High dimensionality is a major challenge for data visualization. Parameter optimization problems require an understanding of the behaviour of an objective function in an n-dimensional space around the optimum - this is multidimensional visualization and is a natural extension of the traditional domain of scientific visualization. Large numeric data tables with observations of many attributes require us to understand the relationship between these attributes - this is multivariate visualization and is an important aspect of information visualization. \ud \ud Common to both types of high dimensional visualization is a need to reduce the dimensionality for display. Although multidimensional and multivariate data are quite distinct, we show that a common approach to dimensionality reduction is possible. This framework makes a contribution to the foundation of the data visualization field, bringing both information and scientific visualization rather closer together. \ud \ud To address this problem we present a uniform approach designed for both abstract and scientific data. It is based on the reduction approach, which is realized through a filtering process that allows extraction of data subject to constraints on their position or value within an n-dimensional window, and on choice of dimensions for display. The framework has been put to proof through a visualization method called HyperCell, which has been applied to several case studies. The results are presented and the system evaluated.\u
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