Object
Title: Sub-gradient algorithms for solving multi-dimensional analysis problems of dissimilarity data
Contributor:
Korbicz, Józef (1951- ) - red. ; Uciński, Dariusz - red.
Group publication title:
Abstract:
The multi-dimensional scaling (MDS) problem, extensively addressed in data analysis, has been investigated in significant works (e.g. De Leeuw, 1977; 1988; De Leeuw and Pruzansky, 1976; Kruskal, 1964; Shepard, 1974). It consists in determination of a configuration x* such that the matrix elements of distances between the points are required to be those of a given matrix called the proximity or dissimilarity matrix or, if this is impossible, it reduces to the nearest optimization problem in which a function (called the loss function) is to be minimized. ; In this paper, the stability and regularity of the Lagrangian duality in convex maximization (non-convex minimization) are considered. We present some convergence results of the DC (Difference of Convex functions) optimization algorithms which are based on DC duality and local optimality conditions for DC optimization. Various regularization techniques are studied in order to improve the quality (robustness, stability, convergence rate) of the DC algorithm (DCA). For solving MDS problems, sub-gradient algorithms (involving or not regularization techniques) in DC optimization are presented. Some numerical applications for large-scale problems are also provided.
Publisher:
Zielona Góra: Uniwersytet Zielonogórski
Resource Identifier:
Pages:
Source:
AMCS, volume 7, number 3 (1997) ; click here to follow the link
Language:
Rights:
Biblioteka Uniwersytetu Zielonogórskiego
Object collections:
- Repository > Faculties > Faculty of Computer, Electrical and Control Engineering
- Repository > Types of work > Articles
- Repository > Scientific journals and UZ publishing series > International Journal of Applied Mathematics and Computer Science (AMCS)
- Repository > Scientific journals and UZ publishing series > International Journal of Applied Mathematics and Computer Science (AMCS) > International Journal of Applied Mathematics and Computer Science (AMCS) (1997)
Last modified:
Nov 5, 2024
In our library since:
Nov 23, 2020
Number of object content hits:
58
All available object's versions:
https://zbc.uz.zgora.pl/repozytorium/publication/64512
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International Journal of Applied Mathematics and Computer Science (AMCS)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 26 (2016)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 25 (2015)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 24 (2014)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 23 (2013)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 22 (2012)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 21 (2011)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 20 (2010)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 19 (2009)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 17 (2007)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 16 (2006)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 15 (2005)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 13 (2003)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 12 (2002)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 11 (2001)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 10 (2000)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 9 (1999)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 8 (1998)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 7 (1997)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 7, number 1 (1997)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 7, number 2 (1997)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 7, number 3 (1997)
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- Optimality conditions for linear 2-D control systems with constraints
- Unreachability and uncontrollability of 2-D linear systems with bounded inputs
- Sub-gradient algorithms for solving multi-dimensional analysis problems of dissimilarity data
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 7, number 4 (1997)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 7, number 1 (1997)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 6 (1996)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 5 (1995)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 4 (1994)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 3 (1993)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 2 (1992)
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International Journal of Applied Mathematics and Computer Science (AMCS),volume 1 (1991)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 26 (2016)
| Edition name | Date |
|---|---|
| Sub-gradient algorithms for solving multi-dimensional analysis problems of dissimilarity data | Nov 5, 2024 |
