Improving Short-term Output Power Forecasting Using Topological Data Analysis and Machine Learning

Senekane, Makhamisa; Matjelo, Naleli Jubert; Taele, B. M.

doi:10.1109/icecet52533.2021.9698599

Cited by 2 publications

(6 citation statements)

References 32 publications

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“…Note however that when a large feature vector is used to represent PDs, the curse of dimensionality comes into play. In this case, variable selection, regularization approaches, or dropout methods should be considered [Pun et al, 2022].…”

Section: Homological Feature Vectorizationsmentioning

confidence: 99%

“…As discussed, vectorization methods can be used in input space, however, kernel-based models are another important way to combine PD information with machine learning models [Kwitt et al, 2015]. Since metrics can be modified into kernels, various approaches have been proposed to induce kernel function from PD information [Pun et al, 2022] and into traditional machine learning approaches like PCA and SVM. Topological-based kernel methods have been used successfully in various ways [Zhu et al, 2016;Kwitt et al, 2015], however techniques based on kernel methods suffer from scalability issues [Pun et al, 2022], as training typically scales poorly with the sample number (e.g., roughly cubic in the case of kernel-SVMs).…”

Section: Homological Feature Vectorizationsmentioning

confidence: 99%

“…Since metrics can be modified into kernels, various approaches have been proposed to induce kernel function from PD information [Pun et al, 2022] and into traditional machine learning approaches like PCA and SVM. Topological-based kernel methods have been used successfully in various ways [Zhu et al, 2016;Kwitt et al, 2015], however techniques based on kernel methods suffer from scalability issues [Pun et al, 2022], as training typically scales poorly with the sample number (e.g., roughly cubic in the case of kernel-SVMs). We do not discuss topological kernel methods any further in this paper.…”

Section: Homological Feature Vectorizationsmentioning

confidence: 99%

“…• TDA is noise-resistant in several different problems, including the classification of 3D surface meshes, the recognition of 2D object shapes, the manifold of natural image patches, analyzing activity patterns of the visual cortex, and clustering [Pun et al, 2022;Ali et al, 2022].…”

Section: Topological Deep Learning (Tdl)mentioning

confidence: 99%

“…Recently, transformers were used for PDs embedding. Persformer [Reinauer et al, 2021] architecture showed superiority in synthetic and graph tasks while having some interpretability features. Note that transformers without positional encoding can be made as expressive as Deep Sets.…”

Section: Learning Topological Features Embeddingmentioning

confidence: 99%

See 4 more Smart Citations

Topological Deep Learning: A Review of an Emerging Paradigm

Zia¹,

Khamis²,

Nichols³

et al. 2023

Preprint

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Topological data analysis (TDA) provides insight into data shape. The summaries obtained by these methods are principled global descriptions of multi-dimensional data whilst exhibiting stable properties such as robustness to deformation and noise. Such properties are desirable in deep learning pipelines but they are typically obtained using non-TDA strategies. This is partly caused by the difficulty of combining TDA constructs (e.g. barcode and persistence diagrams) with current deep learning algorithms. Fortunately, we are now witnessing a growth of deep learning applications embracing topologically-guided components. In this survey, we review the nascent field of topological deep learning by first revisiting core concepts of TDA. We then explore how the use of TDA techniques has evolved over time to support deep learning frameworks, and how they can be integrated into different aspects of deep learning. Furthermore, we touch on TDA usage for analyzing existing deep models; deep topological analytics. Finally, we discuss the challenges and future prospects of topological deep learning.

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Section: Homological Feature Vectorizationsmentioning

confidence: 99%

Section: Homological Feature Vectorizationsmentioning

confidence: 99%

Section: Homological Feature Vectorizationsmentioning

confidence: 99%

Section: Topological Deep Learning (Tdl)mentioning

confidence: 99%

Section: Learning Topological Features Embeddingmentioning

confidence: 99%

See 3 more Smart Citations

Topological Deep Learning: A Review of an Emerging Paradigm

Zia¹,

Khamis²,

Nichols³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

Topological deep learning: a review of an emerging paradigm

Zia,

Khamis,

Nichols

et al. 2024

Artif Intell Rev

View full text Add to dashboard Cite

Topological deep learning (TDL) is an emerging area that combines the principles of Topological data analysis (TDA) with deep learning techniques. TDA provides insight into data shape; it obtains global descriptions of multi-dimensional data whilst exhibiting robustness to deformation and noise. Such properties are desirable in deep learning pipelines, but they are typically obtained using non-TDA strategies. This is partly caused by the difficulty of combining TDA constructs (e.g. barcode and persistence diagrams) with current deep learning algorithms. Fortunately, we are now witnessing a growth of deep learning applications embracing topologically-guided components. In this survey, we review the nascent field of topological deep learning by first revisiting the core concepts of TDA. We then explore how the use of TDA techniques has evolved over time to support deep learning frameworks, and how they can be integrated into different aspects of deep learning. Furthermore, we touch on TDA usage for analyzing existing deep models; deep topological analytics. Finally, we discuss the challenges and future prospects of topological deep learning.

show abstract

Improving Short-term Output Power Forecasting Using Topological Data Analysis and Machine Learning

Cited by 2 publications

References 32 publications

Topological Deep Learning: A Review of an Emerging Paradigm

Topological Deep Learning: A Review of an Emerging Paradigm

Topological deep learning: a review of an emerging paradigm

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