Extracting discriminative features and reducing the dimensionality of data are two main objectives of manifold learning. Among different techniques, nonlinear manifold learning methods have been proposed in order to extract features from data which are not linearly distributed. Kernel trick is one of the famous nonlinear techniques which helps to project the data without an explicit mapping which can be used in combination with different linear techniques (e.g., Linear discriminant analysis and local discriminant embedding (LDE)). In this paper, we propose a Two Subspace-based Kernel Local Discriminant Embedding (TSKLDE) method which extract features from both non-null and null space of the within-class locality preserving scatter matrix of LDE in the kernel space. We evaluated the proposed algorithm using three publicly available face databases. The obtained results demonstrate that the use of both features in TSKLDE leads to more noise tolerant features compared to other kernel methods and to higher discriminant ability than many existing manifold learning techniques.

中文翻译：

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从内核局部判别嵌入的空和非空空间提取特征

提取区分特征并减少数据的维数是流形学习的两个主要目标。在不同的技术中，已经提出了非线性流形学习方法，以便从不是线性分布的数据中提取特征。内核技巧是著名的非线性技术之一，它可以在无需显式映射的情况下帮助投影数据，该显式映射可以与不同的线性技术（例如，线性判别分析和局部判别嵌入（LDE））结合使用。在本文中，我们提出了一种基于两个子空间的内核局部判别嵌入（TSKLDE）方法，该方法从内核空间中LDE的类内局部性保留散布矩阵的非零和零空间中提取特征。我们使用三个可公开获得的人脸数据库评估了提出的算法。