Department of Electronic Engineering, Tsinghua University, Beijing, China.
IEEE Trans Image Process. 2012 Mar;21(3):1381-90. doi: 10.1109/TIP.2011.2169972. Epub 2011 Sep 29.
Canonical correlation has been prevalent for multiset-based pairwise subspace analysis. As an extension, discriminant canonical correlations (DCCs) have been developed for classification purpose by learning a global subspace based on Fisher discriminant modeling of pairwise subspaces. However, the discriminative power of DCCs is not optimal as it only measures the "local" canonical correlations within subspace pairs, which lacks the "global" measurement among all the subspaces. In this paper, we propose a multiset discriminant canonical correlation method, i.e., multiple principal angle (MPA). It jointly considers both "local" and "global" canonical correlations by iteratively learning multiple subspaces (one for each set) as well as a global discriminative subspace, on which the angle among multiple subspaces of the same class is minimized while that of different classes is maximized. The proposed computational solution is guaranteed to be convergent with much faster converging speed than DCC. Extensive experiments on pattern recognition applications demonstrate the superior performance of MPA compared to existing subspace learning methods.
典范相关在多集的基于对子空间分析中非常流行。作为扩展，判别典范相关（DCC）通过基于对子空间的 Fisher 判别建模学习全局子空间，已经被开发用于分类目的。然而，DCC 的判别能力不是最优的，因为它仅测量子空间对中的“局部”典范相关，而缺乏所有子空间之间的“全局”测量。在本文中，我们提出了一种多集判别典范相关方法，即多主角度（MPA）。它通过迭代地学习多个子空间（每个集一个）以及一个全局判别子空间，同时最小化同一类的多个子空间之间的角度，最大化不同类之间的角度，共同考虑“局部”和“全局”典范相关。所提出的计算解决方案是有保证的收敛，与 DCC 相比，收敛速度要快得多。在模式识别应用程序上的广泛实验表明，MPA 与现有的子空间学习方法相比具有更好的性能。
