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.

翻译：减少多维性的方法旨在发现数据范围所在的低维多元体。 如果数据有线性结构,主构分析(PCA)非常有效。但如果数据属于非线性低维体,则无法确定可能的维度减少。对于非线性维度减少,内核主构件分析(kPCA)因其简单和易于实施而受到赞赏。该文件简要审查了五氯苯甲醚和KPCA的主要想法,试图在一份文件中收集通常分散的方面。此外,还设计了一项战略,在尽量减少差异功能的基础上,将减少的维度重新映射到原有的高维空间。