Visualization of high-dimensional data using an association of multidimensional scaling to clustering

A common task in data mining is the visualization of multivariate objects on scatterplots, allowing human observers to perceive subtle inter-relations in the dataset such as outliers, groupings or other regularities. Multidimensional scaling (MDS) is a well known exploratory data analysis family of techniques that produce one display on which inter-object similarity relationships are preserved. The algorithm scales with the square of the number of visualized data, which limits its application to small datasets. In order to alleviate this limitation, we associate MDS with three different clustering models, namely the learning vector quantization, the k-means and the dendrograms. We propose to perform dimensionality reduction on a reduced set of cluster centers, to which the data are added using a relative MDS mapping. Our experiments show that this approach allows to obtain displays of large datasets with fairly good visualization properties, when compared with the display obtained by a direct mapping of the whole dataset.