快速的分区融合多视图子空间聚类

Fast Partition Fusion Multi-View Subspace Clustering

摘要: 近年来，子空间聚类算法的研究取得了显著进展，其中多视图聚类方法因其能够有效地整合多数据来源信息而成为研究热点。新近提出的基于分区融合的多视图子空间聚类方法通过对每个视图分块进行研究，并设计加权融合机制，显著提升了模型对噪声和视图差异的鲁棒性。然而，该方法仍存在一定的局限性：其一，加权机制中的参数优化容易出现极端取值情况，影响模型稳定性；其二，对自表达系数矩阵施加的非负约束限制了其表示能力；其三，在处理大规模数据集时，部分子问题涉及的计算项过多，导致迭代更新过程效率低下，计算消耗过大。针对上述局限性，本文提出以下创新性改进：首先，通过引入亲和矩阵，有效解除了非负约束的限制，从而显著提升了模型的表达能力；其次，创新性地设计中间变量优化策略，重构计算流程，使算法复杂度降低，大幅提升了运算效率；同时，在保留原有加权参数优势的基础上，修改自适应加权机制，有效避免了参数极端化问题。为验证改进效果，我们在4个标准数据集上进行了系统性实验，实验结果表明，我们的方法不仅有效克服了原方法的局限性，同时在处理大规模数据时展现出更高的计算效率。

Abstract: In recent years, the research of subspace clustering algorithms has made significant progress, among which the multi-view clustering method has become a research hotspot because of its ability to effectively integrate multi-data source information. The newly proposed multi-view subspace clustering method based on partition fusion significantly improves the robustness of the model to noise and view differences by studying each view block and designing a weighted fusion mechanism. However, this method still has certain limitations: first, the parameter optimization in the weighting mechanism is prone to extreme values, affecting the stability of the model; second, the non-negative constraints imposed on the self-expression coefficient matrix limit its representation ability; third, when processing large-scale data sets, the calculation items involved in some sub-problems too much, resulting in inefficiency of the iterative update process and excessive computing consumption. In view of the above limitations, this paper proposes the following innovative improvements: first, by introducing the affinity matrix, the restriction of non-negative constraints is effectively lifted, thus significantly improving the expression ability of the model; second, the innovative design of intermediate variable optimization strategies, reconstructing the calculation process, reducing the complexity of the algorithm, and greatly improving the operation calculate efficiency; at the same time, on the basis of retaining the advantages of the original weighting parameters, the adaptive weighting mechanism is modified, which effectively avoids the problem of parameter extremes. In order to verify the improvement effect, we conducted systematic experiments on four standard data sets. The experimental results showed that our method not only effectively overcame the limitations of the original method, but also showed higher computing efficiency when processing large-scale data.