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Title: Manifold learning in ambient space Authors:  Wee Chin Tan - National University of Singapore (Singapore) [presenting]
Abstract: Many real life data lie in high dimensional spaces. For example, a matrix of high dimension is used to represent an image. In the analysis high dimensional data, the curse of dimensionality arises. In recent years, there have been vast developments of linear and nonlinear dimension reduction techniques to overcome the curse of dimensionality. These techniques are sometimes called manifold learning. They assume that there is an underlying manifold of dimension much smaller than the dimension of the space which the data lie in. They aim is to overcome the curse of dimensionality by learning the behavior of the data from a lower dimensional space. In reality, data are very noisy, and it is not easy to extract the relevant information. The method which is proposed extends the idea of subsampling to noisy data sets in higher dimensional space, and utilizes the Moving Least Square method to approximate the underlying manifold. Subsampling is used in computer graphics to reduce the image size. The idea subsampling is to extract a small subset from the input data which preserves a large amount of information regarding the underlying manifold. This will greatly reduce the computation complexity of learning the manifold.