Spectral Embedding

Spectral embedding techniques aim to represent complex data, such as graphs or hyperspectral images, in lower-dimensional spaces while preserving essential structural information. Current research focuses on developing efficient and scalable algorithms, including those based on graph convolutional networks, random Fourier features, and neural networks, to address challenges posed by high dimensionality and large datasets. These advancements are improving performance in various applications, such as graph clustering, hyperspectral image classification, and single-cell genomics analysis, by enabling more effective data analysis and pattern recognition. Furthermore, ongoing work explores connections between spectral embedding and other machine learning paradigms, like contrastive learning and matrix completion, to enhance theoretical understanding and practical applicability.

Papers

July 5, 2022

TractoFormer: A Novel Fiber-level Whole Brain Tractography Analysis Framework Using Spectral Embedding and Vision Transformers
Fan Zhang, Tengfei Xue, Weidong Cai, Yogesh Rathi, Carl-Fredrik Westin, Lauren J O'Donnell
Vision Transformer Spectral Embedding Cranial Nerve Tractography Whole Brain Tractography

June 14, 2022

SpecNet2: Orthogonalization-free spectral embedding by neural networks
Ziyu Chen, Yingzhou Li, Xiuyuan Cheng
Neural Network Kernel Matrix Post Hoc Orthogonalization Spectral Method Spectral Embedding Orthogonal Transforms

May 31, 2022

Generalised Implicit Neural Representations
Daniele Grattarola, Pierre Vandergheynst
Implicit Neural Representation Graph Signal Spectral Embedding Non Euclidean Domain

May 23, 2022

Contrastive and Non-Contrastive Self-Supervised Learning Recover Global and Local Spectral Embedding Methods
Randall Balestriero, Yann LeCun
Self Supervised Learning Spectral Embedding Non Contrastive Self Supervised Learning Laplacian Eigenmaps Spectral Space

March 18, 2022

Hypergraph Modeling via Spectral Embedding Connection: Hypergraph Cut, Weighted Kernel $k$-means, and Heat Kernel
Shota Saito
Spectral Clustering K$ Mean Pairwise Similarity Spectral Embedding Graph Cut Hypergraph Model Heat Kernel

November 22, 2021

A Free Lunch from the Noise: Provable and Practical Exploration for Representation Learning
Tongzheng Ren, Tianjun Zhang, Csaba Szepesvári, Bo Dai
Reinforcement Learning Deep Learning Representation Learning Industrial Disturbing Noise Free Lunch Spectral Embedding Transition Operator

Spectral Embedding

Papers

TractoFormer: A Novel Fiber-level Whole Brain Tractography Analysis Framework Using Spectral Embedding and Vision Transformers

SpecNet2: Orthogonalization-free spectral embedding by neural networks

Generalised Implicit Neural Representations

Contrastive and Non-Contrastive Self-Supervised Learning Recover Global and Local Spectral Embedding Methods

Hypergraph Modeling via Spectral Embedding Connection: Hypergraph Cut, Weighted Kernel $k$-means, and Heat Kernel

A Free Lunch from the Noise: Provable and Practical Exploration for Representation Learning