Visualization of Graphical Data-set on User Specified Axes using the Weighted Isomap Method

Most methods of reducing the dimensionality of a data-set try to maximize the variance of the data in the lower-dimensional space; but the axes that achieve this may have no relation to the meaning of the data. We introduce a new semi-supervised method of dimensionality reduction which can embed data of high dimension in a user-defined coordinate system of lower dimension with axes that are meaningful in terms of the properties of the data. We allow the user to specify the lower-dimensional axes, and embed the data in these axes using a modification of the Isomap method, together with curve-based space warping. Using our method, high-dimensional database, such as image or 3D model list, can be visualized two dimensional space based on the user defined properties. CR Categories: I.3.6 [Computer Graphics]: Applications; I.4.8 [Pattern Recognition]: Design Methodology—Classifier design and evaluation