Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: When is Clustering Perturbation Robust?   Clustering is a fundamental data mining tool that aims to divide data into
groups of similar items. Generally, intuition about clustering reflects the
ideal case -- exact data sets endowed with flawless dissimilarity between
individual instances.
  In practice however, these cases are in the minority, and clustering
applications are typically characterized by noisy data sets with approximate
pairwise dissimilarities. As such, the efficacy of clustering methods in
practical applications necessitates robustness to perturbations.
  In this paper, we perform a formal analysis of perturbation robustness,
revealing that the extent to which algorithms can exhibit this desirable
characteristic is inherently limited, and identifying the types of structures
that allow popular clustering paradigms to discover meaningful clusters in
spite of faulty data.

16
The categories of this paper are: stat
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con