Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Clustering is semidefinitely not that hard: Nonnegative SDP for manifold
  disentangling   In solving hard computational problems, semidefinite program (SDP)
relaxations often play an important role because they come with a guarantee of
optimality. Here, we focus on a popular semidefinite relaxation of K-means
clustering which yields the same solution as the non-convex original
formulation for well segregated datasets. We report an unexpected finding: when
data contains (greater than zero-dimensional) manifolds, the SDP solution
captures such geometrical structures. Unlike traditional manifold embedding
techniques, our approach does not rely on manually defining a kernel but rather
enforces locality via a nonnegativity constraint. We thus call our approach
NOnnegative MAnifold Disentangling, or NOMAD. To build an intuitive
understanding of its manifold learning capabilities, we develop a theoretical
analysis of NOMAD on idealized datasets. While NOMAD is convex and the globally
optimal solution can be found by generic SDP solvers with polynomial time
complexity, they are too slow for modern datasets. To address this problem, we
analyze a non-convex heuristic and present a new, convex and yet efficient,
algorithm, based on the conditional gradient method. Our results render NOMAD a
versatile, understandable, and powerful tool for manifold learning.

28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph