No Pressure! Addressing Problem of Local Minima in Manifold Learning

33th Annual Conference on Neural Information Processing Systems(2019)
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Nonlinear embedding manifold learning methods provide an invaluable visual insights into a structure of the high-dimensional data. However due to a complicated nonlinear objective function, these methods can be easily stuck in local minima and their embedding quality can be poor. We propose a natural extension to several manifold learning methods aimed at identifying pressured points, i.e. points that stuck in the poor local minima and have poor embedding quality. We show that the pressure can be decreased by temporarily allowing these points to make use of an extra dimension in the embedding space. In the evaluation we show that our method is able to improve the objective function value of existing methods even after they get stuck in a poor local minimum.

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