论文标题
内核主成分分析（KPCA）摘要具有新的向后映射（预图像重建）策略
A kernel Principal Component Analysis (kPCA) digest with a new backward mapping (pre-image reconstruction) strategy
论文作者
论文摘要
多维性降低的方法旨在发现数据范围的低维流形。如果数据具有线性结构，则主成分分析（PCA）非常有效。但是，如果数据属于非线性低维歧管，则无法识别可能的维度降低。对于降低非线性维度，内核主成分分析（KPCA）由于其简单性和轻松实现而受到赞赏。该论文对PCA和KPCA的主要思想进行了简要的评论，试图在经常分散的单个文档方面收集。此外，基于差异功能的最小化，还设计了将简化尺寸映射到原始高维空间中的策略。
Methodologies for multidimensionality reduction aim at discovering low-dimensional manifolds where data ranges. Principal Component Analysis (PCA) is very effective if data have linear structure. But fails in identifying a possible dimensionality reduction if data belong to a nonlinear low-dimensional manifold. For nonlinear dimensionality reduction, kernel Principal Component Analysis (kPCA) is appreciated because of its simplicity and ease implementation. The paper provides a concise review of PCA and kPCA main ideas, trying to collect in a single document aspects that are often dispersed. Moreover, a strategy to map back the reduced dimension into the original high dimensional space is also devised, based on the minimization of a discrepancy functional.
