An analysis of dimensionality reduction techniques for visualizing evolution

Lorenzo, Andrea De; Medvet, Eric; Tušar, Tea; Bartoli, Alberto

doi:10.1145/3319619.3326868

Cited by 19 publications

(22 citation statements)

References 23 publications

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“…Dimensionality reduction techniques that have been used for this aim include principal component analysis [6], Sammon mapping [7], and tdistributed stochastic neighbour embedding [8]. With this approach, the positions of solutions relative to each other and the movement of individuals in a population can be visualised over an algorithm run using a sequence of 2-D frames or a 3-D stacking of 2-D frames [9]. STNs are similar to these approaches in that they also provide a visualisation of search dynamics and trajectories, but the main difference is that the location information and movement through the search space is captured in a graph object, allowing the information to be analysed using a wealth of mathematical and visualisation tools.…”

Section: Related Workmentioning

confidence: 99%

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Search trajectory networks: A tool for analysing and visualising the behaviour of metaheuristics

Ochoa

Malan

Blum

2021

Applied Soft Computing

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A large number of metaheuristics inspired by natural and social phenomena have been proposed in the last few decades, each trying to be more powerful and innovative than others. However, there is a lack of accessible tools to analyse, contrast and visualise the behaviour of metaheuristics when solving optimisation problems. When the metaphors are stripped away, are these algorithms different in their behaviour? To help to answer this question, we propose a data-driven, graph-based model, search trajectory networks (STNs) in order to analyse, visualise and directly contrast the behaviour of different types of metaheuristics. One strength of our approach is that it does not require any additional sampling or algorithmic methods. Instead, the models are constructed from data gathered while the metaheuristics are solving the optimisation problems. We present our methodology, and consider in detail two case studies covering both continuous and combinatorial optimisation. In terms of metaheuristics, our case studies cover the main current paradigms: evolutionary, swarm, and stochastic local search approaches.

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Section: Related Workmentioning

confidence: 99%

“…Others have proposed techniques for visualising the behaviour of search algorithms [6][7][8][9]. These approaches use dimensionality reduction to map search spaces to two or three dimensions and in this way track search progress.…”

Section: Introductionmentioning

confidence: 99%

Search trajectory networks: A tool for analysing and visualising the behaviour of metaheuristics

Ochoa

Malan

Blum

2021

Applied Soft Computing

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“…For example, GP has been used to visualise the quality of solutions in job shop scheduling [33], and as one criteria in a multi-objective GP classification problem [16]. There has also been recent research on using non-EC manifold learning to visualise EC methods themselves [26,30].…”

Section: Gp-malmentioning

confidence: 99%

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

Lensen

Zhang

Xue

2020

Genet Program Evolvable Mach

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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 tradeoffs 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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Section: Gp-malmentioning

confidence: 99%

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

Lensen¹,

Zhang²,

Xue³

2020

Preprint

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© 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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An analysis of dimensionality reduction techniques for visualizing evolution

Cited by 19 publications

References 23 publications

Search trajectory networks: A tool for analysing and visualising the behaviour of metaheuristics

Search trajectory networks: A tool for analysing and visualising the behaviour of metaheuristics

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

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

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