Visualizing data as objects by DC (difference of convex) optimization
نویسندگان
چکیده
In this paper we address the problem of visualizing in a bounded region a set of individuals, which has attached a dissimilarity measure and a statistical value. This problem, which extends the standard Multidimensional Scaling Analysis, is written as a global optimization problem whose objective is the difference of two convex functions (DC). Suitable DC decompositions allow us to use the DCA algorithm in a very efficient way. Our algorithmic approach is used to visualize two real-world datasets.
منابع مشابه
A framework of discrete DC programming by discrete convex analysis
A theoretical framework of difference of discrete convex functions (discrete DC functions) and optimization problems for discrete DC functions is established. Standard results in continuous DC theory are exported to the discrete DC theory with the use of discrete convex analysis. A discrete DC algorithm, which is a discrete analogue of the continuous DC algorithm (Concave-Convex Procedure in ma...
متن کاملSequential Convex Programming Methods for Solving Nonlinear Optimization Problems with DC constraints
This paper investigates the relation between sequential convex programming (SCP) as, e.g., defined in [24] and DC (difference of two convex functions) programming. We first present an SCP algorithm for solving nonlinear optimization problems with DC constraints and prove its convergence. Then we combine the proposed algorithm with a relaxation technique to handle inconsistent linearizations. Nu...
متن کاملSolving Indefinite Kernel Support Vector Machine with Difference of Convex Functions Programming
Indefinite kernel support vector machine (IKSVM) has recently attracted increasing attentions in machine learning. Different from traditional SVMs, IKSVM essentially is a non-convex optimization problem. Some algorithms directly change the spectrum of the indefinite kernel matrix at the cost of losing some valuable information involved in the kernels so as to transform the non-convex problem in...
متن کاملCharacterizing global optimality for DC optimization problems under convex inequality constraints
Characterizations of global optimality are given for general difference convex (DC) optimization problems involving convex inequality constraints. These results are obtained in terms of E-subdifferentials of the objective and constraint functions and do not require any regularity condition. An extension of Farkas’ lemma is obtained for inequality systems involving convex functions and is used t...
متن کاملDC programming and DCA for enhancing physical layer security via cooperative jamming
The explosive development of computational tools these days is threatening security of cryptographic algorithms those are regarded as primary traditional methods for ensuring information security. Physical layer security approach is introduced as a method for both improving confidentiality of the secret key distribution in cryptography and enabling the data transmission without relaying on high...
متن کامل