A kernel Principal Component Analysis (kPCA) digest with a new backward mapping (pre-image reconstruction) strategy

• URL: http://arxiv.org/abs/2001.01958v2
• Date: Wed, 13 Jan 2021 18:28:20 GMT
• Title: A kernel Principal Component Analysis (kPCA) digest with a new backward mapping (pre-image reconstruction) strategy
• Authors: Alberto Garc\'ia-Gonz\'alez, Antonio Huerta, Sergio Zlotnik and Pedro D\'iez
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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