Directional Clustering Through Matrix Factorization.
Directional Clustering Through Matrix Factorization.
复制标题
通过矩阵分解进行定向聚类。
DOI：
10.1109/tnnls.2015.2505060
复制
发表时间：
2016
影响因子：
10.4
通讯作者：
Blumensath T
中科院分区：
文献类型：
--
作者：
Blumensath T
本文研究了基于特征向量之间的角度对特征向量进行聚类的聚类问题，即如果特征向量大致指向相同的方向，则将特征向量聚在一起。这种定向距离测量出现在许多应用中，包括文档分类和人脑成像。利用约束低秩矩阵分解和稀疏逼近领域的思想，提出了一种新的聚类方法，它不同于经典的聚类方法，如半负矩阵分解、K-EVD或k-means聚类，但结合了所有这些方法的某些方面。与非负矩阵分解和K-EVD一样，迭代改进矩阵分解以优化数据保真度项；然而，不直接强制执行正性约束，也不需要显式地计算特征向量。与k-means和K-EVD一样，每个优化步骤之后都是一个硬集群分配。这导致了一种高效的算法，在聚类性能和/或计算速度方面优于常见的竞争对手。除了对该算法的一些主要特性进行详细的理论分析外，该方法还在一系列玩具问题、几个标准文本聚类数据集和脑成像中的高维问题上进行了经验评估，其中功能磁共振成像数据用于将人类大脑皮层划分为不同的功能区。
This paper deals with a clustering problem where feature vectors are clustered depending on the angle between feature vectors, that is, feature vectors are grouped together if they point roughly in the same direction. This directional distance measure arises in several applications, including document classification and human brain imaging. Using ideas from the field of constrained low-rank matrix factorization and sparse approximation, a novel approach is presented that differs from classical clustering methods, such as seminonnegative matrix factorization, K-EVD, or k-means clustering, yet combines some aspects of all these. As in nonnegative matrix factorization and K-EVD, the matrix decomposition is iteratively refined to optimize a data fidelity term; however, no positivity constraint is enforced directly nor do we need to explicitly compute eigenvectors. As in k-means and K-EVD, each optimization step is followed by a hard cluster assignment. This leads to an efficient algorithm that is shown here to outperform common competitors in terms of clustering performance and/or computation speed. In addition to a detailed theoretical analysis of some of the algorithm's main properties, the approach is empirically evaluated on a range of toy problems, several standard text clustering data sets, and a high-dimensional problem in brain imaging, where functional magnetic resonance imaging data are used to partition the human cerebral cortex into distinct functional regions.