arXiv:2608. 08704v1 Announce Type: cross Abstract: Kernel spectral clustering with a single bandwidth can be inadequate for data exhibiting multiple characteristic pairwise-distance scales, a problem particularly prevalent in the high-dimensional regime.
arXiv:2411. 12438v2 Announce Type: replace-cross Abstract: We develop a new approach for clustering non-spherical (i.
arXiv:2608. 19067v1 Announce Type: cross Abstract: The empirical success of diffusion models in generative modelling has motivated theoretical work, including quantitative error bounds and qualitative analyses that characterise the different phases of denoising.
The paper systematically evaluates how five dimensionality reduction methods—PCA, Kernel PCA, VAE, Isomap, and MDS—affect the performance of four clustering algorithms (k‑means, AHC, GMM, and OPTICS). Using the Adjusted Rand Index, the study compares clustering quality with and without dimensionality reduction at levels of k‑1, 25%, and 50% of the original dimensions. Results highlight that the choice of reduction technique and its level must be carefully matched to the data’s geometry and the clustering algorithm used.
arXiv:2608.21466v1 Announce Type: new Abstract: We develop spectral algorithms for selecting state-space partitions that define averaging kernels for finite, ergodic and reversible Markov chains. For...
arXiv:2608. 15313v1 Announce Type: cross Abstract: In this paper, we propose SHOPCA (Shape Operator-based Principal Component Analysis), a novel method for unsupervised metric learning and dimensionality reduction that incorporates differential geometric information into the covariance structure of classical PCA.
arXiv:2603.19657v2 Announce Type: replace-cross Abstract: We study model-order selection and component-mean estimation for multidimensional Gaussian mixture models with a known common covariance matr...
arXiv:2509. 22879v2 Announce Type: replace-cross Abstract: Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions.
The paper introduces a new dimensionality reduction technique that enhances nearest‑neighbour relationships to estimate high‑information projections. It constructs a matrix encoding local covariance via nearest‑neighbour pairs and shows that, under standard regularity conditions, this matrix consistently estimates the Density Information Matrix (DIM), a non‑parametric analogue of the Fisher Information Matrix. The authors also demonstrate the method’s practical usefulness for clustering and outlier detection.
arXiv:2606.20811v2 Announce Type: replace-cross Abstract: We study the problem of system identification in heterogeneous settings, where different systems may follow distinct underlying dynamics. Exi...
arXiv:2505.18918v4 Announce Type: replace-cross Abstract: Principal component analysis (PCA) is a key tool in the field of data dimensionality reduction. Various methods have been proposed to extend...
The paper introduces two randomized approaches to accelerate spectral co‑clustering of word‑document matrices: one based on randomized SVD via random projection, and another combining partial SVD with element‑wise random sampling. Experiments on real and synthetic data show both methods cut runtime compared to full SVD, with the projection technique offering more consistent performance across varied sparsity levels, while the sampling method excels on denser matrices. The study highlights that the choice of approximation should align with the data’s structural properties.