sv_kernel.ps

一种新颖的SVM算法

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1 0 bop 1227 912 a Fl(RHBNC)43 b(SVM)h(Kernels)1585 1223
y Fk(M.)33 b(O.)f(Stitson)1548 1485 y(Marc)m(h)i(23,)e(1998)382
1929 y Fj(1)135 b(SV)44 b(Kernels)382 2190 y Fi(This)28
b(is)i(a)h(list)e(of)h(the)h(k)m(ernel)f(functions)f(in)g(the)h(RHUL)h
(SV)f(Mac)m(hine:)518 2436 y Fh(\017)46 b Fi(1.)41 b(The)30
b(simple)e(dot)j(pro)s(duct:)1699 2699 y Fg(K)7 b Fi(\()p
Fg(x;)15 b(y)s Fi(\))26 b(=)f Fg(x)20 b Fh(\001)h Fg(y)518
2903 y Fh(\017)46 b Fi(2.)41 b(The)30 b(simple)e(p)s(olynomial)g(k)m
(ernel:)1530 3167 y Fg(K)7 b Fi(\()p Fg(x;)15 b(y)s Fi(\))26
b(=)f(\(\()p Fg(x)c Fh(\001)f Fg(y)s Fi(\))h(+)f(1\))2409
3129 y Ff(d)609 3371 y Fi(where)30 b Fg(d)h Fi(is)e(user)h(de\014ned.)
609 3521 y(T)-8 b(ak)m(en)31 b(from)f([V)-8 b(ap95)r(].)518
3709 y Fh(\017)46 b Fi(3.)41 b(V)-8 b(o)m(vk's)32 b(real)e(p)s
(olynomial:)1555 4008 y Fg(K)7 b Fi(\()p Fg(x;)15 b(y)s
Fi(\))26 b(=)1981 3946 y(1)21 b Fh(\000)f Fi(\()p Fg(x)g
Fh(\001)h Fg(y)s Fi(\))2374 3913 y Ff(d)p 1981 3987 434
4 v 2001 4070 a Fi(1)g Fh(\000)f Fi(\()p Fg(x)h Fh(\001)f
Fg(y)s Fi(\))609 4261 y(where)30 b Fg(d)h Fi(is)e(user)h(de\014ned)f
(and)h(where)g Fh(\000)p Fi(1)25 b Fg(<)g Fi(\()p Fg(x)20
b Fh(\001)h Fg(y)s Fi(\))k Fg(<)g Fi(1.)609 4411 y(F)-8
b(rom)31 b(priv)-5 b(ate)30 b(comm)m(unications)g(with)f(V.)h(V)-8
b(o)m(vk.)518 4599 y Fh(\017)46 b Fi(4.)41 b(V)-8 b(o)m(vk's)32
b(real)e(in\014nite)e(p)s(olynomial:)1576 4877 y Fg(K)7
b Fi(\()p Fg(x;)15 b(y)s Fi(\))26 b(=)2175 4816 y(1)p
2001 4856 393 4 v 2001 4940 a(1)21 b Fh(\000)f Fi(\()p
Fg(x)h Fh(\001)f Fg(y)s Fi(\))609 5130 y(where)30 b Fh(\000)p
Fi(1)25 b Fg(<)g Fi(\()p Fg(x)c Fh(\001)f Fg(y)s Fi(\))26
b Fg(<)f Fi(1.)609 5281 y(F)-8 b(rom)31 b(priv)-5 b(ate)30
b(comm)m(unications)g(with)f(V.)h(V)-8 b(o)m(vk.)1854
5652 y(1)p eop
%%Page: 2 2
2 1 bop 518 548 a Fh(\017)46 b Fi(5.)41 b(Radial)29 b(Basis)i
(function:)1673 811 y(exp\()p Fh(\000)p Fg(\015)5 b Fh(j)p
Fg(x)21 b Fh(\000)f Fg(y)s Fh(j)2232 774 y Fe(2)2271
811 y Fi(\))609 1015 y(where)30 b Fg(\015)35 b Fi(is)30
b(user)g(de\014ned.)609 1166 y(T)-8 b(ak)m(en)31 b(from)f([V)-8
b(ap95)r(].)518 1353 y Fh(\017)46 b Fi(6.)41 b(Tw)m(o)31
b(la)m(y)m(er)g(neural)e(net)m(w)m(ork:)1641 1642 y(tanh\()1868
1580 y Fg(b)p Fi(\()p Fg(x)21 b Fh(\001)f Fg(y)s Fi(\))p
1868 1620 276 4 v 1983 1704 a(1)2173 1642 y Fh(\000)g
Fg(c)p Fi(\))609 1867 y(where)30 b Fg(b)g Fi(and)g Fg(c)h
Fi(are)g(user)e(de\014ned.)609 2017 y(T)-8 b(ak)m(en)31
b(from)f([V)-8 b(ap95)r(].)518 2205 y Fh(\017)46 b Fi(7.)41
b(Linear)30 b(splines)e(with)h(an)h(in\014nite)e(n)m(um)m(b)s(er)h(of)i
(p)s(oin)m(ts:)609 2355 y(F)-8 b(or)31 b(the)g(one-dimensional)d(case:)
672 2742 y(1)21 b(+)f Fg(x)881 2756 y Ff(i)909 2742 y
Fg(x)961 2756 y Ff(j)1018 2742 y Fi(+)g Fg(x)1161 2756
y Ff(i)1189 2742 y Fg(x)1241 2756 y Ff(j)1292 2742 y
Fi(min)o(\()p Fg(x)1531 2756 y Ff(i)1559 2742 y Fg(;)15
b(x)1651 2756 y Ff(j)1688 2742 y Fi(\))21 b Fh(\000)1845
2680 y Fg(x)1897 2694 y Ff(i)1945 2680 y Fi(+)f Fg(x)2088
2694 y Ff(j)p 1845 2721 280 4 v 1962 2804 a Fi(2)2134
2742 y(\(min)o(\()p Fg(x)2408 2756 y Ff(i)2437 2742 y
Fg(x)2489 2756 y Ff(j)2525 2742 y Fi(\)\))2595 2704 y
Fe(2)2655 2742 y Fi(+)2756 2680 y(\(min)o(\()p Fg(x)3030
2694 y Ff(i)3059 2680 y Fg(;)15 b(x)3151 2694 y Ff(j)3188
2680 y Fi(\)\))3258 2647 y Fe(3)p 2756 2721 542 4 v 3004
2804 a Fi(3)609 3020 y(F)-8 b(or)31 b(the)g(m)m(ulti-dimensional)26
b(case)32 b Fg(K)7 b Fi(\()p Fg(x;)15 b(y)s Fi(\))26
b(=)2278 2956 y Fd(Q)2356 2982 y Ff(n)2356 3043 y(k)r
Fe(=1)2504 3020 y Fg(K)2581 3035 y Ff(k)2624 3020 y Fi(\()p
Fg(x)2711 2987 y Ff(k)2754 3020 y Fg(;)15 b(y)2842 2987
y Ff(k)2885 3020 y Fi(\))609 3171 y(T)-8 b(ak)m(en)31
b(from)f([V)m(GS)q(].)518 3358 y Fh(\017)46 b Fi(8.)41
b(F)-8 b(ull)29 b(p)s(olynomial)f(k)m(ernel:)1767 3622
y(\()1812 3560 y Fg(x)20 b Fh(\001)h Fg(y)p 1812 3600
166 4 v 1871 3684 a(a)2008 3622 y Fi(+)e Fg(b)p Fi(\))2173
3577 y Ff(d)609 3847 y Fi(where)30 b Fg(a)p Fi(,)h Fg(b)f
Fi(and)g Fg(d)g Fi(are)h(user)f(de\014ned.)609 3997 y(F)-8
b(rom)31 b([V)-8 b(ap95)r(])30 b(and)g(generalized.)518
4185 y Fh(\017)46 b Fi(9.)41 b(Regularized)30 b(F)-8
b(ourier)30 b(\(w)m(eak)m(er)i(mo)s(de)e(regularization\))609
4335 y(F)-8 b(or)31 b(the)g(one-dimensional)d(case:)1684
4608 y Fg(\031)p 1662 4648 98 4 v 1662 4732 a Fi(2)p
Fg(\015)1780 4591 y Fi(cosh)1977 4543 y Ff(\031)r Fc(\000j)p
Ff(x)2135 4553 y Fb(i)2161 4543 y Fc(\000)p Ff(x)2256
4553 y Fb(j)2288 4543 y Fc(j)p 1977 4570 331 4 v 2122
4622 a Ff(\015)p 1780 4648 538 4 v 1929 4732 a Fi(sinh)2116
4696 y Ff(\031)p 2116 4711 43 4 v 2117 4763 a(\015)609
4944 y Fi(where)i(0)c Fh(\024)f(j)p Fg(x)1116 4958 y
Ff(i)1164 4944 y Fh(\000)20 b Fg(x)1307 4958 y Ff(j)1344
4944 y Fh(j)25 b(\024)g Fi(2)p Fg(\031)34 b Fi(and)c
Fg(\015)35 b Fi(is)30 b(user)f(de\014ned.)609 5094 y(F)-8
b(or)31 b(the)g(m)m(ulti-dimensional)26 b(case)32 b Fg(K)7
b Fi(\()p Fg(x;)15 b(y)s Fi(\))26 b(=)2278 5030 y Fd(Q)2356
5056 y Ff(n)2356 5117 y(k)r Fe(=1)2504 5094 y Fg(K)2581
5109 y Ff(k)2624 5094 y Fi(\()p Fg(x)2711 5061 y Ff(k)2754
5094 y Fg(;)15 b(y)2842 5061 y Ff(k)2885 5094 y Fi(\))609
5244 y(F)-8 b(rom)31 b([V)m(GS)q(])f(and)g([V)-8 b(apng)q(].)1854
5652 y(2)p eop
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3 2 bop 518 548 a Fh(\017)46 b Fi(10.)c(Semi)29 b(Lo)s(cal)h(Kernel)
1309 811 y([\()p Fg(x)1421 825 y Ff(i)1469 811 y Fh(\001)21
b Fg(x)1567 825 y Ff(j)1603 811 y Fi(\))g(+)f(1])1820
774 y Ff(d)1876 811 y Fi(exp\()p Fh(\000jj)p Fg(x)2223
825 y Ff(i)2272 811 y Fh(\000)g Fg(x)2415 825 y Ff(j)2451
811 y Fh(jj)2501 774 y Fe(2)2541 811 y Fg(\033)2596 774
y Fe(2)2636 811 y Fi(\))609 1015 y(where)35 b Fg(d)g
Fi(and)g Fg(\033)j Fi(are)d(user)g(de\014ned)f(and)g(w)m(eigh)m(t)i(b)s
(et)m(w)m(een)f(global)g(and)f(lo)s(cal)609 1128 y(appro)m(ximation.)
609 1279 y(F)-8 b(rom)31 b(priv)-5 b(ate)30 b(comm)m(unications)g(with)
f(V.)h(V)-8 b(apnik.)518 1466 y Fh(\017)46 b Fi(11.)c(Regularized)29
b(F)-8 b(ourier)30 b(\(stronger)h(mo)s(de)f(regularization\))609
1616 y(F)-8 b(or)31 b(the)g(one-dimensional)d(case:)1866
1851 y(1)21 b Fh(\000)e Fg(\015)2074 1818 y Fe(2)p 1460
1891 1061 4 v 1460 1975 a Fi(2\(1)i Fh(\000)f Fi(2)p
Fg(\015)h Fi(cos)q(\()p Fg(x)2019 1989 y Ff(i)2067 1975
y Fh(\000)f Fg(x)2210 1989 y Ff(j)2247 1975 y Fi(\))g(+)g
Fg(\015)2445 1948 y Fe(2)2485 1975 y Fi(\))609 2169 y(where)30
b(0)c Fh(\024)f(j)p Fg(x)1116 2183 y Ff(i)1164 2169 y
Fh(\000)20 b Fg(x)1307 2183 y Ff(j)1344 2169 y Fh(j)25
b(\024)g Fi(2)p Fg(\031)34 b Fi(and)c Fg(\015)35 b Fi(is)30
b(user)f(de\014ned.)609 2319 y(F)-8 b(or)31 b(the)g(m)m
(ulti-dimensional)26 b(case)32 b Fg(K)7 b Fi(\()p Fg(x;)15
b(y)s Fi(\))26 b(=)2278 2255 y Fd(Q)2356 2281 y Ff(n)2356
2342 y(k)r Fe(=1)2504 2319 y Fg(K)2581 2334 y Ff(k)2624
2319 y Fi(\()p Fg(x)2711 2286 y Ff(k)2754 2319 y Fg(;)15
b(y)2842 2286 y Ff(k)2885 2319 y Fi(\))609 2470 y(F)-8
b(rom)31 b([V)m(GS)q(])f(and)g([V)-8 b(apng)q(].)518
2657 y Fh(\017)46 b Fi(17.)c(Ano)m(v)-5 b(a)31 b(1)1285
2958 y Fg(K)7 b Fi(\()p Fg(x;)15 b(y)s Fi(\))26 b(=)f(\()1779
2853 y Ff(n)1740 2878 y Fd(X)1736 3062 y Ff(k)r Fe(=1)1880
2958 y Fi(exp\()p Fh(\000)p Fg(\015)5 b Fi(\()p Fg(x)2264
2921 y Ff(k)2327 2958 y Fh(\000)20 b Fg(y)2466 2921 y
Ff(k)2509 2958 y Fi(\))2544 2921 y Fe(2)2584 2958 y Fi(\)\))2654
2921 y Ff(d)609 3233 y Fi(where)30 b(the)h(degree)g Fg(d)f
Fi(and)g Fg(\015)36 b Fi(are)30 b(user)g(de\014ned.)609
3383 y(F)-8 b(rom)31 b(priv)-5 b(ate)30 b(comm)m(unications)g(with)f
(V.)h(V)-8 b(apnik.)518 3571 y Fh(\017)46 b Fi(18.)c(Generic)30
b(Kernel)f(1)609 3721 y(This)d(is)h(a)h(k)m(ernel)f(in)m(tended)f(for)i
(exp)s(erimen)m(ts,)f(just)g(mo)s(dify)f(the)i(appropriate)609
3834 y(function)42 b(in)f(k)m(ernel)p 1339 3834 28 4
v 32 w(generic)p 1649 3834 V 33 w(1)p 1727 3834 V 33
w(c.C.)i(Y)-8 b(ou)43 b(can)g(use)g(the)g(parameters)g(a)p
3204 3834 V 33 w(v)-5 b(al,)609 3947 y(b)p 665 3947 V
32 w(v)g(al,)31 b(c)p 907 3947 V 33 w(v)-5 b(al,)30 b(d)p
1160 3947 V 32 w(v)-5 b(al)30 b(and)g(e)p 1553 3947 V
33 w(v)-5 b(al.)518 4135 y Fh(\017)46 b Fi(19.)c(Generic)30
b(Kernel)f(2)609 4285 y(This)d(is)h(a)h(k)m(ernel)f(in)m(tended)f(for)i
(exp)s(erimen)m(ts,)f(just)g(mo)s(dify)f(the)i(appropriate)609
4398 y(function)42 b(in)f(k)m(ernel)p 1339 4398 V 32
w(generic)p 1649 4398 V 33 w(2)p 1727 4398 V 33 w(c.C.)i(Y)-8
b(ou)43 b(can)g(use)g(the)g(parameters)g(a)p 3204 4398
V 33 w(v)-5 b(al,)609 4511 y(b)p 665 4511 V 32 w(v)g(al,)31
b(c)p 907 4511 V 33 w(v)-5 b(al,)30 b(d)p 1160 4511 V
32 w(v)-5 b(al)30 b(and)g(e)p 1553 4511 V 33 w(v)-5 b(al.)1854
5652 y(3)p eop
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4 3 bop 382 548 a Fj(References)382 788 y Fi([V)-8 b(ap95])52
b(Vladimir)38 b(N.)i(V)-8 b(apnik.)69 b Fa(The)42 b(Natur)-5
b(e)42 b(of)g(Statistic)-5 b(al)43 b(L)-5 b(e)g(arning)43
b(The)-5 b(ory)p Fi(.)730 901 y(Springer,)29 b(New)h(Y)-8
b(ork,)32 b(1995.)382 1089 y([V)-8 b(apng])46 b(Vladimir)31
b(N.)j(V)-8 b(apnik.)50 b Fa(Statistic)-5 b(al)37 b(L)-5
b(e)g(arning)37 b(The)-5 b(ory)p Fi(.)52 b(J.)33 b(Wiley)-8
b(,)35 b(forth-)730 1202 y(coming.)382 1389 y([V)m(GS])111
b(Vladimir)23 b(N.)i(V)-8 b(apnik,)26 b(Stev)m(en)f(E.)g(Golo)m(wic)m
(h,)i(and)e(Alex)f(Smola.)32 b(Supp)s(ort)730 1502 y(v)m(ector)44
b(metho)s(d)e(for)g(function)f(appro)m(ximation,)j(regression)e
(estimation)730 1615 y(and)30 b(signal)f(pro)s(cessing.)1854
5652 y(4)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
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