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Global Optimality of the Successive MaxBet
Algorithm
Summary. 1. The Successive MaxBet Problem
(SMP). 2. The MaxBet Algorithm. 3. Global
Optimality Motivation/Problems. 4. Conclusions
and Open questions.
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1. The Successive MaxBet Problem (S.M.P)
s.p.s.d
Blocks Matrix
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1. The Successive MaxBet Problem (S.M.P)
order 1
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1. The Successive MaxBet Problem (S.M.P)
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Order 1
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Order s
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Property 1 Convergence of the MaxBet Algorithm
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Property 2 Necessary Condition of Convergence
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3. Motivation and results
1. MaxBet Algorithm depends on the starting
vector
2. MaxBet algorithm does not guarantee the
computation of the global solution of SMP
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3. Motivation and results an example
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3. Motivation and results Two Questions
Q1. How can we know that the solution computed
by the Maxbet algorithm is global or not ?
Q2. When the solution is not global, how can we
reach using this solution the global solution ?
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3. Motivation and Results Proceeding
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RESULT 1
Result 1
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ELEMENTS OF PROOF (Result 1)
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3. Motivation and Results
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RESULT 2
Result 2
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ELEMENTS OF PROOF (Result 2)
1. w is block-normed vector
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1. w is block-normed vector
w is better solution than u
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2. w is not block-normed vector 2.1. w is not
block orthogonal to u
v is better solution than u
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w is not block-normed vector 2.2. w is block
orthogonal to u
v is better solution than u
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RESULT 2
Result 3
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ELEMENTS OF PROOF (Result 3)
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ELEMENTS OF PROOF (Result 3)
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Result 4
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ELEMENTS OF PROOF (Result 4)
45 -20 5 6 16
3 -20 77 -20 -25 -8 -21
5 -20 74 47 18 -32 6
-25 47 54 7 -11 16
-8 18 7 21 -7 3
-21 -32 -11 -7 70
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ELEMENTS OF PROOF (Result 4)
Random research with 10.000.000 starting vectors
0.49 -0.87 0.80 0.59 0.56 -0.82
F(u) 378.96
u
s 0.48
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4. General Conclusions
1. Generalized canonical correlationAnalysis
Horst (1961)
3. Soft Modeling Approach Estimation of latent
variables under mode B Wold (1984) Hanafi
(2001)
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4. Perspective and Little Open Question
-
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Motivation Illustration 1
MaxBet Algorithm depends on the starting vector
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The Successive MaxBet Problem (S.M.P) and
Multivariate Methods
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Some multivarite methods
Generalized canonical correlation methods
Rotation methods(Agreement methods)
SOFT MODELING APPRAOCH(Approch)
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Rotation methods
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Generalized canonical correlation methods
SVD
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Multivariate Eigenvalue Problem Watterson and
Chu(1993)