Rank-Constrained Spectral Clustering With Flexible Embedding
Rank-Constrained Spectral Clustering With Flexible Embedding
复制标题
具有灵活嵌入的秩约束谱聚类
DOI：
10.1109/tnnls.2018.2817538
复制
发表时间：
2018-12-01
影响因子：
10.4
通讯作者：
Yang, Yi
中科院分区：
文献类型：
--
作者：
Li, Zhihui;Nie, Feiping;Yang, Yi
谱聚类（SC）已被证明是有效的，在各种应用。然而，SC的学习方案是次优的，因为它从固定的图结构中学习聚类指示符，这通常需要舍入过程来进一步划分数据。此外，所获得的聚类数不能反映图中连通分量的地面真值数。为了减轻这些缺点，我们提出了一个具有灵活嵌入框架的秩约束SC。具体地说，一个自适应的概率邻域学习过程中恢复块对角亲和矩阵的理想图。同时，在低维子空间中采用灵活的嵌入方法来揭示聚类的内在结构，有效地抑制了高维数据中的无关信息和噪声.该方法与以往的SC方法相比具有上级的优点：1）在自适应图构造过程中同时学习的块对角亲和矩阵，更显式地诱导出聚类成员，而无需进一步离散化; 2）通过对拉普拉斯矩阵的秩约束，保证聚类数收敛到地面真值;以及3）嵌入特征和投影特征之间的失配允许在低维子空间中找到适当的聚类结构以及学习相应的投影矩阵的更大自由度。在合成数据集和真实数据集上的实验结果证明了该算法的良好性能。
Spectral clustering (SC) has been proven to be effective in various applications. However, the learning scheme of SC is suboptimal in that it learns the cluster indicator from a fixed graph structure, which usually requires a rounding procedure to further partition the data. Also, the obtained cluster number cannot reflect the ground truth number of connected components in the graph. To alleviate these drawbacks, we propose a rank-constrained SC with flexible embedding framework. Specifically, an adaptive probabilistic neighborhood learning process is employed to recover the block-diagonal affinity matrix of an ideal graph. Meanwhile, a flexible embedding scheme is learned to unravel the intrinsic cluster structure in low-dimensional subspace, where the irrelevant information and noise in high-dimensional data have been effectively suppressed. The proposed method is superior to previous SC methods in that: 1) the block-diagonal affinity matrix learned simultaneously with the adaptive graph construction process, more explicitly induces the cluster membership without further discretization; 2) the number of clusters is guaranteed to converge to the ground truth via a rank constraint on the Laplacian matrix; and 3) the mismatch between the embedded feature and the projected feature allows more freedom for finding the proper cluster structure in the low-dimensional subspace as well as learning the corresponding projection matrix. Experimental results on both synthetic and real-world data sets demonstrate the promising performance of the proposed algorithm.