Discriminant Feature Extraction by Generalized Difference Subspace
Discriminant Feature Extraction by Generalized Difference Subspace
复制标题
通过广义差分子空间提取判别特征
DOI：
10.1109/tpami.2022.3168557
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发表时间：
2022
影响因子：
23.6
通讯作者：
A. Maki
中科院分区：
文献类型：
--
作者：
K. Fukui;Naoya Sogi;Takumi Kobayashi;Jing;A. Maki
在本文中，我们在理论上和实验上揭示了正交数据投影在广义差异子空间（GDS）上的判别能力。在我们以前的工作中，我们证明了GDS投影是类别子空间的准正交化，这是基于子空间的分类器的有效特征提取。在这里，我们进一步表明，GDS投影还可以通过与Fisher判别分析（FDA）相似的机制作为判别特征提取。由于其制剂的显着差异，很难证明GDS投影与FDA之间的联系很困难。为了避免并发症，我们首先基于简化的Fisher标准引入几何渔民判别分析（GFDA）。它源自启发式但实际上合理的假设：鉴于在没有数据中心的情况下应用主成分分析（PCA），因此类别的样本平均向量在很大程度上与该类的第一个主要成分向量保持一致。 GFDA即使在几个样本下也稳定地工作，绕过了FDA的小样本量（SSS）问题。然后，我们证明GFDA等于具有较小校正项的GDS投影。这种等价可确保GDS投影通过GFDA继承FDA的判别能力。此外，我们讨论了这些方法的两个有用的扩展，1）内核技巧的非线性扩展，2）与CNN特征的组合。通过对扩展的耶鲁大学B+，CMU面部数据库，ALOI，ETH80，MNIST和CIFAR10进行的广泛实验，已经验证了扩展的等效性和有效性，主要集中在小样本下的图像识别上。
In this paper, we reveal the discriminant capacity of orthogonal data projection onto the generalized difference subspace (GDS), both theoretically and experimentally. In our previous work, we demonstrated that the GDS projection works as a quasi-orthogonalization of class subspaces, which is an effective feature extraction for subspace based classifiers. Here, we further show that GDS projection also works as a discriminant feature extraction through a similar mechanism to the Fisher discriminant analysis (FDA). A direct proof of the connection between GDS projection and FDA is difficult due to the significant difference in their formulations. To circumvent the complication, we first introduce geometrical Fisher discriminant analysis (gFDA) based on a simplified Fisher criterion. It is derived from a heuristic yet practically plausible assumption: the direction of the sample mean vector of a class is largely aligned to the first principal component vector of the class, given that the principal component analysis (PCA) is applied without data centering. gFDA works stably even under few samples, bypassing the small sample size (SSS) problem of FDA. We then prove that gFDA is equivalent to GDS projection with a small correction term. This equivalence ensures GDS projection to inherit the discriminant ability from FDA via gFDA. Furthermore, we discuss two useful extensions of these methods, 1) a nonlinear extension by kernel trick, 2) a combination with CNN features. The equivalence and the effectiveness of the extensions have been verified through extensive experiments on the extended Yale B+, CMU face database, ALOI, ETH80, MNIST, and CIFAR10, mainly focusing on image recognition under small samples.
影响因子：
2.4
作者：
Gatto, Bernardo B.;Souza, Lincon S.;dos Santos, Kenny V.
通讯作者：
dos Santos, Kenny V.