MATRIX RANK MINIMIZATION WITH APPLICATIONS A dissErtAtion ...
Recommend Documents
a d i ss er t a t i on fo r t he d e g ree of Do c to r of P h i l osop hy . P r of e sso r Jo h nT.G i ll III. App r ov
Mar 17, 2008 - least squares (IRLS-p, [20]) with 0 < p ⤠1 have been proposed to ..... corresponds to the top L singular values of Z. Define the projection ...
Mar 6, 2014 - + sRkâ1 â sdkâ1, sPk. ã ⥠0. Similarly, let Q = Qk in (33) and Q =Qâ in (36), and let R = Rk in (34) and R = Râ in (37), we obtain λãâ sQk. + sPk.
Let (Pâ,Qâ,Râ) be an optimal solution of (5.1). We introduce the short hand notations. sPk =Pk âPâ,sQk =Qk âQâ, and sRk =Rk âRâ. sbk =bk âbâ,sdk =dk âdâ ...
Nov 24, 2006 - LG] 24 Nov 2006. Low-rank matrix factorization with attributes. Jacob Abernethy. Computer Science Division. University of California. Berkeley ...
Aug 9, 2018 - Matrix pencil, symmetric pencil, strict equivalence, congruence, orbit, ..... For a symmetric matrix pencil λA+ B, define the congruence bundle ...
This paper presents the rank minimization approach to solve general bilinear matrix inequality (BMI) problems. Due to the NP-hardness of BMI problems, ...
be used to find a low rank factorization of the matrix. In practice, it is ... lems with occlusion and tracking failure lead to missing data. In this case .... forced to approximate this program by dropping the non convex term âr||X||2. F , yieldin
Aug 4, 2013 - arXiv:1308.4716v1 [math.CO] 4 Aug 2013. NONNEGATIVE RANK OF A MATRIX. WITH ONE NEGATIVE EIGENVALUE. YAROSLAV SHITOV.
HIERARCHICAL RANK AGGREGATION WITH APPLICATIONS TO NANOTOXICOLOGY 161. Figure 1. Heatmap of HTS data assessing the cytotoxicity of 8 ...
3 The multiplicative complexity of a function is the number of GF(2) multiplications ... linear components of several candidates to the SHA-3 competition. The.
Nov 19, 2013 - IT] 11 Jan 2014. Characteristic-Dependent Linear Rank Inequalities with. Applications to Network Coding. â. Randall Dougherty, Eric Freiling, ...
Email: {shi, ki}@cvl.iis.u-tokyo.ac.jp .... images of objects of interest to a fixed canonical template .... where RI is a scalar parameter for signal-dependent shot.
Feb 23, 2011 ... bear this notice and the full citation on the first page. .... wise methods is that they
are much more complete than the ... Fullmetal Alchemist.
Oct 23, 2015 - cantly outperforms ALM for (33) with convex rank surrogate. This is because the nonconvex surrogates approximate the rank function much ...
Jan 12, 2017 - January 13, 2017 ...... [18] M. Laurent, A tour d'horizon on positive semidefinite and ... of California Davis, Davis, CA 95616, June 2016.
via Semi-Definite Programs, with Applications to the Fixed Order Output ... of minimizing the rank of a positive semi-definite matrix, subject the constraint that a.
efficient algorithms for the eigenvalue optimization problems, and more generally, for the semidefinite programming (SDP) and the linear matrix inequality (LMI) ...
Aug 3, 2005 - Scheffé). He also constructed conservative GCIs for all pairwise ..... Lehmann-Scheffé theorem: Suppose t is a complete and sufficient vector for.
Sep 18, 2011 - isomorphic group structures, we derived new tensor decompositions which ..... Moreover, the group structure can be cast a ring isomorphism.
Aug 31, 2016 - Abstract. In this paper we study properties and invariants of matrix codes endowed with the rank metric, and relate them to the covering radius.
Jan 5, 2017 - A regular matrix pencil sE â A and its rank one perturbations are considered. ... for regular matrix pencils at λ correspond to Jordan chains of the ...
In many cases, it is reasonable to assume that the unknown m à n matrix Z can ... mum A Posteriori (MAP) estimate when assuming that the singular values of Z ... F + λ Zâ. (4) where ·F is the Frobenius norm. The solution to Eq. (4) in the .....
MATRIX RANK MINIMIZATION WITH APPLICATIONS A dissErtAtion ...
t ha t t he s e p r o b lem s, al t h oug h rela t e d to t he R M P, are not R M Pst ...... Sometimes a rank minimizati
! #"
&$ %('*)+)+,.-0/1$2/3'*465 )+798;:@(, G>46:T T 3 ]_U bT 3 U aM] M] XU ]_] ` U a 3 ^ ea V
! #"
%$& #
%'
(
U ] U ] aM] V U 3 ` 3 T^ 3 ] U *)+ / '
'
' (-, .
10* 2
43
`_] U 3 V a T a T ]!U ] T a 3 3 ] U bT 3 T a T 3 Y V 3 3 3 3 ^P^ V T M] T ] 3 ` ] T T ^ 3 V >T T 3 ]_U bT 3 U aM] M] XU ]_] ` U a 3 ^ ea V
! #"
%'
506(-)
7
(
U ] UT ; 3 T ] S 3 3 Y Y ] ` U 3 3 3] a T 3B ] U Y T 3 U 3 ] U 3 S ?Xd>` U 3 ]_U 3 Z U a 3 U ^ ] Y a ` U 3 ] U 3 T U ] ^ 3 T MU T 3 ` ` 3 a2] U T ] a T X] c KT S M ^ c ] aMT aM] ] U 5 ^P]_Y T^ a a UW] ^PT ] aM] S ?TUW] S aM] Y ]_^ X] ] a T 3 3 ] a2] U 5 ^P]_Y U ] `_] c a ] 3 Y T^ W] ` 3 X] T^ ]
M
#
#
#
7
"
3
#
/
9
?
3
3
"
"
/
/ +( 3 (
3
#
/
/
/
3
3
3
/ .( 3
7
/
3
3
#
7 #
/
'
/ .( 3
$
#
.
;
"
/ 0 ? 3
0*?
/
(
1A
(
3
2
$
.3
0
/
/
/
3
" #
3
/
"
/
3
/
$
7
3
"
7
7
/
3 (
'
#A
/ "
3
/
(3
_] U Y `T ] 3 c O aM] 3 Y T^ 3 c = ] 3 Y ^ V ]_] `baM]_` aM] T^ ] a 3 5 W] ` 3 ] U ] ] L5= (T U ] ] U ] ` ] aM] UW] 3 aM] ] TU ] ] TY ^P] S T U ]_^=T ] U ^ ] Y a T ` T L ] ^ X] T T^ V 3 `T^P^ V ] ] U a 3 Y TV ] 33 ^ ] 3 ]a T X] T 3 3 T^L` U T 3 ] Y TVaMT ] ] U T ^ ]_U aM] TU 3 T `_] Y] U a T U ] TY ^ ] T a T ] T a 3 Xa2] U ` UWU ] ^PT 3 a T T 3 a `ba T 3 3 T^6` U T 3 a2] UW] ^ 3 S 3 ` Y bT 3 T^P^ V a TU
3
9
"
"
'
7
(
3 (
(
(
7
7
7
!
/ +( 3
/
7
(
Y X]_` U
7
*,+ 2 + :;(" 3]# ) - ] T U T
)3 a
#
;
'
;7 !
Y]T U ]_Y ]
7
/ .( 3 ( 9
7 "
77
#
7
` TU 3 T ` ] Y T U 3
/ 3
(
) 721
] A] aMT ]
#
/ 3
/ 3
aM]_U ] aM] Y]T WU ] Y] -3 ] a T \ ]_U Y]T 3 ` UWU ]_^=T ] )3 a JT a T T ^ ^ a T 3 T T^H` TU 3 T `_] Y T U 3 a # aM]_U ] M] ] aM] ` TU 3 T `_] aM] U ^P]_Y 3 3 M] 3 V U Y 3 V ]_U T 3 aM] ^PTU ] Y ] U ^ 3 ] TU U ]_^=T 3 TY aM] M] UW^ V 3 T T a 3 ` UU] aM] Y 3 3 Y Y U T 3 `_] aM] U T MU D V ] U6] T`ba ^ 3 ]TU(U ]_^=T aM] D A] T Y ] ] `T ] 3 Y T ] )3 a a 3 Xa ` M] ` ] 3 a T ] 03 TY ) ]` 3 M]_U 3 a 3 U ^P]_Y ` T ] ] UW] ] T aM]
#
3
"
#
# 7 &
9
;7
7
] T 3 aM] UW] 3 ]_` 3 a T aM] U T U P^ ] 3 Y T V bT 3 3 ` T^>Y] a T T 3 aM]Y T U 3 aMT 3 Y 3 ^=TU 3 ^P]_Y 3 V ]_Y aM] U VT 3 T^ U `_] 3 aMT M] T^ )3 aUW] ` U 3 X] ] ] `_] aM]_U ] aM] a2] U T T T U U 3 T ] A4B[u,jB;9;! ?*f"4!AK?*e4414#.[?J / !N$?* !OQJtNI>'("49;,+9;,&/4!A4,"9