mailitics

Category: math.DG

  • Central limit theorems for the eigenvalues of graph Laplacians on data clouds

    Central limit theorems for the eigenvalues of graph Laplacians on data clouds arXiv:2507.18803v1 Announce Type: new Abstract: Given i.i.d. samples $X_n ={ x_1, dots, x_n }$ from a distribution supported on a low dimensional manifold ${M}$ embedded in Eucliden space, we consider the graph Laplacian operator $Delta_n$ associated to an $varepsilon$-proximity graph over $X_n$ and…

  • A Survey of Dimension Estimation Methods

    A Survey of Dimension Estimation Methods arXiv:2507.13887v1 Announce Type: new Abstract: It is a standard assumption that datasets in high dimension have an internal structure which means that they in fact lie on, or near, subsets of a lower dimension. In many instances it is important to understand the real dimension of the data, hence…

  • Categorical and geometric methods in statistical, manifold, and machine learning

    Categorical and geometric methods in statistical, manifold, and machine learning arXiv:2505.03862v1 Announce Type: new Abstract: We present and discuss applications of the category of probabilistic morphisms, initially developed in cite{Le2023}, as well as some geometric methods to several classes of problems in statistical, machine and manifold learning which shall be, along with many other topics,…

  • Supervised Quadratic Feature Analysis: An Information Geometry Approach to Dimensionality Reduction

    Supervised Quadratic Feature Analysis: An Information Geometry Approach to Dimensionality Reduction arXiv:2502.00168v1 Announce Type: new Abstract: Supervised dimensionality reduction aims to map labeled data to a low-dimensional feature space while maximizing class discriminability. Despite the availability of methods for learning complex non-linear features (e.g. Deep Learning), there is an enduring demand for dimensionality reduction methods…