Nonlinear Dimension Reduction using ISOMap based on Class Information

Image processing and machine learning communities have long addressed the problems involved in the analysis of large high-dimensional data sets. To deal with high-dimensional data efficiently, learning core properties of given data set is important. The manifold learning methods such as ISOMap try to identify a low-dimensional manifold from a set of unorganized samples. ISOMap method is an extension of the classical multidimensional scaling method for dimension reduction, which find a linear subspace in which dissimilarity between data points is preserved. In order to measure dissimilarity, ISOMap uses the geodesic distances on the manifold instead of Euclidean distance. In this paper, we propose a modification of ISOMap using class information, which is often given in company with input data in many applications such as pattern classification. Since the conventional ISOMap does not use class information in approximating true geodesic distance between each pair of data points, it is difficult to construct a data structure related to class-membership that may give important information for given task such as data visualization and classification. The proposed method utilizes class-membership for measuring distance of data pair so as to find a low-dimensional manifold preserving the distance between classes as well as the distance between data points. Through computational experiments on artificial data sets and real facial data sets, we confirm that the proposed method gives better performance than the conventional ISOMap.