The paper extends the h‑plot multidimensional scaling technique to handle three‑way asymmetric dissimilarities, enabling the extraction of archetypal profiles and clustering in a unified Euclidean space. It provides an explicit eigenvector‑based solution that avoids local minima, is scale‑invariant, computationally efficient, and includes a straightforward goodness‑of‑fit assessment. The method is benchmarked against existing models and demonstrated on a financial dataset, with all data and code made publicly available for reproducibility.
arXiv:2604.02535v2 Announce Type: replace Abstract: Dimensionality reduction (DR) involves two longstanding trade-offs. First, preserving local neighborhoods can come at the cost of global structure....
arXiv:2608. 14951v1 Announce Type: new Abstract: Low-rank matrix decompositions can uncover patterns and structure in data and have a number of different applications across many disciplines.
A Survey on Archetypal Analysis reviews the method introduced by Cutler and Breiman in 1994 for extracting archetypes—distinct aspects—from data, where each observation is expressed as a convex combination of these archetypes. The survey covers AA’s role in feature extraction, dimensionality reduction, and its interpretability, discusses its nonconvex optimization challenges, and surveys applications across various scientific fields. It also outlines best practices, limitations, and future research directions for AA.
arXiv:2607. 05464v1 Announce Type: cross Abstract: The success of categorical data clustering generally much relies on the distance metric that measures the dissimilarity degree between two objects.
arXiv:2608. 06990v1 Announce Type: cross Abstract: Clustering is a fundamental data mining technique for pattern recognition through unsupervised learning.
arXiv:2509.04603v4 Announce Type: replace-cross Abstract: When faced with new data, we often conduct a cluster analysis to obtain a better understanding of the data's structure and the archetypical s...
arXiv:2507.23559v2 Announce Type: replace-cross Abstract: Certain data are naturally modeled by networks or weighted graphs, be they biological networks or mobility networks. When there is no canonic...
The paper introduces View distance, a novel metric that projects high‑dimensional data onto all pairwise two‑dimensional planes and sums the Euclidean distances across these projections. It satisfies metric axioms, couples features, suppresses redundancy, and captures anisotropic geometry. To make it scalable, the authors propose a plane‑selection strategy using iterative Maximum Weight Matching, reducing complexity from ω(n²) to ω(k) and demonstrating competitive performance on twelve datasets.
arXiv:2608. 11269v1 Announce Type: cross Abstract: Omics datasets, particularly single-cell RNA sequencing data, are high-dimensional, sparse, noisy, and dominated by zero values, making faithful low-dimensional representation challenging.
arXiv:2607. 08746v1 Announce Type: cross Abstract: While UMAP is widely used for exploring high-dimensional data, typical workflows focus on its lower-dimensional embedding, largely overlooking the rich k-nearest-neighbor (kNN) graph that UMAP constructs internally.
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.
This paper examines how metric adjustments to Multidimensional Scaling (MDS) can enhance its effectiveness as a visual tool for pattern recognition. The distance under consideration, referred to as Max-D-SW, is an adjustment of the Max-Sliced Wasserstein distance.