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Distance-based discriminant analysis method and its applications

机译:基于距离的判别分析方法及其应用

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摘要

This paper proposes a method of finding a discriminative linear transformation that enhances the data’s degree of conformance to the compactness hypothesis and its inverse. The problem formulation relies on inter-observation distances only, which is shown to improve non-parametric and non-linear classifier performance on benchmark and real-world data sets. The proposed approach is suitable for both binary and multiple-category classification problems, and can be applied as a dimensionality reduction technique. In the latter case, the number of necessary discriminative dimensions can be determined exactly. Also considered is a kernel-based extension of the proposed discriminant analysis method which overcomes the linearity assumption of the sought discriminative transformation imposed by the initial formulation. This enhancement allows the proposed method to be applied to non-linear classification problems and has an additional benefit of being able to accommodate indefinite kernels.
机译:本文提出了一种发现判别线性变换的方法,该方法可以增强数据与紧实度假设及其逆的符合程度。问题表述仅依赖于观察之间的距离,这表明可以提高基准数据和实际数据集的非参数和非线性分类器性能。所提出的方法适用于二进制和多类别分类问题,并且可以用作降维技术。在后一种情况下,可以准确确定必要的区分尺寸的数量。还考虑了所提出的判别分析方法的基于核的扩展,该方法克服了由初始公式施加的所寻求判别变换的线性假设。此增强功能允许将所提出的方法应用于非线性分类问题,并具有能够容纳不确定内核的其他好处。

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