Supervised learning of explicit maps with ability to correct distortions in the target output for manifold learning

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Research Article

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Information Sciences


Most manifold learning algorithms are non-parametric, use unsupervised approaches, and hence lack prediction capability. Some of these methods have been adapted for out of sample points, but often they require the training data. We propose a framework to estimate an explicit map for manifold learning in a supervised setting. Although different modeling tools can be used, we study the performance with polynomials and neural networks. The quality of output of any regression system depends on the quality of the target data. We consider outputs from an unsupervised manifold learning method as the target. However, even for simple data, often the outputs (target) get severely distorted. For high-dimensional data, it is difficult to assess and correct if the target data are distorted. Our approach can predict as well as eliminate such distortions to a great extent in the output. We suggest three regularizers, each of which can be used to augment the loss function. For image data, even for a low order polynomial, the number of free parameters becomes large demanding a large training set. For this, we propose a scheme exploiting the spatial characteristics of neighboring pixels. The effectiveness of our framework is demonstrated using synthetic and real data for both polynomial and neural network-based models.

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