LoomSC：基于投影子因子分解与精确谱约简的可扩展深度子空间聚类
LoomSC: Scalable Deep Subspace Clustering with Projector Factorization and Exact Spectral Reduction
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中文总结 AI 辅助
LoomSC通过投影子因子分解和精确谱约简，实现了线性复杂度的大规模子空间聚类，在多个基准上取得最优性能。
中文摘要 AI 辅助
稠密的自表达矩阵和全亲和度谱聚类限制了子空间聚类的可扩展性。我们提出了子空间聚类的潜在正交优化模型（LoomSC），该框架通过投影子因子分解和精确谱约简解决了这两个瓶颈。受最小二乘回归的谱结构启发，LoomSC通过两个薄因子联合学习潜在特征和投影子自表示。交替的Procrustes和最小二乘更新在保持系数矩阵隐式的同时，维持样本因子的正交性。我们构造了一个非负二次亲和度，以保留投影子的支撑集。一个精确的特征映射将其归一化谱问题约简为一个特征值问题，其维度仅取决于因子宽度。既不需要形成完整的亲和度，也不需要形成样本拉普拉斯矩阵。我们的分析量化了投影子近似，并识别了子空间保持和子空间内连通性的条件。对于固定的维度和迭代预算，完整流程在样本数量上具有线性的时间和内存复杂度。在五个图像聚类基准上，LoomSC在全部15项数据集-指标比较中，相对于9个最先进的基线，排名第一或第二。其平均准确率超过最高基线平均值6.66个百分点。合成实验可扩展到500,000个样本，同时保持至少99.8%的准确率。
英文摘要
Dense self-expression matrices and full-affinity spectral clustering limit the scalability of subspace clustering. We introduce the Latent Orthogonal Optimization Model for Subspace Clustering (LoomSC), a framework that addresses both bottlenecks through projector factorization and exact spectral reduction. Motivated by the spectral structure of least-squares regression, LoomSC jointly learns latent features and a projector self-representation through two thin factors. Alternating Procrustes and least-squares updates preserve the sample factor's orthogonality while keeping the coefficient matrix implicit. We construct a nonnegative quadratic affinity that preserves the projector's support. An exact feature map then reduces its normalized spectral problem to an eigenproblem whose dimension depends only on the factor width. Neither the full affinity nor the sample Laplacian needs to be formed. Our analysis quantifies the projector approximation and identifies conditions for subspace preservation and within-subspace connectivity. For fixed dimensions and iteration budgets, the complete pipeline has linear time and memory complexity in the number of samples. Across five image-clustering benchmarks, LoomSC ranks first or second in all 15 dataset-metric comparisons against 9 state-of-the-art baselines. Its mean accuracy exceeds the highest baseline mean by 6.66 percentage points. Synthetic experiments scale to 500,000 samples while maintaining at least 99.8% accuracy.
发表机构
- École de technologie supérieure (ÉTS)（高等技术学院）
- University of Bahrain (UOB)（巴林大学）
- Université du Québec à Montréal (UQAM)（魁北克大学蒙特利尔分校）
- COMSATS University Islamabad（伊斯兰堡COMSATS大学）
机构由 AI 辅助整理，请以论文原文为准。
