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Despite the empirical success and practical significance of (relational) knowledge distillation that matches (the relations of) features between teacher and student models, the corresponding theoretical interpretations remain limited for…

Machine Learning · Statistics 2023-10-25 Yijun Dong , Kevin Miller , Qi Lei , Rachel Ward

We investigate the question of studying spectral clustering in a Hilbert space where the set of points to cluster are drawn i.i.d. according to an unknown probability distribution whose support is a union of compact connected components. We…

Statistics Theory · Mathematics 2016-06-22 Ilaria Giulini

Despite tremendous advancements in Artificial Intelligence, learning from large sets of data in an unsupervised manner remains a significant challenge. Classical clustering algorithms often fail to discover complex dependencies in large…

Machine Learning · Computer Science 2023-07-18 Adam Piróg , Halina Kwaśnicka

Multi-label image classification is a fundamental but challenging task in computer vision. Great progress has been achieved by exploiting semantic relations between labels in recent years. However, conventional approaches are unable to…

Computer Vision and Pattern Recognition · Computer Science 2017-04-03 Feng Zhu , Hongsheng Li , Wanli Ouyang , Nenghai Yu , Xiaogang Wang

Kernel spectral clustering corresponds to a weighted kernel principal component analysis problem in a constrained optimization framework. The primal formulation leads to an eigen-decomposition of a centered Laplacian matrix at the dual…

Social and Information Networks · Computer Science 2014-12-03 Raghvendra Mall , Rocco Langone , Johan A. K. Suykens

Spectral clustering (SC) and graph-based semi-supervised learning (SSL) algorithms are sensitive to how graphs are constructed from data. In particular if the data has proximal and unbalanced clusters these algorithms can lead to poor…

Machine Learning · Statistics 2013-02-22 Jing Qian , Venkatesh Saligrama

In this paper, we design a hierarchical clustering algorithm for high-resolution hyperspectral images. At the core of the algorithm, a new rank-two nonnegative matrix factorizations (NMF) algorithm is used to split the clusters, which is…

Computer Vision and Pattern Recognition · Computer Science 2015-02-18 Nicolas Gillis , Da Kuang , Haesun Park

Commonly-used clustering algorithms usually find ellipsoidal, spherical or other regular-structured clusters, but are more challenged when the underlying groups lack formal structure or definition. Syncytial clustering is the name that we…

Methodology · Statistics 2020-07-30 Israel Almodóvar-Rivera , Ranjan Maitra

We take an image science perspective on the problem of determining brain network connectivity given functional activity. But adapting the concept of image resolution to this problem, we provide a new perspective on network partitioning for…

Neurons and Cognition · Quantitative Biology 2020-02-14 Keith Dillon , Yu-Ping Wang

Graph clustering aims at discovering a natural grouping of the nodes such that similar nodes are assigned to a common cluster. Many different algorithms have been proposed in the literature: for simple graphs, for graphs with attributes…

Machine Learning · Computer Science 2023-11-06 Ylli Sadikaj , Yllka Velaj , Sahar Behzadi , Claudia Plant

This paper considers metric spaces where distances between a pair of nodes are represented by distance intervals. The goal is to study methods for the determination of hierarchical clusters, i.e., a family of nested partitions indexed by a…

Social and Information Networks · Computer Science 2016-10-17 Weiyu Huang , Alejandro Ribeiro

Subspace clustering is the problem of clustering data that lie close to a union of linear subspaces. In the abstract form of the problem, where no noise or other corruptions are present, the data are assumed to lie in general position…

Computer Vision and Pattern Recognition · Computer Science 2020-02-13 Manolis C. Tsakiris , Rene Vidal

Clustering techniques are very attractive for extracting and identifying patterns in datasets. However, their application to very large spatial datasets presents numerous challenges such as high-dimensionality data, heterogeneity, and high…

Databases · Computer Science 2018-02-27 Malika Bendechache , Nhien-An Le-Khac , M-Tahar Kechadi

Spectral Clustering is a popular technique to split data points into groups, especially for complex datasets. The algorithms in the Spectral Clustering family typically consist of multiple separate stages (such as similarity matrix…

Machine Learning · Computer Science 2019-11-04 Yifei Wang , Rui Liu , Yong Chen , Hui Zhangs , Zhiwen Ye

In this paper we study variants of the widely used spectral clustering that partitions a graph into k clusters by (1) embedding the vertices of a graph into a low-dimensional space using the bottom eigenvectors of the Laplacian matrix, and…

Data Structures and Algorithms · Computer Science 2017-02-01 Richard Peng , He Sun , Luca Zanetti

Spectral clustering is known as a powerful technique in unsupervised data analysis. The vast majority of approaches to spectral clustering are driven by a single modality, leaving the rich information in multi-modal representations…

Computer Vision and Pattern Recognition · Computer Science 2026-03-17 Bo Peng , Yuanwei Hu , Bo Liu , Ling Chen , Jie Lu , Zhen Fang

Medical image segmentation is a critical step in computer-aided diagnosis, and convolutional neural networks are popular segmentation networks nowadays. However, the inherent local operation characteristics make it difficult to focus on the…

Computer Vision and Pattern Recognition · Computer Science 2023-05-18 Fenghe Tang , Jianrui Ding , Lingtao Wang , Min Xian , Chunping Ning

Cluster structure detection is a fundamental task for the analysis of graphs, in order to understand and to visualize their functional characteristics. Among the different cluster structure detection methods, spectral clustering is…

Machine Learning · Statistics 2020-04-09 Camille Champion , Blazère Mélanie , Burcelin Rémy , Loubes Jean-Michel , Risser Laurent

Given the potential difficulties in obtaining large quantities of labelled data, many works have explored the use of deep semi-supervised learning, which uses both labelled and unlabelled data to train a neural network architecture. The…

Machine Learning · Computer Science 2021-09-02 Philip Sellars , Angelica Aviles-Rivero , Carola Bibiane Schönlieb

Spectral clustering is one of the most popular methods for community detection in graphs. A key step in spectral clustering algorithms is the eigen decomposition of the $n{\times}n$ graph Laplacian matrix to extract its $k$ leading…

Machine Learning · Statistics 2018-09-10 Muni Sreenivas Pydi , Ambedkar Dukkipati