Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Learning with Cross-Kernels and Ideal PCA   We describe how cross-kernel matrices, that is, kernel matrices between the
data and a custom chosen set of `feature spanning points' can be used for
learning. The main potential of cross-kernels lies in the fact that (a) only
one side of the matrix scales with the number of data points, and (b)
cross-kernels, as opposed to the usual kernel matrices, can be used to certify
for the data manifold. Our theoretical framework, which is based on a duality
involving the feature space and vanishing ideals, indicates that cross-kernels
have the potential to be used for any kind of kernel learning. We present a
novel algorithm, Ideal PCA (IPCA), which cross-kernelizes PCA. We demonstrate
on real and synthetic data that IPCA allows to (a) obtain PCA-like features
faster and (b) to extract novel and empirically validated features certifying
for the data manifold.

22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th