Learning Reconstructive Embeddings in Reproducing Kernel Hilbert Spaces via the Representer Theorem

📰 ArXiv cs.AI

Learn to reconstruct high-dimensional data using Reproducing Kernel Hilbert Spaces and the Representer Theorem for manifold learning

advanced Published 7 May 2026

Action Steps

Apply the Representer Theorem to optimize vector autorepresentation in RKHS
Reconstruct each observation as a linear combination of other samples in the RKHS
Utilize the reconstructed embeddings for manifold learning and dimensionality reduction
Implement the algorithm using a suitable programming language, such as Python or MATLAB
Evaluate the performance of the reconstructive embeddings using metrics like reconstruction error or manifold similarity

Who Needs to Know This

Data scientists and machine learning engineers can benefit from this technique to improve their representation learning approaches and uncover latent structures in complex data

Key Insight

💡 The Representer Theorem can be used to optimize vector autorepresentation in RKHS, enabling effective reconstruction-based manifold learning

Full Article

Title: Learning Reconstructive Embeddings in Reproducing Kernel Hilbert Spaces via the Representer Theorem

Abstract:
arXiv:2601.05811v1 Announce Type: cross Abstract: Motivated by the growing interest in representation learning approaches that uncover the latent structure of high-dimensional data, this work proposes new algorithms for reconstruction-based manifold learning within Reproducing-Kernel Hilbert Spaces (RKHS). Each observation is first reconstructed as a linear combination of the other samples in the RKHS, by optimizing a vector form of the Representer Theorem for their autorepresentation property.

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