hierarchical methods

 While partitioning methods meet the basic clustering
requirement of organizing a set of objects into a number of
exclusive groups, in some situations we may want to partition
our data into groups at different levels such as in a hierarchy.
 A hierarchical clustering method works by grouping data objects
into a hierarchy or “tree” of clusters.
 Representing data objects in the form of a hierarchy is usefull
for data summarization and visualization.
 The multiple-phase (or multiphase) clustering.

I. Agglomerative versus Divisive Hierarchical Clustering:
 A hierarchical clustering method can be either agglomerative or divisive,
depending on whether the hierarchical decomposition is formed in a
bottom-up or top-down fashion.
 An agglomerative hierarchical clustering method uses a bottom-up
strategy. The single cluster becomes the hierarchy`s root.
 A divisive hierarchical clustering method employs a top-down strategy. It
starts by placing all objects in one cluster, which is the hierarchy`s root.

 This is a single-linkage approach in that each cluster is represented by all
the objects in the cluster, and the similarity between two clusters is
measured by the similarity of the closest pair of data points belonging to
different cluster.
 The cluster-splitting process repeats until, eventually, each new cluster
contains only a single objects.
 A tree structure called a dendrogram is commonly used to represent the
process of hierarchical clustering.

II. Distance Measures in Algorithmic Methods:
 whether using an agglomerative method or a divisive method, a core need
is to measure the distance between two clusters, where each cluster is
generally a set of objects.
 Four widely used measures for distance between clusters, where |p-p`| is
the distance between two objects or points, p and p`; mi is the mean for
cluster, Ci and ni is the number of objects in Ci.
 They are also known as linkage measures.

 Minimum distance: distmin(Ci, Cj)= min {|p-p`|}
pCᵢ;p`Cj
 Maximum distance: distmax(Ci, Cj)= min {|p-p`|}
pCᵢ;p`Cj
 Mean distance: distmin(Ci, Cj)=  Mᵢ- Mj
 Average distance: distmin(Ci, Cj)= 1/ nᵢnj p - p`
pCᵢ;p`Cj

III. BIRCH: Multiphase Hierarchical Clustering Using
Clustering Feature Trees
 Balanced Iterative Reducing and Clustering using Hierarchical (BIRCH)
is designed for clustering a large amount of numeric data by integrating
hierarchical clustering(at the initial micro clustering stage) and other
clustering methods such as iterative partitioning(at the macro clustering
stage).
 The two difficulties in agglomerative clustering methods:
Scalability
Inability

 BIRCH uses the notions of clustering feature to summarize a cluster, and
clustering feature tree(CF-tree) to represent a cluster hierarchy.
 Consider a cluster of n d-dimensional data objects or points.
 A clustering feature is essentially a summary of the statistics for the given
cluster. The cluster`s centroid, xₒ, radius, R, and diameter, D, are

 Phase 1:
BIRCH scans the database to build an initial in-memory CF-
tree, which can be viewed as a multilevel compression of the
data that tries to preserve the data`s inherent clustering structure.
 Phase 2:
BIRCH applies a (selected) clustering algorithm to cluster the
leaf nodes of the CF-tree, which removes sparse clusters and
groups dense cluster into larger ones.

IV. Chameleon: Multiphase Hierarchical Clustering Using
Dynamic Modeling
 Chameleon is a hierarchical clustering algorithm that uses dynamic modeling
to determine the similarity between pairs of clusters.
 The connected objects are within a clusters and the proximity of clusters.
 That is, two clusters are merged if their interconnectivity high and they are
close together.
 Chameleon uses a k-nearest-neighbor graph approach to construct a sparse
graph.

 Chameleon uses a graph partitioning algorithm to partition the
k-nearest-neighbor graph into a large number of relatively small
subclusters such that it minimizes the edge cut.
 Chameleon determines the similarity between each pair of
clusters Cᵢ and Cj according to their relative interconnectivity,
RI(Cᵢ,Cj), and their relative closeness, RC(Ci,Cj).
 The processing cost for high-dimensional data may require
O(n²) time for n objects in the worst case.

V. Probabilistic Hierarchical Clustering
 Algorithmic hierarchical clustering methods using linkage measures tend
to be easy to understand and are often efficient in clustering.
 They are commonly used in many clustering analysis applications.
 Algorithmic hierarchical clustering methods can suffer from several
drawbacks.
 One way to look at the clustering problem is to regard the set of data
objects to be clustered as sample of the underlying data generation
mechanism to be analyzed or, formally, the generative model.

hierarchical methods

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hierarchical methods