Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Clustering Semi-Random Mixtures of Gaussians   Gaussian mixture models (GMM) are the most widely used statistical model for
the $k$-means clustering problem and form a popular framework for clustering in
machine learning and data analysis. In this paper, we propose a natural
semi-random model for $k$-means clustering that generalizes the Gaussian
mixture model, and that we believe will be useful in identifying robust
algorithms. In our model, a semi-random adversary is allowed to make arbitrary
"monotone" or helpful changes to the data generated from the Gaussian mixture
model.
  Our first contribution is a polynomial time algorithm that provably recovers
the ground-truth up to small classification error w.h.p., assuming certain
separation between the components. Perhaps surprisingly, the algorithm we
analyze is the popular Lloyd's algorithm for $k$-means clustering that is the
method-of-choice in practice. Our second result complements the upper bound by
giving a nearly matching information-theoretic lower bound on the number of
misclassified points incurred by any $k$-means clustering algorithm on the
semi-random model.

22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat