Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A kernel Principal Component Analysis (kPCA) digest with a new backward
  mapping (pre-image reconstruction) strategy   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.

26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio