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Title: The extension of isometric feature mapping for interval-valued symbolic data Authors:  Han-Ming Wu - National Taipei University (Taiwan) [presenting]
Abstract: The dimension reduction of the interval-valued data is one of the active research topics in symbolic data analysis (SDA). The main thread has been focused on the extensions of the linear algorithms such as the principal component analysis (PCA) and the sliced inverse regression (SIR). We extend the isometric feature mapping (ISOMAP) to the interval-valued data which we called interval ISOMAP (iISOMAP). ISOMAP is a global geometric framework for nonlinear dimensionality reduction (NLDR) techniques using the shortest-path distance in a neighbor graph. The ISOMAP algorithm advances PCA and the multidimensional scaling (MDS) by providing a better understanding of the data's intrinsic structure. Applying interval MDS to the estimation of the geodesic distance between interval data points is the key step of the ISOMAP. For the estimation of the geodesic distance between interval type symbolic objects, we compare the various input distance measures proposed previously. The maximum covering area rectangle (MCAR) method is used to display the interval objects onto a 2D NLDR subspace in order to visualize the geometric structure of a nonlinear manifold dataset. We evaluate the method for the low-dimensional discriminative and visualization purposes by means of the simulation studies and real data sets. The comparison with those obtained with the symbolic PCA and the symbolic MDS were also reported.