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Multi-objective genetic programming for manifold learning: balancing quality and dimensionality

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posted on 2020-06-16, 22:21 authored by Andrew LensenAndrew Lensen, Mengjie ZhangMengjie Zhang, Bing XueBing Xue
© 2020, Springer Science+Business Media, LLC, part of Springer Nature. Manifold learning techniques have become increasingly valuable as data continues to grow in size. By discovering a lower-dimensional representation (embedding) of the structure of a dataset, manifold learning algorithms can substantially reduce the dimensionality of a dataset while preserving as much information as possible. However, state-of-the-art manifold learning algorithms are opaque in how they perform this transformation. Understanding the way in which the embedding relates to the original high-dimensional space is critical in exploratory data analysis. We previously proposed a Genetic Programming method that performed manifold learning by evolving mappings that are transparent and interpretable. This method required the dimensionality of the embedding to be known a priori, which makes it hard to use when little is known about a dataset. In this paper, we substantially extend our previous work, by introducing a multi-objective approach that automatically balances the competing objectives of manifold quality and dimensionality. Our proposed approach is competitive with a range of baseline and state-of-the-art manifold learning methods, while also providing a range (front) of solutions that give different trade-offs between quality and dimensionality. Furthermore, the learned models are shown to often be simple and efficient, utilising only a small number of features in an interpretable manner.


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Lensen, A., Xue, B. & Zhang, M. (2020). Multi-objective genetic programming for manifold learning: balancing quality and dimensionality. Genetic Programming and Evolvable Machines, 1-33.

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Genetic Programming and Evolvable Machines

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Springer Science and Business Media LLC

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