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Correlation Metric for Generalized Feature Extraction

机译：广义特征提取的相关度量

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摘要

Beyond linear and kernel-based feature extraction, we propose in this paper the generalized feature extraction formulation based on the so-called graph embedding framework. Two novel correlation metric based algorithms are presented based on this formulation. correlation embedding analysis (CEA), which incorporates both correlational mapping and discriminating analysis, boosts the discriminating power by mapping data from a high-dimensional hypersphere onto another low-dimensional hypersphere and preserving the intrinsic neighbor relations with local graph modeling. correlational principal component analysis (CPCA) generalizes the conventional Principal Component Analysis (PCA) algorithm to the case with data distributed on a high-dimensional hypersphere. Their advantages stem from two facts: 1) tailored to normalized data, which are often the outputs from the data preprocessing step, and 2) directly designed with correlation metric, which shows to be generally better than Euclidean distance for classification purpose. Extensive comparisons with existing algorithms on visual classification experiments demonstrate the effectiveness of the proposed algorithms.
机译：除了基于线性和基于核的特征提取外，我们还提出了基于所谓的图嵌入框架的广义特征提取公式。基于此公式，提出了两种基于相关度量的新颖算法。相关嵌入分析（CEA）结合了相关映射和判别分析，通过将数据从高维超球映射到另一个低维超球上并通过局部图建模保留固有的邻居关系，从而增强了判别能力。相关主成分分析（CPCA）将常规的主成分分析（PCA）算法推广到数据分布在高维超球面上的情况。它们的优势来自两个事实：1）针对标准化数据进行量身定制，这通常是数据预处理步骤的输出，以及2）直接设计为具有相关度量，这在分类方面通常要优于欧几里得距离。与现有算法在视觉分类实验上的广泛比较证明了所提出算法的有效性。

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