Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Unified Algorithmic Framework for Multi-Dimensional Scaling   In this paper, we propose a unified algorithmic framework for solving many
known variants of \mds. Our algorithm is a simple iterative scheme with
guaranteed convergence, and is \emph{modular}; by changing the internals of a
single subroutine in the algorithm, we can switch cost functions and target
spaces easily. In addition to the formal guarantees of convergence, our
algorithms are accurate; in most cases, they converge to better quality
solutions than existing methods, in comparable time. We expect that this
framework will be useful for a number of \mds variants that have not yet been
studied.
  Our framework extends to embedding high-dimensional points lying on a sphere
to points on a lower dimensional sphere, preserving geodesic distances. As a
compliment to this result, we also extend the Johnson-Lindenstrauss Lemma to
this spherical setting, where projecting to a random $O((1/\eps^2) \log
n)$-dimensional sphere causes $\eps$-distortion.

6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
2
The categories of this paper are: math
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph