DD-HDS homepage
To
Sylvain Lespinats's homepage

The Data-Driven High Dimensional Scaling is a dimensionality reduction technique belonging to non-linear Multi Dimensional Scaling (MDS). This method is designed (I) to avoid "false neighborhood" and "tears" and (II) to take the specific properties of high dimensional data. 

Example: Non-linear représentation on a tow-dimensional space (rigth insert) of 273 large cities around the world (left insert).

The reference: Lespinats, S., Verleysen, M., Giron, A. and Fertil, B. (2007), “DD-HDS: a tool for visualization and exploration of highdimensional data.” IEEE transactions on Neural Networks, 18(5), pp 1265-1279.

Abstract : Visualization of high-dimensional data is generally achieved by a projection into a low (usually 2- or 3-) dimensional space. Visualization is intended to facilitate the understanding of datasets by preserving some "essential" information. This paper presents DD-HDS (Data Driven High-Dimensional Scaling), a non-linear Multi-Dimensional Scaling (MDS) method relying on the Force Directed Placement (FDP) paradigm to help dynamically discover features of interest in data sets. Through a specific weighting of distances taking into account the concentration of measures phenomenon, and a symmetric handling of short distances in the original and output spaces, the method is particularly adapted to the projection of high-dimensional data. A single user-defined parameter in the optimization procedure implements the compromise between local neighborhood preservation and global mapping. The projection of low- and high-dimensional examples illustrates the features and advantages of the proposed algorithm.

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Mapping of two 3-D open boxes in a 2-D space by DD-HDS and some other techniques. The color codes for the position of the data in the original space (except for the local mapping efficiency and global mapping efficiency plots). Upper left—original data (3-D space), upper right—mapping by DD-HDS (2-D space), lower left—pressure (see the article for more information), and lower right—pairwise distance preservation (color codes for density of distances). Other subplots are self-explanatory. 

Contrary to others methods, DD-HDS does not lead to “false neighborhoods” nor “tears”.

 

An algorithm, closely related to DD-HDS, has been recently delevopped: visite the RankVisu homepage.