Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unraveling the Veil of Subspace RIP Through Near-Isometry on Subspaces   Dimensionality reduction is a popular approach to tackle high-dimensional
data with low-dimensional nature. Subspace Restricted Isometry Property, a
newly-proposed concept, has proved to be a useful tool in analyzing the effect
of dimensionality reduction algorithms on subspaces. In this paper, we provide
a characterization of subspace Restricted Isometry Property, asserting that
matrices which act as a near-isometry on low-dimensional subspaces possess
subspace Restricted Isometry Property. This points out a unified approach to
discuss subspace Restricted Isometry Property. Its power is further
demonstrated by the possibility to prove with this result the subspace RIP for
a large variety of random matrices encountered in theory and practice,
including subgaussian matrices, partial Fourier matrices, partial Hadamard
matrices, partial circulant/Toeplitz matrices, matrices with independent
strongly regular rows (for instance, matrices with independent entries having
uniformly bounded $4+\epsilon$ moments), and log-concave ensembles. Thus our
result could extend the applicability of random projections in subspace-based
machine learning algorithms including subspace clustering and allow for the
application of some useful random matrices which are easier to implement on
hardware or are more efficient to compute.

5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess