Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Probabilistic $\ell_1$ Method for Clustering High Dimensional Data   In general, the clustering problem is NP-hard, and global optimality cannot
be established for non-trivial instances. For high-dimensional data,
distance-based methods for clustering or classification face an additional
difficulty, the unreliability of distances in very high-dimensional spaces. We
propose a distance-based iterative method for clustering data in very
high-dimensional space, using the $\ell_1$-metric that is less sensitive to
high dimensionality than the Euclidean distance. For $K$ clusters in
$\mathbb{R}^n$, the problem decomposes to $K$ problems coupled by
probabilities, and an iteration reduces to finding $Kn$ weighted medians of
points on a line. The complexity of the algorithm is linear in the dimension of
the data space, and its performance was observed to improve significantly as
the dimension increases.

29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom