%PDF-1.5
%
1 0 obj
<< /S /GoTo /D (section.1) >>
endobj
4 0 obj
(Introduction)
endobj
5 0 obj
<< /S /GoTo /D (section.2) >>
endobj
8 0 obj
(Existing Methods)
endobj
9 0 obj
<< /S /GoTo /D (subsection.2.1) >>
endobj
12 0 obj
(Solving Sparse PCA)
endobj
13 0 obj
<< /S /GoTo /D (subsection.2.2) >>
endobj
16 0 obj
(Solving Sparse CCA)
endobj
17 0 obj
<< /S /GoTo /D (section.3) >>
endobj
20 0 obj
(A Unified A-ManPG Algorithm)
endobj
21 0 obj
<< /S /GoTo /D (subsection.3.1) >>
endobj
24 0 obj
(Semi-Smooth Newton Method for the Subproblems)
endobj
25 0 obj
<< /S /GoTo /D (section.4) >>
endobj
28 0 obj
(Numerical Experiments)
endobj
29 0 obj
<< /S /GoTo /D (subsection.4.1) >>
endobj
32 0 obj
(Sparse PCA)
endobj
33 0 obj
<< /S /GoTo /D (subsection.4.2) >>
endobj
36 0 obj
(Sparse CCA: Vector Case)
endobj
37 0 obj
<< /S /GoTo /D (subsection.4.3) >>
endobj
40 0 obj
(Sparse CCA: Matrix Case)
endobj
41 0 obj
<< /S /GoTo /D (section.5) >>
endobj
44 0 obj
(Conclusion)
endobj
45 0 obj
<< /S /GoTo /D (appendix.A) >>
endobj
48 0 obj
(Preliminaries on Manifold Optimization)
endobj
49 0 obj
<< /S /GoTo /D (subsection.A.1) >>
endobj
52 0 obj
(Preliminaries of Generalized Stiefel manifold)
endobj
53 0 obj
<< /S /GoTo /D (subsection.A.2) >>
endobj
56 0 obj
(Optimality Condition of Manifold Optimization)
endobj
57 0 obj
<< /S /GoTo /D (appendix.B) >>
endobj
60 0 obj
(Semi-smoothness of Proximal Mapping)
endobj
61 0 obj
<< /S /GoTo /D (appendix.C) >>
endobj
64 0 obj
(Global Convergence of A-ManPG \(Algorithm 1\))
endobj
65 0 obj
<< /S /GoTo /D [66 0 R /Fit] >>
endobj
71 0 obj
<<
/Length 3623
/Filter /FlateDecode
>>
stream
xioF{~>X#AHfm"hhPCR_J$5:\t~9If׳ddOy阳T.?63X$r9{"ы˛*^gU.ߛ>*/VYI#7ٲ+0
-~{5m_rDZo^d Tr$f85zkb{S#иhN-cLBx~K:C8IR83@/N#0M&yyeпuAvK,})|X[EK_gN$"Ujf6
8c)bø̫kEgp{[c`0\%(1\z}:mjQ:=Dul6xVeC[oI맗Xt{Ƣ-K0vRzʬ`ƎgvqFyzz
BTuǦ^цf,VyۮXmUFcPȉVTE`9;:xF31^xe\%̺,>Kiok}U+BmN
^4r/7Է]*nĥz4}WЁ*TvbqLD'mNj4=_t4$9ED4chE{1)(u7'4bV&A)-P^a>Т@Q^^l!bV
~mi]%L-eW-)hU`j(+LD:op(uMNe*֨j~(y;Jي+z<㽓oKS߈N6!M8M5vg (>>Ѱ|u²:k27f*T4Lo3tR`9
8S0@AkHF?U~oafG$2V-&f J}"@FV>0khK7R|w_ڹ/WvC#=aCJG_eN-XWw2_Ū&tJ+:zD%olb.d6D XPwk&k?+]+2ίuv/EL% i$)EXD8"7{sA R33RX
I1ěEyN>'M\3y,o!Ye,Sj7q $|ыs!0sƉshO4cC2@!jDУle?.t$"
@v8w#p) l{pLcy!aLX@@xwXL?3=IoxEC8MBWFX'$nQIc&Lj p~$vB;U)7J/o4ʺѻ
_05
-Yk$˒F8(z"(h9<_3n9Vh!@Br>-~rZB-(?ej\C
c0CQ=S2N~1`ROA'S~%6z|/EL^"s:!Z퐽oKrTTꅜ{br|ȯKaXcѨ)X~iqiqZGٴZW`BCծмrBbcҹp KQYgCw!31 s7}b7TQ,[f{LȦh՛̗[W),01R+i_A{YI'{ݴacmM DJ6 A sȉ=@
`g`T ,_`,͉Sa0e/Y
nB\dH'K^R<0-ʥ"OF̎
@9qp$I9͔G7
g.xl2xz
m}rt&ߺ=zAC4EP!2M{
ɢ" $uGE@C~0IS
_s
\
|Vjb1 nfN{@IT"')Br\Uup9G%
C{2e.AwĵT_~ o0.³P2BSH:T/#M,
!Omc.x2^ Dާz>wZԦ:{PZ+Tg,TSvT_Lt!LJZj$g魈v6[ݖ{AKkeю ύ?'{3>xT!~+a߂Y +SM$O_ʟ:MN/Oz$]GP5ؼ+k,;6 5
1Pd?
GFnVbd*ATJFIIPV'AtOGC$ր 1bxmvtm4BywEBErsCvM@qo.T4^=-uP;G54z%6s*'i8()V˦.9-릿AKGGb{{*= &jο56MvWtLWgBYY4#Ckc6ny'C{mWt#0NI#u]CJ&{f%EP!5cw~֮'ۦW$'Xa5ݓqpGcWxq !^=G͛ជ#$6i\AqxvP
ʢn;۟|i\nA7Q%ߗޝOa1w߫ئ벤wryԟRTCƥRE6!K5yla)v-c(NB0:>Î,}Nj fճ/l*6C*3!g0=v[m3߀V!,ԣƛӓ.|~,#] 9[̖0L;t53il8Dлqy[ƓCmJɧ
JbuqYq!`x\U!c ZEg[5!6<IV.Rx.0;-0hdfI@ٚaŬojl2kCIw_ 蘹"hVh?w#c]'\z'I3D(mt-uo,=`i;LIݛ(7e/4tN]U_BK/ƘPPxxK`G#iщԿ έ2|zN3BrHcTE}CE>-G37IU>mWm{;S~@՞ŷ#=d"z]T;u}=tL
1fP9]˘
endstream
endobj
66 0 obj
<<
/Type /Page
/Contents 71 0 R
/Resources 70 0 R
/MediaBox [0 0 612 792]
/Parent 90 0 R
/Annots [ 67 0 R 68 0 R ]
>>
endobj
67 0 obj
<<
/Type /Annot
/Subtype /Link
/Border[0 0 0]/H/I/C[0 1 0]
/Rect [377.527 371.397 390.429 380.42]
/A << /S /GoTo /D (cite.pearson1901liii) >>
>>
endobj
68 0 obj
<<
/Type /Annot
/Subtype /Link
/Border[0 0 0]/H/I/C[0 1 0]
/Rect [389.766 203.53 402.668 212.552]
/A << /S /GoTo /D (cite.hotelling1936relations) >>
>>
endobj
72 0 obj
<<
/D [66 0 R /XYZ 71 757.862 null]
>>
endobj
73 0 obj
<<
/D [66 0 R /XYZ 72 720 null]
>>
endobj
2 0 obj
<<
/D [66 0 R /XYZ 72 412.741 null]
>>
endobj
86 0 obj
<<
/D [66 0 R /XYZ 237.091 149.126 null]
>>
endobj
70 0 obj
<<
/Font << /F19 74 0 R /F20 75 0 R /F29 76 0 R /F58 77 0 R /F8 78 0 R /F66 79 0 R /F67 80 0 R /F23 81 0 R /F26 82 0 R /F68 83 0 R /F71 84 0 R /F69 85 0 R /F27 87 0 R /F30 88 0 R /F43 89 0 R >>
/ProcSet [ /PDF /Text ]
>>
endobj
115 0 obj
<<
/Length 5233
/Filter /FlateDecode
>>
stream
x\mƑ_-ȼ.jrWN (J뵒}"ktO7@3_~o͂,'9]ZGdAf&yF<-~^ޔmyb\,Fx}Bg&kSF
:D]s=R\ҸˢܯC!2wi;I30usÅp*굿\V6F883iAPܝT/dFl,J\-=L,..\>Rɜsq9^䙁p2^uNj`W0r G_#`1
`Q$ㄇ"IEv2{8wӒeZ-fL4Ayf2x`|4A#`P'`ˇ
32X jHb`` :+`g>e /)s)m˄ԋr+|BmԌM[Z`1RC,sɫ$½i7]Y
1S,,U6Ѥ긏&2cl4瓸GL\L/pq9D$ ȶ8TNn
̮pɏ+m5˔
ogK4HMlT+>Vƃ4EY:m|ԑ7#Fǀ
rgaa%-)bͥNBsS@5&CnF(Zp86VR_}HFǞv4;ЀI&:&Ä_`etTh+8okb( 2B}]N|/mnA+)J\I4(:L=zKLmZLQ)Ă'ߞ~NnIhƂJ6eJyDImIW%ТfllYqcNȜջrHC|YvjNx}}t)p\r8\6Ȍ.T G}J}BɮPY xjK[e=c/s n&lkMEթfc,MWoU@"T:&T۹7%N?