Dimensional Representation

Dimensional representation focuses on finding efficient and informative lower-dimensional representations of high-dimensional data, aiming to preserve crucial information while reducing computational complexity and improving interpretability. Current research explores various approaches, including contrastive learning for optimal sample complexity, manifold learning techniques for nonlinear data structures, and the development of novel clustering algorithms that leverage lower-dimensional projections for improved visualization and analysis. These advancements have significant implications for diverse fields, enhancing the performance of machine learning models in applications such as image classification, speech recognition, and the analysis of complex systems by enabling more efficient and interpretable data processing.

Papers

January 17, 2024

A Characterization Theorem for Equivariant Networks with Point-wise Activations
Marco Pacini, Xiaowen Dong, Bruno Lepri, Gabriele Santin
Equivariant Network Equivariant Neural Network Equivariant Layer Dimensional Representation Dynamic Activation

December 1, 2023

Optimal Sample Complexity of Contrastive Learning
Noga Alon, Dmitrii Avdiukhin, Dor Elboim, Orr Fischer, Grigory Yaroslavtsev
Contrastive Learning Sample Complexity Point Set \Ell_p$ Distance Dimensional Representation

May 17, 2023

Transcending Grids: Point Clouds and Surface Representations Powering Neurological Processing
Kishore Babu Nampalle, Pradeep Singh, Vivek Narayan Uppala, Sumit Gangwar, Rajesh Singh Negi, Balasubramanian Raman
Point Cloud Brain Tumor Sparse Point Cloud Neural Surface Grid World Dimensional Representation

November 7, 2022

visClust: A visual clustering algorithm based on orthogonal projections
Anna Breger, Clemens Karner, Martin Ehler
Image Processing State of the Art Algorithm Orthogonal prOjection Visual Clustering Dimensional Representation

October 27, 2022

Implications of sparsity and high triangle density for graph representation learning
Hannah Sansford, Alexander Modell, Nick Whiteley, Patrick Rubin-Delanchy
Graph Representation Learning Sparsity Increase Node Representation Future Implication Low Dimensional Manifold Sparse Graph Dense Environment Dimensional Representation

June 21, 2022

Analysis of Self-Supervised Learning and Dimensionality Reduction Methods in Clustering-Based Active Learning for Speech Emotion Recognition
Einari Vaaras, Manu Airaksinen, Okko Räsänen
Self Supervised Learning General Analysis Speech Emotion Recognition Dimensionality Reduction Feature Space Contrastive Predictive Coding Clustering Based Active Learning Dimensional Representation

June 7, 2022

NOMAD: Nonlinear Manifold Decoders for Operator Learning
Jacob H. Seidman, Georgios Kissas, Paris Perdikaris, George J. Pappas
Supervised Learning Operator Learning Low Dimensional Representation Linear Representation Dimensional Representation Nonlinear Manifold Decoder

November 4, 2021

ExClus: Explainable Clustering on Low-dimensional Data Representations
Xander Vankwikelberge, Bo Kang, Edith Heiter, Jefrey Lijffijt
Dimensionality Reduction Data Clustering Cluster Structure Explainable Clustering Interpretable Clustering Mutual Exclusivity Dimensional Representation