arXiv Machine Learning
6d ago
Spectral graph clustering with inhomogeneous latent geometry
arXiv:2608. 11321v1 Announce Type: cross Abstract: We study spectral clustering in the presence of a confounding latent geometry.
Analytic Torsion and Spectral Gap Capture Persistent-Laplacian Performance
arXiv:2606. 16990v1 Announce Type: new Abstract: While persistent Laplacians (PL) offer a richer geometric representation of data than persistent homology, utilizing their full eigenspectrum for learning tasks is often hampered by high dimensionality and the ``varying length'' problem across different filtration scales.
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PIEFS: Physics-Informed Eigenfunction Features with Learnable Scaling
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Group Invariant Spectral Embedding
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Topological Neural Operators
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Topology-Driven Clustering: Enhancing Performance with Betti Number Filtration
arXiv:2505. 04346v2 Announce Type: replace Abstract: Clustering aims at partitioning data points into groups of similar objects without knowing about the class labels.
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Topology-Preserving Neural Operator Learning via Hodge Decomposition
arXiv:2605. 13834v2 Announce Type: replace-cross Abstract: In this paper, we study solution operators of physical field equations on geometric meshes from a function-space perspective.
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Non-negative Matrix Factorisation with Topological Regularisation
arXiv:2606. 17531v1 Announce Type: new Abstract: We investigate the learning of interpretable bases in non-negative matrix factorisation (NMF) by regularising the topology of the learned basis functions.
arXiv Machine Learning
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Robust Tangent Space Estimation via Laplacian Eigenvector Gradient Orthogonalization
arXiv:2510. 02308v2 Announce Type: replace Abstract: Estimating the tangent spaces of a data manifold is a fundamental problem in geometric data analysis.
arXiv AI
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SFO: Learning PDE Operators via Spectral Filtering
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arXiv Machine Learning
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Quantum Topological Data Encoding
arXiv:2607. 13847v1 Announce Type: cross Abstract: Many datasets encountered across a wide range of domains possess rich geometric and topological structure that is difficult to capture using conventional vector-based representations.
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Unreduced Persistence Diagrams for Topological Machine Learning
arXiv:2507. 07156v2 Announce Type: replace-cross Abstract: Supervised machine learning pipelines trained on features derived from persistent homology have been experimentally observed to ignore much of the information contained in a persistence diagram.
arXiv AI
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Dimensionality reduction for homological stability and global structure preservation
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