A Quadratically Converging Algorithm of Multidimensional Scaling
نویسنده
چکیده
Multidimensional scaling (MDS) is well known technique for analysis of multidimensional data. The most important part of implementation of MDS is minimization of STRESS function. The convergence rate of known local minimization algorithms of STRESS function is no better than superlinear. The regularization of the minimization problem is proposed which enables the minimization of STRESS by means of the conjugate gradient algoritm with quadratic rate of convergence.
منابع مشابه
A Quadratically Convergent Interior-Point Algorithm for the P*(κ)-Matrix Horizontal Linear Complementarity Problem
In this paper, we present a new path-following interior-point algorithm for -horizontal linear complementarity problems (HLCPs). The algorithm uses only full-Newton steps which has the advantage that no line searchs are needed. Moreover, we obtain the currently best known iteration bound for the algorithm with small-update method, namely, , which is as good as the linear analogue.
متن کاملPrimal-dual Aane-scaling Algorithms Fail for Semideenite Programming
In this paper, we give an example of a semide nite programming problem in which primaldual a ne-scaling algorithms using the HRVW/KSH/M, MT, and AHO directions fail. We prove that each of these algorithm can generate a sequence converging to a non-optimal solution, and that, for the AHO direction, even its associated continuous trajectory can converge to a non-optimal point. In contrast with th...
متن کاملLinear scaling approaches to quantum macromolecular similarity: Evaluating the similarity function
The evaluation of the electron density based similarity function scales quadratically with respect to the size of the molecules for simplified, atomic shell densities. Due to the exponential decay of the function's atom-atom terms most interatomic contributions are numerically negligible on large systems. An improved algorithm for the evaluation of the Quantum Molecular Similarity function is p...
متن کاملUsing Multidimensional Scaling for Assessment Economic Development of Regions
Addressing socio-economic development issues are strategic and most important for any country. Multidimensional statistical analysis methods, including comprehensive index assessment, have been successfully used to address this challenge, but they donchr('39')t cover all aspects of development, leaving some gap in the development of multidimensional metrics. The purpose of the study is to const...
متن کاملConstrained Best Euclidean Distance Embedding on a Sphere: A Matrix Optimization Approach
The problem of data representation on a sphere of unknown radius arises from various disciplines such as Statistics (spatial data representation), Psychology (constrained multidimensional scaling), and Computer Science (machine learning and pattern recognition). The best representation often needs to minimize a distance function of the data on a sphere as well as to satisfy some Euclidean dista...
متن کامل