title: Interpretable non-linear dimensionality reduction using gaussian
    weighted linear transformation
summary: Dimensionality reduction techniques are fundamental for analyzing and
  visualizing high-dimensional data. With established methods like t-SNE and PCA
  presenting a trade-off between representational power and interpretability.
  This paper introduces a novel approach that bridges this gap by combining the
  interpretability of linear methods with the expressiveness of non-linear
  transformations. The proposed algorithm constructs a non-linear mapping between
  high-dimensional and low-dimensional spaces through a combination of linear
  transformations, each weighted by Gaussian functions. This architecture enables
  complex non-linear transformations while preserving the interpretability
  advantages of linear methods, as each transformation can be analyzed
  independently. The resulting model provides both powerful dimensionality
  reduction and transparent insights into the transformed space. Techniques for
  interpreting the learned transformations are presented, including methods for
  identifying suppressed dimensions and how space is expanded and contracted.
  These tools enable practitioners to understand how the algorithm preserves and
  modifies geometric relationships during dimensionality reduction. To ensure the
  practical utility of this algorithm, the creation of user-friendly software
  packages is emphasized, facilitating its adoption in both academia and
  industry.
paper_authors._id: 680b2b8c6bd146aa35a48222
paper_authors.name: Erik Bergh
paper_authors.status: extracted_confirmed
paper_authors.statusLastChangedAt: 2025-04-25T06:39:03.785Z
paper_authors._id: 64d496b04ab89be0de7fb1a9
paper_authors.avatarUrl: /avatars/fe60082c26e0d98126e62ee6257a374f.svg
paper_authors.fullname: Erik Bergh
paper_authors.type: user
paper_authors.user: erikbergh
paper_title: Interpretable non-linear dimensionality reduction using gaussian
    weighted linear transformation
paper_summary: Dimensionality reduction techniques are fundamental for analyzing and
  visualizing high-dimensional data. With established methods like t-SNE and PCA
  presenting a trade-off between representational power and interpretability.
  This paper introduces a novel approach that bridges this gap by combining the
  interpretability of linear methods with the expressiveness of non-linear
  transformations. The proposed algorithm constructs a non-linear mapping between
  high-dimensional and low-dimensional spaces through a combination of linear
  transformations, each weighted by Gaussian functions. This architecture enables
  complex non-linear transformations while preserving the interpretability
  advantages of linear methods, as each transformation can be analyzed
  independently. The resulting model provides both powerful dimensionality
  reduction and transparent insights into the transformed space. Techniques for
  interpreting the learned transformations are presented, including methods for
  identifying suppressed dimensions and how space is expanded and contracted.
  These tools enable practitioners to understand how the algorithm preserves and
  modifies geometric relationships during dimensionality reduction. To ensure the
  practical utility of this algorithm, the creation of user-friendly software
  packages is emphasized, facilitating its adoption in both academia and
  industry.
paper_ai_summary: A new dimensionality reduction approach combines linear interpretability with non-linear expressiveness through Gaussian-weighted linear transformations, offering powerful reductions and transparent insights.
paper_ai_keywords: t-SNE PCA non-linear transformations Gaussian functions interpretability dimensionality reduction high-dimensional data low-dimensional spaces user-friendly software packages