149{15154,)34 b(2001.)45 b(The)29 b(data)g(are)g(a)n(v)l(ailable) 663 3807 y(from)c Ff(http://www-)t(genome.wi.mit.edu)q(/mpr)q(/GCM)q (.html)q Fu(.)523 3906 y(26.)43 b(A.)20 b(Smola,)h(T.T.)h(F)-6 b(riess,)22 b(and)e(B.)h(Sc)n(h\177)-38 b(olk)n(opf.)26 b(Semiparametric)20 b(supp)r(ort)g(v)n(ector)h(and)f(linear)663 3997 y(programming)e(mac)n(hines.)k(In)c Fa(Neur)l(al)k(and)f (Information)h(Pr)l(o)l(c)l(essing)h(Systems)p Fu(,)d(v)n(olume)e(11.) 663 4088 y(MIT)26 b(Press,)h(Cam)n(bridge)e(MA,)h(1999.)523 4187 y(27.)43 b(T.)32 b(Sorlie,)g(C.M.)g(P)n(erou,)g(R.)f(Tibshirani,)i (T.)f(Aas,)f(S.)g(Geisler,)i(H.)e(Johnsen,)h(T.)g(Hastie,)663 4278 y(M.B.)26 b(Eisen,)h(M.)f(v)l(an)f(de)g(Rijn,)h(S.S.)f(Je\013rey) -6 b(,)25 b(T.)i(Thorsen,)f(H.)f(Quist,)h(J.C.)h(Matese,)g(P)-6 b(.O.)663 4369 y(Bro)n(wn,)24 b(D.)f(Botstein,)i(P)-6 b(.E.)24 b(Lonning,)g(and)f(A.-L.)g(Borresen-Dale.)32 b(Gene)24 b(expression)f(pat-)663 4461 y(terns)h(of)h(breast)g (carcinomas)h(distinguish)e(tumor)g(sub)r(classes)i(with)f(clinical)h (implications.)663 4552 y Fa(Pr)l(o)l(c.)i(Natl.)f(A)l(c)l(ad.)h(Sci.)p Fu(,)d(98:10869{10874,)32 b(2001.)523 4650 y(28.)43 b(A.I.)20 b(Su,)g(J.B.)h(W)-6 b(elsh,)21 b(L.M.)g(Sapinoso,)g(S.G.)g(Kern,)f(P)-6 b(.)21 b(Dimitro)n(v,)e(H.)h(Lapp,)g(P)-6 b(.G.)21 b(Sc)n(h)n(ultz,)663 4742 y(S.M.)36 b(P)n(o)n(w)n(ell,)h(C.A.)e(Mosk)l(aluk,)h(H.F.)g(F)-6 b(rierson)35 b(Jr,)h(and)f(G.M.)i(Hampton.)61 b(Molecular)663 4833 y(classi\014cation)32 b(of)f(h)n(uman)d(carcinomas)j(b)n(y)e(use)h (of)h(gene)f(expression)h(signatures.)49 b Fa(Canc)l(er)663 4924 y(R)l(ese)l(ar)l(ch)p Fu(,)28 b(61:7388{7393,)i(2001.)p eop %%Page: 11 11 11 10 bop 523 448 a Fu(29.)43 b(L.J.)30 b(v)l(an)e('t)i(V)-6 b(eer,)29 b(H.)g(Dai,)g(M.J.)i(v)l(an)d(de)h(Vijv)n(er,)h(Y.D.)f(He,)g (A.A.)g(Hart,)g(M.)h(Mao,)h(H.L.)663 540 y(P)n(eterse,)36 b(v)l(an)e(der)h(Ko)r(o)n(y)g(K.,)h(M.J.)g(Marton,)g(A.T.)g(Wittev)n (een,)f(G.J.)h(Sc)n(hreib)r(er,)f(R.M.)663 631 y(Kerkho)n(v)n(en,)16 b(C.)i(Rob)r(erts,)g(P)-6 b(.S.)18 b(Linsley)-6 b(,)18 b(R.)f(Bernards,)h(and)g(S.H.)f(F)-6 b(riend.)21 b(Gene)c(expression) 663 722 y(pro\014ling)26 b(predicts)g(clinical)h(outcome)e(of)h(breast) g(cancer.)35 b Fa(Natur)l(e)p Fu(,)28 b(415:530{536,)i(2002.)523 814 y(30.)43 b(V.)25 b(V)-6 b(apnik.)33 b Fa(Statistic)l(al)c(L)l(e)l (arning)g(The)l(ory)p Fu(.)35 b(Wiley)-6 b(,)26 b(New)g(Y)-6 b(ork,)25 b(1998.)523 905 y(31.)43 b(J.B.)20 b(W)-6 b(elsh,)18 b(L.M.)i(Sapinoso,)f(A.I.)g(Su,)f(S.G.)h(Kern,)f(J.)h(W)-6 b(ang-Ro)r(driguez,)19 b(C.A.)g(Mosk)l(aluk,)663 996 y(J.F.)30 b(F)-6 b(rierson)31 b(Jr,)f(and)f(G.M.)i(Hampton.)44 b(Analysis)30 b(of)h(gene)f(expression)g(iden)n(ti\014es)f(can-)663 1088 y(didate)d(mark)n(ers)g(and)g(pharmacological)i(targets)g(in)e (prostate)h(cancer.)37 b Fa(Canc)l(er)29 b(R)l(ese)l(ar)l(ch)p Fu(,)663 1179 y(61:5974{5978,)h(2001.)523 1270 y(32.)43 b(J.)26 b(W)-6 b(eston,)26 b(Mukherjee)f(S.,)h(O.)g(Chap)r(elle,)h(M.)f (P)n(on)n(til,)g(T.)h(P)n(oggio,)h(and)d(V.)g(V)-6 b(apnik.)33 b(F)-6 b(ea-)663 1362 y(ture)26 b(Selection)i(for)g(SVMs.)39 b(In)27 b Fa(A)l(dvanc)l(es)j(in)f(Neur)l(al)g(Information)g(Pr)l(o)l (c)l(essing)i(Systems)p Fu(,)663 1453 y(v)n(olume)24 b(13,)j(2000.)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF