Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two-way kernel matrix puncturing: towards resource-efficient PCA and
  spectral clustering   The article introduces an elementary cost and storage reduction method for
spectral clustering and principal component analysis. The method consists in
randomly "puncturing" both the data matrix $X\in\mathbb{C}^{p\times n}$ (or
$\mathbb{R}^{p\times n}$) and its corresponding kernel (Gram) matrix $K$
through Bernoulli masks: $S\in\{0,1\}^{p\times n}$ for $X$ and
$B\in\{0,1\}^{n\times n}$ for $K$. The resulting "two-way punctured" kernel is
thus given by $K=\frac{1}{p}[(X \odot S)^{\sf H} (X \odot S)] \odot B$. We
demonstrate that, for $X$ composed of independent columns drawn from a Gaussian
mixture model, as $n,p\to\infty$ with $p/n\to c_0\in(0,\infty)$, the spectral
behavior of $K$ -- its limiting eigenvalue distribution, as well as its
isolated eigenvalues and eigenvectors -- is fully tractable and exhibits a
series of counter-intuitive phenomena. We notably prove, and empirically
confirm on GAN-generated image databases, that it is possible to drastically
puncture the data, thereby providing possibly huge computational and storage
gains, for a virtually constant (clustering of PCA) performance. This
preliminary study opens as such the path towards rethinking, from a large
dimensional standpoint, computational and storage costs in elementary machine
learning models.

19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
2
The categories of this paper are: math
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th