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Mathematics
Special Issues
Machine Learning and Optimization for Clustering Algorithms
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Machine Learning and Optimization for Clustering Algorithms

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: 10 January 2026 | Viewed by 251

Special Issue Editor

Dr. Yalan Qin

E-Mail Website
Guest Editor
School of Communication and Information Engineering, Shanghai University, Shanghai 200444, China
Interests: machine learning; artificial intelligence security
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues, 

Subspace clustering in machine learning is useful for clustering data points according to the underlying subspaces. Many methods have been presented in recent years, among which Sparse Subspace Clustering (SSC), Low-Rank Representation (LRR) and Least Squares Regression clustering (LSR) are three representative methods. These approaches achieve good results by assuming the structure of errors as a prior and removing errors in the original input space by modeling them in their objective functions, followed by the optimization process. Subspace clustering aims to fit each category of data points by learning an underlying subspace and then conduct clustering according to the learned subspace. Ideally, the learned subspace is expected to be block diagonal such that the similarities between clusters are zeros. 

In this Special Issue, original research articles and reviews are welcome. I look forward to receiving your contributions.

Dr. Yalan Qin
Guest Editor

Manuscript Submission Information

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Keywords

  • machine learning
  • clustering
  • optimization

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Published Papers (1 paper)

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Research

23 pages, 21197 KiB  
Article
DLPLSR: Dual Label Propagation-Driven Least Squares Regression with Feature Selection for Semi-Supervised Learning
by Shuanghao Zhang, Zhengtong Yang and Zhaoyin Shi
Mathematics 2025, 13(14), 2290; https://doi.org/10.3390/math13142290 - 16 Jul 2025
Viewed by 145
Abstract
In the real world, most data are unlabeled, which drives the development of semi-supervised learning (SSL). Among SSL methods, least squares regression (LSR) has attracted attention for its simplicity and efficiency. However, existing semi-supervised LSR approaches suffer from challenges such as the insufficient [...] Read more.
In the real world, most data are unlabeled, which drives the development of semi-supervised learning (SSL). Among SSL methods, least squares regression (LSR) has attracted attention for its simplicity and efficiency. However, existing semi-supervised LSR approaches suffer from challenges such as the insufficient use of unlabeled data, low pseudo-label accuracy, and inefficient label propagation. To address these issues, this paper proposes dual label propagation-driven least squares regression with feature selection, named DLPLSR, which is a pseudo-label-free SSL framework. DLPLSR employs a fuzzy-graph-based clustering strategy to capture global relationships among all samples, and manifold regularization preserves local geometric consistency, so that it implements the dual label propagation mechanism for comprehensive utilization of unlabeled data. Meanwhile, a dual-feature selection mechanism is established by integrating orthogonal projection for maximizing feature information with an ℓ2,1-norm regularization for eliminating redundancy, thereby jointly enhancing the discriminative power. Benefiting from these two designs, DLPLSR boosts learning performance without pseudo-labeling. Finally, the objective function admits an efficient closed-form solution solvable via an alternating optimization strategy. Extensive experiments on multiple benchmark datasets show the superiority of DLPLSR compared to state-of-the-art LSR-based SSL methods. Full article
(This article belongs to the Special Issue Machine Learning and Optimization for Clustering Algorithms)
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