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Identifying non-disjoint clusters is an important issue in clustering referred to as

Overlapping Clustering. While traditional clustering methods ignore the possibility
that an observation can be assigned to several groups and lead to k exhaustive and
exclusive clusters representing the data, Overlapping Clustering methods offer a
richer model for fitting existing structures in several applications requiring a non-
disjoint partitioning. In fact, the issue of overlapping clustering has been studied
since the last four decades leading to several methods in the literature adopting
many usual approaches such as hierarchical, generative, graphical and k-means
based approach. We review in this paper the fundamental concepts of overlapping
clustering while we survey the widely known overlapping partitional clustering
algorithms and the existing techniques to evaluate the quality of non-disjoint
partitioning. Furthermore, a comparative theoretical and experimental study of
used techniques to model overlaps is given over different multi-labeled

In this paper, we address the problem of designing a joint scheduling and power
control algorithm in a downlink coordinated multi-point (CoMP) cluster supporting
CoMP joint transmission. The objective is to maximize the cell-edge throughput
under per-point power constraints. By an analytical derivation, binary power
control is proved to be the optimal solution for any given selected user group.
Utilizing this analytical result, a centralized and a semi-distributed version of joint
user selection and power control algorithms are proposed. Compared to algorithms
without considering joint transmission and algorithms without considering power
control, simulation results show that the proposed algorithms achieve a good trade-
off between joint transmission and interference coordination, which helps to
improve the cell-edge performance.

The overlapping clustering model that we present here is a generalization of the

SBK model described in Section 2. The SBK model minimizes the squared loss
between X and MA, and their proposed algorithms is not applicable for estimating
the optimal M and A corresponding to other loss functions. In MOC, we generalize
the SBK model to work with a broad class of probability distributions, instead of
just Gaussians, and propose an alternate minimization algorithm for the general
model. The most important difference between MOC and the mixture model is that
we remove the multinomial constraint on the matrix Z, so that it can now be an
arbitrary boolean matrix. To distinguish from the constrained matrix Z, we denote
this unconstrained boolean matrix as the membership matrix M. Every point Xi
now has a corresponding k-dimensional boolean membership vector Mi : the h th
component Mh i of this membership vector is a Bernoulli random variable
indicating whether Xi belongs to the h th cluster. The membership vector Mi for
the point Xi effectively encodes 2k configurations, starting from [00 : : : 0℄,
indicating that Xi does not belong to any cluster, to [11 : : : 1℄, indicating that Xi
belongs to all k clusters. So, a vector Mi with multiple 1’s directly encodes the fact
that the point Xi belongs to multiple clusters.