Beyond Linear Subspace Clustering: A Comparative Study of Nonlinear Manifold Clustering Algorithms

• URL: http://arxiv.org/abs/2103.10656v1
• Date: Fri, 19 Mar 2021 06:34:34 GMT
• Title: Beyond Linear Subspace Clustering: A Comparative Study of Nonlinear Manifold Clustering Algorithms
• Authors: Maryam Abdolali, Nicolas Gillis
• Abstract summary: Subspace clustering is an important unsupervised clustering approach. We introduce a new taxonomy to classify the state-of-the-art approaches into three categories, namely locality preserving, kernel based, and neural network based. The detailed analysis of these approaches unfolds potential research directions and unsolved challenges in this field.
• Score: 22.564682739914424
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 prominent subspace clustering algorithms rely on the representation of the data points as linear combinations of other data points, which is known as a self-expressive representation. To overcome the restrictive linearity assumption, numerous nonlinear approaches were proposed to extend successful subspace clustering approaches to data on a union of nonlinear manifolds. In this comparative study, we provide a comprehensive overview of nonlinear subspace clustering approaches proposed in the last decade. We introduce a new taxonomy to classify the state-of-the-art approaches into three categories, namely locality preserving, kernel based, and neural network based. The major representative algorithms within each category are extensively compared on carefully designed synthetic and real-world data sets. The detailed analysis of these approaches unfolds potential research directions and unsolved challenges in this field.

Related papers

• Synergistic eigenanalysis of covariance and Hessian matrices for enhanced binary classification [75.90957645766676]
  We present a novel approach that combines the eigenanalysis of a covariance matrix evaluated on a training set with a Hessian matrix evaluated on a deep learning model. Our approach is substantiated by formal proofs that establish its capability to maximize between-class mean distance and minimize within-class variances.
  arXiv  Detail & Related papers  (2024-02-14T16:10:42Z)
• Unsupervised Manifold Linearizing and Clustering [19.879641608165887]
  We propose to optimize the Maximal Coding Reduction metric with respect to both the data representation and a novel doubly cluster membership. Experiments on CIFAR-10, -20, -100, and TinyImageNet-200 datasets show that the proposed method is much more accurate and scalable than state-of-the-art deep clustering methods.
  arXiv  Detail & Related papers  (2023-01-04T20:08:23Z)
• Unified Multi-View Orthonormal Non-Negative Graph Based Clustering Framework [74.25493157757943]
  We formulate a novel clustering model, which exploits the non-negative feature property and incorporates the multi-view information into a unified joint learning framework. We also explore, for the first time, the multi-model non-negative graph-based approach to clustering data based on deep features.
  arXiv  Detail & Related papers  (2022-11-03T08:18:27Z)
• Deep Clustering: A Comprehensive Survey [53.387957674512585]
  Clustering analysis plays an indispensable role in machine learning and data mining. Deep clustering, which can learn clustering-friendly representations using deep neural networks, has been broadly applied in a wide range of clustering tasks. Existing surveys for deep clustering mainly focus on the single-view fields and the network architectures, ignoring the complex application scenarios of clustering.
  arXiv  Detail & Related papers  (2022-10-09T02:31:32Z)
• Enriched Robust Multi-View Kernel Subspace Clustering [5.770309971945476]
  Subspace clustering is to find underlying low-dimensional subspaces and cluster the data points correctly. Most existing methods suffer from two critical issues. We propose a novel multi-view subspace clustering method.
  arXiv  Detail & Related papers  (2022-05-21T03:06:24Z)
• Provable Data Clustering via Innovation Search [32.530406356676274]
  This paper studies the subspace clustering problem in which data points collected from high-dimensional ambient space lie in a union of linear subspaces. A recently proposed clustering method termed Innovation Pursuit, computed a set of optimal directions to build the adjacency matrix.
  arXiv  Detail & Related papers  (2021-08-16T04:16:38Z)
• Spatially Coherent Clustering Based on Orthogonal Nonnegative Matrix Factorization [0.0]
  We introduce in this work clustering models based on a total variation (TV) regularization procedure on the cluster membership matrix. We provide a numerical evaluation of all proposed methods on a hyperspectral dataset obtained from a matrix-assisted laser desorption/ionisation imaging measurement.
  arXiv  Detail & Related papers  (2021-04-25T23:40:41Z)
• Clustering Ensemble Meets Low-rank Tensor Approximation [50.21581880045667]
  This paper explores the problem of clustering ensemble, which aims to combine multiple base clusterings to produce better performance than that of the individual one. We propose a novel low-rank tensor approximation-based method to solve the problem from a global perspective. Experimental results over 7 benchmark data sets show that the proposed model achieves a breakthrough in clustering performance, compared with 12 state-of-the-art methods.
  arXiv  Detail & Related papers  (2020-12-16T13:01:37Z)
• Scalable Hierarchical Agglomerative Clustering [65.66407726145619]
  Existing scalable hierarchical clustering methods sacrifice quality for speed. We present a scalable, agglomerative method for hierarchical clustering that does not sacrifice quality and scales to billions of data points.
  arXiv  Detail & Related papers  (2020-10-22T15:58:35Z)
• A Critique of Self-Expressive Deep Subspace Clustering [23.971512395191308]
  Subspace clustering is an unsupervised clustering technique designed to cluster data that is supported on a union of linear subspaces. We show that there are a number of potential flaws with this approach which have not been adequately addressed in prior work.
  arXiv  Detail & Related papers  (2020-10-08T00:14:59Z)
• Unsupervised Multi-view Clustering by Squeezing Hybrid Knowledge from Cross View and Each View [68.88732535086338]
  This paper proposes a new multi-view clustering method, low-rank subspace multi-view clustering based on adaptive graph regularization. Experimental results for five widely used multi-view benchmarks show that our proposed algorithm surpasses other state-of-the-art methods by a clear margin.
  arXiv  Detail & Related papers  (2020-08-23T08:25:06Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.