Page 27 - Data Science Algorithms in a Week

12 Ramazan Ünlü

they showed both samples and clusters of the ensemble simultaneously as
vertices in the bipartite graph. In this graph, edges are only between clusters and
samples and there is no edge if the weight is zero meaning the sample does not
belong to the cluster. The final partition is obtained by using a graph similarity-
based algorithm.
 Based on information theory: Information theory based algorithms define the
ensembling problem as the finding median partition by a heuristic solution. In
these methods, the category utility function is used to determine the similarity
measures between clusters. Within the context of clustering, the category utility
function (Gluck, 1989) can be defined as the partition quality scoring function. It
is proved that this function is same as within cluster variance minimization
problem and it can be maximized by using k-means algorithm (Mirkin, 2001).
Using k-means algorithms, on the other hand, bring a deficiency which is the
necessity of determining the number of cluster as an initial parameter. Besides,
the method should be run multiple times to avoid bad local minima. For the
methodological details and implementation of the method, readers can refer to
(Gluck, 1989; Topchy et al., 2005).
 Based on local adaptation: Local adoption based algorithm combines multiple
partitions using locally adaptive clustering algorithm (LAC) which is proposed
by (Domeniconi et al., 2007) with different parameters initialization. Weighty
similarity partition algorithm (WSPA), weighty bipartite partition algorithm
(WBPA) (Domeniconi & Al-Razgan, 2009), and weighted subspace bipartite
partitioning algorithm (WSPA). To obtain final partition, each method uses a
graph partitioning algorithm such as METIS. The strong restriction of these kinds
of methods is that LAC algorithms can be applied to only numerical data.
 Based on kernel method: Weighted partition consensus via Kernels (WPCK) is
proposed by (Vega-Pons, Correa-Morris, & Ruiz-Shulcloper, 2010). This method
uses an intermediate step called Partition Relevance Analysis to assign weights to
represent the significance of the partition in the ensemble. Also, this approach
defines the consensus clustering via the median partition problem by using a
kernel function as the similarity measure between the clusters (Vega-Pons &
Ruiz-Shulcloper, 2011). Other proposed methods using the same idea can be
found in (Vega-Pons, Correa-Morris, & Ruiz-Shulcloper, 2008; Vega-Pons &
Ruiz-Shulcloper, 2009).
 Based on fuzzy theory: So far, it has been explained ensemble clustering methods
whose methodology is developed based on hard partitioning. However, the soft
partitioning might also work in various cases. There are clustering methods like
EM and fuzzy-c-means that produce soft partition or fuzzy partition of the data.
Thus, to combine fuzzy partition instead of hard ones as an internal step of the