Class Angular Distortion Index for Dimensionality Reduction

• URL: http://arxiv.org/abs/2605.00637v1
• Date: Fri, 01 May 2026 13:19:38 GMT
• Title: Class Angular Distortion Index for Dimensionality Reduction
• Abstract summary: Class Angular Distortion Index (CADI) is a metric that uses internal angles among point triples to determine the faithfulness of cluster organization in a projection.<n>We show cases on both real and synthetic data where existing cluster metrics fail, but CADI provides an interpretable result.
• Score: 0.22940141855172028
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Dimensionality reduction (DR) techniques are often characterized by whether they preserve global, high-level structures in the data or local, neighborhood structures. This distinction matters in visualization: global methods can obscure clusters while local methods can over-emphasize them. Yet, even when clusters appear distinct, their relative arrangement in the projection may be arbitrary or misleading, a common issue in techniques such as t-SNE and UMAP. Existing cluster quality metrics either only measure cluster separability or assume spherical, globular clusters in the original space. We introduce the Class Angular Distortion Index (CADI), a metric that uses internal angles among point triples to determine the faithfulness of cluster organization in a projection. We show cases on both real and synthetic data where existing cluster metrics fail, but CADI provides an interpretable result. Since it relies on computing angles, CADI is also differentiable, enabling optimization. We demonstrate this with a CADI-based DR technique.

Related papers

• Central Description Length (CDL) Clustering Validation Index [3.3517146652431378]
  Clustering validation indices (CVIs) provide internal scores for ranking candidate clusterings.<n>Most popular CVIs are built from Euclidean compactness and separation terms.<n>This paper introduces the Central Description Length (CDL) clustering validation index.
  arXiv  Detail & Related papers  (2026-06-02T22:47:09Z)
• Scalable Context-Preserving Model-Aware Deep Clustering for Hyperspectral Images [51.95768218975529]
  Subspace clustering has become widely adopted for the unsupervised analysis of hyperspectral images (HSIs)<n>Recent model-aware deep subspace clustering methods often use a two-stage framework, involving the calculation of a self-representation matrix with complexity of O(n2), followed by spectral clustering.<n>We propose a scalable, context-preserving deep clustering method based on basis representation, which jointly captures local and non-local structures for efficient HSI clustering.
  arXiv  Detail & Related papers  (2025-06-12T16:43:09Z)
• Categorical Data Clustering via Value Order Estimated Distance Metric Learning [53.28598689867732]
  This paper introduces a novel order distance metric learning approach to intuitively represent categorical attribute values.<n>A new joint learning paradigm is developed to alternatively perform clustering and order distance metric learning.<n>The proposed method achieves superior clustering accuracy on categorical and mixed datasets.
  arXiv  Detail & Related papers  (2024-11-19T08:23:25Z)
• Self-Supervised Graph Embedding Clustering [70.36328717683297]
  K-means one-step dimensionality reduction clustering method has made some progress in addressing the curse of dimensionality in clustering tasks. We propose a unified framework that integrates manifold learning with K-means, resulting in the self-supervised graph embedding framework.
  arXiv  Detail & Related papers  (2024-09-24T08:59:51Z)
• Can an unsupervised clustering algorithm reproduce a categorization system? [1.0485739694839669]
  We investigate whether unsupervised clustering can reproduce ground truth classes in a labeled dataset. We show that success depends on feature selection and the chosen distance metric.
  arXiv  Detail & Related papers  (2024-08-19T18:27:14Z)
• ABCDE: Application-Based Cluster Diff Evals [49.1574468325115]
  It aims to be practical: it allows items to have associated importance values that are application-specific, it is frugal in its use of human judgements when determining which clustering is better, and it can report metrics for arbitrary slices of items. The approach to measuring the delta in the clustering quality is novel: instead of trying to construct an expensive ground truth up front and evaluating the each clustering with respect to that, ABCDE samples questions for judgement on the basis of the actual diffs between the clusterings.
  arXiv  Detail & Related papers  (2024-07-31T08:29:35Z)
• High-dimensional Clustering onto Hamiltonian Cycle [30.17605416237686]
  Clustering aims to group unlabelled samples based on their similarities. This paper proposes a new framework called High-dimensional Clustering onto Hamiltonian Cycle.
  arXiv  Detail & Related papers  (2023-04-27T20:59:45Z)
• Enhancing cluster analysis via topological manifold learning [0.3823356975862006]
  We show that inferring the topological structure of a dataset before clustering can considerably enhance cluster detection. We combine manifold learning method UMAP for inferring the topological structure with density-based clustering method DBSCAN.
  arXiv  Detail & Related papers  (2022-07-01T15:53:39Z)
• Swarm Intelligence for Self-Organized Clustering [6.85316573653194]
  A swarm system called Databionic swarm (DBS) is introduced which is able to adapt itself to structures of high-dimensional data. By exploiting the interrelations of swarm intelligence, self-organization and emergence, DBS serves as an alternative approach to the optimization of a global objective function in the task of clustering.
  arXiv  Detail & Related papers  (2021-06-10T06:21:48Z)
• Towards Uncovering the Intrinsic Data Structures for Unsupervised Domain Adaptation using Structurally Regularized Deep Clustering [119.88565565454378]
  Unsupervised domain adaptation (UDA) is to learn classification models that make predictions for unlabeled data on a target domain. We propose a hybrid model of Structurally Regularized Deep Clustering, which integrates the regularized discriminative clustering of target data with a generative one. Our proposed H-SRDC outperforms all the existing methods under both the inductive and transductive settings.
  arXiv  Detail & Related papers  (2020-12-08T08:52:00Z)
• Scalable Hierarchical Agglomerative Clustering [65.66407726145619]
  Existing scalable hierarchical clustering methods sacrifice quality for speed. We present a scalable, agglomerative method for hierarchical clustering that does not sacrifice quality and scales to billions of data points.
  arXiv  Detail & Related papers  (2020-10-22T15:58:35Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.