Multi-Objective Genetic Programming for Manifold Learning: Balancing Quality and Dimensionality

• URL: http://arxiv.org/abs/2001.01331v1
• Date: Sun, 5 Jan 2020 23:24:33 GMT
• Title: Multi-Objective Genetic Programming for Manifold Learning: Balancing Quality and Dimensionality
• Authors: Andrew Lensen, Mengjie Zhang, Bing Xue
• Abstract summary: State-of-the-art manifold learning algorithms are opaque in how they perform this transformation. We introduce 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.
• Score: 4.4181317696554325
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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