Visual Data Mining and Discovery in Multivariate Data Using Monotone n-D Structure

Visual data mining (VDM) is an emerging research area of Data Mining and Visual Analytics gaining a deep visual understanding of data. A border between patterns can be recognizable visually, but its analytical form can be quite complex and difficult to discover. VDM methods have shown benefits in many areas, but these methods often fail in visualizing highly overlapped multidimensional data and data with little variability. We address this problem by combining visual techniques with the theory of monotone Boolean functions and data monotonization. The major novelty is in visual presentation of structural relations between n-dimensional objects instead of traditional attempts to visualize each attribute value of n-dimensional objects. The method relies on n-D monotone structural relations between vectors. Experiments with real data show advantages of this approach to uncover a visual border between malignant and benign classes