ALPCAHUS: Subspace Clustering for Heteroscedastic Data

• URL: http://arxiv.org/abs/2505.18918v2
• Date: Sun, 01 Jun 2025 14:48:10 GMT
• Title: ALPCAHUS: Subspace Clustering for Heteroscedastic Data
• Authors: Javier Salazar Cavazos, Jeffrey A Fessler, Laura Balzano,
• Abstract summary: This paper develops a heteroscedastic-focused subspace clustering method, named ALPCAHUS.<n>It estimates the sample-wise noise variances and uses this information to improve the estimate of the subspace bases associated with the low-rank structure of the data.
• Score: 15.812312064457867
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Principal component analysis (PCA) is a key tool in the field of data dimensionality reduction. Various methods have been proposed to extend PCA to the union of subspace (UoS) setting for clustering data that come from multiple subspaces like K-Subspaces (KSS). However, some applications involve heterogeneous data that vary in quality due to noise characteristics associated with each data sample. Heteroscedastic methods aim to deal with such mixed data quality. This paper develops a heteroscedastic-focused subspace clustering method, named ALPCAHUS, that can estimate the sample-wise noise variances and use this information to improve the estimate of the subspace bases associated with the low-rank structure of the data. This clustering algorithm builds on K-Subspaces (KSS) principles by extending the recently proposed heteroscedastic PCA method, named LR-ALPCAH, for clusters with heteroscedastic noise in the UoS setting. Simulations and real-data experiments show the effectiveness of accounting for data heteroscedasticity compared to existing clustering algorithms. Code available at https://github.com/javiersc1/ALPCAHUS.

Related papers

• ALPCAH: Subspace Learning for Sample-wise Heteroscedastic Data [15.812312064457867]
  This paper develops a subspace learning method, named ALPCAH, that can estimate the sample-wise noise variances.<n>Our method makes no distributional assumptions of the low-rank component and does not assume that the noise variances are known.<n> Additionally, this paper develops a matrix factorized version of ALPCAH, named LR-ALPCAH, that is much faster and more memory efficient at the cost of requiring subspace dimension to be known or estimated.
  arXiv  Detail & Related papers  (2025-05-12T06:49:47Z)
• Tackling Diverse Minorities in Imbalanced Classification [80.78227787608714]
  Imbalanced datasets are commonly observed in various real-world applications, presenting significant challenges in training classifiers. We propose generating synthetic samples iteratively by mixing data samples from both minority and majority classes. We demonstrate the effectiveness of our proposed framework through extensive experiments conducted on seven publicly available benchmark datasets.
  arXiv  Detail & Related papers  (2023-08-28T18:48:34Z)
• ALPCAH: Sample-wise Heteroscedastic PCA with Tail Singular Value Regularization [17.771454131646312]
  Principal component analysis is a key tool in the field of data dimensionality reduction. This paper develops a PCA method that can estimate the sample-wise noise variances. It is done without distributional assumptions of the low-rank component and without assuming the noise variances are known.
  arXiv  Detail & Related papers  (2023-07-06T03:11:11Z)
• Adaptive Graph Convolutional Subspace Clustering [10.766537212211217]
  Spectral-type subspace clustering algorithms have shown excellent performance in many subspace clustering applications. In this paper, inspired by graph convolutional networks, we use the graph convolution technique to develop a feature extraction method and a coefficient matrix constraint simultaneously. We claim that by using AGCSC, the aggregated feature representation of original data samples is suitable for subspace clustering.
  arXiv  Detail & Related papers  (2023-05-05T10:27:23Z)
• Differentially Private Federated Clustering over Non-IID Data [59.611244450530315]
  clustering clusters (FedC) problem aims to accurately partition unlabeled data samples distributed over massive clients into finite clients under the orchestration of a server. We propose a novel FedC algorithm using differential privacy convergence technique, referred to as DP-Fed, in which partial participation and multiple clients are also considered. Various attributes of the proposed DP-Fed are obtained through theoretical analyses of privacy protection, especially for the case of non-identically and independently distributed (non-i.i.d.) data.
  arXiv  Detail & Related papers  (2023-01-03T05:38:43Z)
• A One-shot Framework for Distributed Clustered Learning in Heterogeneous Environments [54.172993875654015]
  The paper proposes a family of communication efficient methods for distributed learning in heterogeneous environments. One-shot approach, based on local computations at the users and a clustering based aggregation step at the server is shown to provide strong learning guarantees. For strongly convex problems it is shown that, as long as the number of data points per user is above a threshold, the proposed approach achieves order-optimal mean-squared error rates in terms of the sample size.
  arXiv  Detail & Related papers  (2022-09-22T09:04:10Z)
• Subspace clustering in high-dimensions: Phase transitions \& Statistical-to-Computational gap [24.073221004661427]
  A simple model to study subspace clustering is the high-dimensional $k$-Gaussian mixture model. We provide an exact characterization of the statistically optimal reconstruction error in this model in the high-dimensional regime with extensive sparsity.
  arXiv  Detail & Related papers  (2022-05-26T17:47:35Z)
• Determinantal consensus clustering [77.34726150561087]
  We propose the use of determinantal point processes or DPP for the random restart of clustering algorithms. DPPs favor diversity of the center points within subsets. We show through simulations that, contrary to DPP, this technique fails both to ensure diversity, and to obtain a good coverage of all data facets.
  arXiv  Detail & Related papers  (2021-02-07T23:48:24Z)
• A Method for Handling Multi-class Imbalanced Data by Geometry based Information Sampling and Class Prioritized Synthetic Data Generation (GICaPS) [15.433936272310952]
  This paper looks into the problem of handling imbalanced data in a multi-label classification problem. Two novel methods are proposed that exploit the geometric relationship between the feature vectors. The efficacy of the proposed methods is analyzed by solving a generic multi-class recognition problem.
  arXiv  Detail & Related papers  (2020-10-11T04:04:26Z)
• LSD-C: Linearly Separable Deep Clusters [145.89790963544314]
  We present LSD-C, a novel method to identify clusters in an unlabeled dataset. Our method draws inspiration from recent semi-supervised learning practice and proposes to combine our clustering algorithm with self-supervised pretraining and strong data augmentation. We show that our approach significantly outperforms competitors on popular public image benchmarks including CIFAR 10/100, STL 10 and MNIST, as well as the document classification dataset Reuters 10K.
  arXiv  Detail & Related papers  (2020-06-17T17:58:10Z)
• Stable and consistent density-based clustering via multiparameter persistence [77.34726150561087]
  We consider the degree-Rips construction from topological data analysis. We analyze its stability to perturbations of the input data using the correspondence-interleaving distance. We integrate these methods into a pipeline for density-based clustering, which we call Persistable.
  arXiv  Detail & Related papers  (2020-05-18T19:45:04Z)
• Learnable Subspace Clustering [76.23527400396151]
  We develop a learnable subspace clustering paradigm to efficiently solve the large-scale subspace clustering problem. The key idea is to learn a parametric function to partition the high-dimensional subspaces into their underlying low-dimensional subspaces. To the best of our knowledge, this paper is the first work to efficiently cluster millions of data points among the subspace clustering methods.
  arXiv  Detail & Related papers  (2020-04-09T12:53:28Z)

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.