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We present a simple and fast geometric method for modeling data by a union of affine subspaces. The method begins by forming a collection of local best-fit affine subspaces, i.e., subspaces approximating the data in local neighborhoods. The…

Computer Vision and Pattern Recognition · Computer Science 2012-10-08 Teng Zhang , Arthur Szlam , Yi Wang , Gilad Lerman

Subspace clustering refers to the problem of clustering unlabeled high-dimensional data points into a union of low-dimensional linear subspaces, assumed unknown. In practice one may have access to dimensionality-reduced observations of the…

Information Theory · Computer Science 2014-04-29 Reinhard Heckel , Michael Tschannen , Helmut Bölcskei

Subspace clustering is an important unsupervised clustering approach. It is based on the assumption that the high-dimensional data points are approximately distributed around several low-dimensional linear subspaces. The majority of the…

Machine Learning · Computer Science 2021-12-20 Maryam Abdolali , Nicolas Gillis

Clustering real world data often faced with curse of dimensionality, where real world data often consist of many dimensions. Multidimensional data clustering evaluation can be done through a density-based approach. Density approaches based…

Databases · Computer Science 2010-12-30 Rahmat Widia Sembiring , Jasni Mohamad Zain

There is a growing interest in computer science, engineering, and mathematics for modeling signals in terms of union of subspaces and manifolds. Subspace segmentation and clustering of high dimensional data drawn from a union of subspaces…

Information Theory · Computer Science 2012-05-16 Akram Aldroubi , Ali Sekmen

This paper introduces {\em fusion subspace clustering}, a novel method to learn low-dimensional structures that approximate large scale yet highly incomplete data. The main idea is to assign each datum to a subspace of its own, and minimize…

Machine Learning · Computer Science 2022-05-24 Usman Mahmood , Daniel Pimentel-Alarcón

Extracting an understanding of the underlying system from high dimensional data is a growing problem in science. Discovering informative and meaningful features is crucial for clustering, classification, and low dimensional data embedding.…

Machine Learning · Statistics 2019-12-10 Samuel Melton , Sharad Ramanathan

Diffusion models recently have been successfully applied for the visual synthesis of strikingly realistic appearing images. This raises strong concerns about their potential for malicious purposes. In this paper, we propose using the…

Computer Vision and Pattern Recognition · Computer Science 2023-09-29 Peter Lorenz , Ricard Durall , Janis Keuper

We consider the problem of clustering a set of high-dimensional data points into sets of low-dimensional linear subspaces. The number of subspaces, their dimensions, and their orientations are unknown. We propose a simple and low-complexity…

Information Theory · Computer Science 2013-03-18 Reinhard Heckel , Helmut Bölcskei

Clustering is a fundamental unsupervised representation learning task with wide application in computer vision and pattern recognition. Deep clustering utilizes deep neural networks to learn latent representation, which is suitable for…

Computer Vision and Pattern Recognition · Computer Science 2023-12-27 Wenhao Wu , Weiwei Wang , Shengjiang Kong

This paper describes the systematic application of local topological methods for detecting interfaces and related anomalies in complicated high-dimensional data. By examining the topology of small regions around each point, one can…

Algebraic Topology · Mathematics 2022-05-25 Bernadette J Stolz , Jared Tanner , Heather A Harrington , Vidit Nanda

We propose a method to reconstruct and cluster incomplete high-dimensional data lying in a union of low-dimensional subspaces. Exploring the sparse representation model, we jointly estimate the missing data while imposing the intrinsic…

Computer Vision and Pattern Recognition · Computer Science 2017-09-06 João Carvalho , Manuel Marques , João P. Costeira

Subspace clustering is an unsupervised clustering technique designed to cluster data that is supported on a union of linear subspaces, with each subspace defining a cluster with dimension lower than the ambient space. Many existing…

Machine Learning · Computer Science 2021-03-23 Benjamin D. Haeffele , Chong You , René Vidal

This paper considers the problem of clustering a collection of unlabeled data points assumed to lie near a union of lower-dimensional planes. As is common in computer vision or unsupervised learning applications, we do not know in advance…

Information Theory · Computer Science 2013-01-31 Mahdi Soltanolkotabi , Emmanuel J. Candés

This letter presents a new spectral-clustering-based approach to the subspace clustering problem. Underpinning the proposed method is a convex program for optimal direction search, which for each data point d finds an optimal direction in…

Computer Vision and Pattern Recognition · Computer Science 2017-11-28 Mostafa Rahmani , George Atia

While convolution and self-attention are extensively used in learned image compression (LIC) for transform coding, this paper proposes an alternative called Contextual Clustering based LIC (CLIC) which primarily relies on clustering…

Image and Video Processing · Electrical Eng. & Systems 2024-01-23 Yichi Zhang , Zhihao Duan , Ming Lu , Dandan Ding , Fengqing Zhu , Zhan Ma

Subspace clustering is the problem of partitioning unlabeled data points into a number of clusters so that data points within one cluster lie approximately on a low-dimensional linear subspace. In many practical scenarios, the…

Machine Learning · Statistics 2019-01-24 Yining Wang , Yu-Xiang Wang , Aarti Singh

The concept of dimension is essential to grasp the complexity of data. A naive approach to determine the dimension of a dataset is based on the number of attributes. More sophisticated methods derive a notion of intrinsic dimension (ID)…

Machine Learning · Computer Science 2023-04-18 Maximilian Stubbemann , Tom Hanika , Friedrich Martin Schneider

It is a key to construct a similarity graph in graph-oriented subspace learning and clustering. In a similarity graph, each vertex denotes a data point and the edge weight represents the similarity between two points. There are two popular…

Machine Learning · Computer Science 2017-05-17 Liangli Zhen , Zhang Yi , Xi Peng , Dezhong Peng

High-dimensional datasets often contain multiple meaningful clusterings in different subspaces. For example, objects can be clustered either by color, weight, or size, revealing different interpretations of the given dataset. A variety of…

Machine Learning · Computer Science 2025-04-08 Collin Leiber , Dominik Mautz , Claudia Plant , Christian Böhm