Nonnegative Tucker Factorization (NTF) minimizes the euclidean distance or Kullback-Leibler divergence between the original data and its low-rank approximation which often suffers from grossly corruptions or outliers and the neglect of manifold structures of data. In particular, NTF suffers from rotational ambiguity, whose solutions with and without rotation transformations are equally in the sense of yielding the maximum likelihood. In this paper, we propose three Robust Manifold NTF algorithms to handle outliers by incorporating structural knowledge about the outliers. They first applies a half-quadratic optimization algorithm to transform the problem into a general weighted NTF where the weights are influenced by the outliers. Then, we introduce the correntropy induced metric, Huber function and Cauchy function for weights respectively, to handle the outliers. Finally, we introduce a manifold regularization to overcome the rotational ambiguity of NTF. We have compared the proposed method with a number of representative references covering major branches of NTF on a variety of real-world image databases. Experimental results illustrate the effectiveness of the proposed method under two evaluation metrics (accuracy and nmi).
翻译:无偏向的塔车门因素(NTF) 最大限度地缩小了原始数据与其低级近似之间的超clidean 距离或 Kullback- Leiber 差异,这种差异往往存在严重的腐败或异常现象,而且对数据结构的忽视。特别是, NTF 存在轮换的模糊性,其解决办法与不进行轮换的转换在产生最大可能性的意义上是相等的。在本文中,我们建议采用三种粗略的Manform NTF算法,通过纳入关于外部线的结构知识来处理外部线。它们首先应用半赤道优化算法,将问题转化为一般加权NTF,其重量受到外部线的影响。然后,我们引入了可伦性诱导导体、Huber函数和重量的宽度功能,分别用于处理外部线。最后,我们引入了一种多元的规范,以克服NTF的轮换模糊性。我们比较了拟议方法,把NTF在各种真实世界图像数据库中涵盖主要分支的一些有代表性的参考资料进行了比较。实验性结果说明两种指标下的拟议方法的有效性。