Analyzing facial expressions with fuzzy quantification theory II: indefinite generalized eigenvalue problem
Analyzing facial expressions with fuzzy quantification theory II: indefinite generalized eigenvalue problem
复制标题
DOI：
10.1007/s13160-011-0035-z
复制
发表时间：
2011-03
影响因子：
0.9
通讯作者：
L. Diago;Tetsuko Kitaoka;I. Hagiwara;Sayuri Ishiguro
中科院分区：
文献类型：
--
作者：
L. Diago;Tetsuko Kitaoka;I. Hagiwara;Sayuri Ishiguro
机器理解人类的交互行为是一项具有挑战性的任务。在本文中，面部表情被用来诱导一组主题的情感和感觉模糊的人类互动行为。当模糊量化理论II被用来分析面部表情所引起的情绪时，通过求解稠密广义特征值问题来线性化所引起的情绪和面部特征之间的关系。由于在小样本人脸表情数据集上，矩阵的病态性和不确定性，使得描述特征值问题可能解的理论变得复杂。本文提出了一种扰动的特征值问题，使用的Moore-Penrose伪逆，保持误差范围内的广泛使用的GUPTRI算法的解决方案的误差范围。实验结果表明，GUPTRI算法在某些情况下失败的样本数很小，而所提出的方法提供的解决方案从来没有失败，更准确。
Machine understanding of human interactive behaviour is a challenging task. In this paper, facial expressions are used to induce emotions on a group of subjects and sense fuzzy human interactive behaviour. When fuzzy quantification theory II is used to analyze the emotions induced by facial expressions, the relationship between induced emotions and facial features is linearized by solving a dense generalized eigenvalue problem. As the matrices are ill-conditioned and indefinite when small data set of facial expressions is used, the theory describing the possible solutions of the eigenvalue problem gets complicated. This paper proposes a perturbation of the eigenvalue problem by using the Moore–Penrose pseudoinverse that keeps the error bounds of the solution within the error bounds of the widely used GUPTRI algorithm. Experimental results show that GUPTRI algorithm fails in some cases where the number of samples is very small while the solution provided by proposed approach never fails and is more accurate.