Multidimensional Data Visualization

Abstract

Aims and ScopeOptimization has been expanding in all directions at an astonishing rate during the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace, and our knowledge of all aspects of the field has grown even more profound. At the same time, one of the most striking trends in optimization is the constantly increasing emphasis on the interdisciplinary nature of the field. Optimization has been a basic tool in all areas of applied mathematics, engineering, medicine, economics, and other sciences.The series Springer Optimization and Its Applications publishes undergraduate and graduate textbooks, monographs and state-of-the-art expository work that focus on algorithms for solving optimization problems and also study applications involving such problems. Some of the topics covered include nonlinear optimization (convex and nonconvex), network flow problems, stochastic optimization, optimal control, discrete optimization, multi-objective programming, description of software packages, approximation techniques and heuristic approaches.

Method for Visual Detection of Similarities in Medical Streaming Data

“…The points from matrix Z are mapped on the plane using the Multidimensional Scaling [6] (or are other algorithm of nonlinear projection of multidimensional points on the plane). Denote the resulting matrix by Y , that contains km + 2 rows, corresponding to different comparisons of the sample with other subsequences, and 2 columns.…”

“…One of these methods is the principal component analysis (PCA). The well-known principal component analysis [6] can be used to display the data as a linear projection on a subspace of the original data space such that best preserves the variance in the data. PCA cannot embrace nonlinear structures, consisting of arbitrarily shaped clusters or curved manifolds, since it describes the data in terms of a linear subspace.…”

“…PCA cannot embrace nonlinear structures, consisting of arbitrarily shaped clusters or curved manifolds, since it describes the data in terms of a linear subspace. Therefore, several methods have been proposed for reproducing nonlinear higher-dimensional structures on a lower-dimensional display: multidimensional scaling and its modifications [6], [20], [21], [22], Isomap [23], locally linear embedding [24], etc. Various neural network approaches are used for this aims as well (see e.g.…”

“…In this paper, we suggest using the specific visualization tools and methods (multidimensional data visualization [6]) that are effective and also do not require intensive training of the users. Moreover, we show a possibility of making the decision, based on five criteria of similarity of the sample with the subsequence of real-time data stream by representing the similarity as a point on a plane.…”

“…Moreover, we show a possibility of making the decision, based on five criteria of similarity of the sample with the subsequence of real-time data stream by representing the similarity as a point on a plane. Dimensionality reduction and visual analysis of multidimensional data [6] have been applied when comparing the best found subsequences in X a .…”