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The canonical algorithm for cluster analysis is K-Means Clustering. The basic idea with the
procedure is to assign all N elements of a feature space into K separate and non-overlapping
clusters.
To achieve this a simple iterative algorithm is used. All elements of the feature space are
initially randomly assigned a cluster k ∈ {1, . . . , K}. At this point the algorithm iterates and
for each step of the iteration calculates the mean vector–the centroid–for each cluster k. It then
assigns each element to the cluster possessing the nearest centroid using a Euclidean distance
metric. The algorithm is iterated until the centroid locations remain fixed to within a certain
pre-specified tolerance distance.
In quantitative finance clustering is commonly used to identify assets that have similar characteristics,
which is useful in constructing diversified portfolios. It can also be utilised for detecting
market regimes and thus potentially acting as a risk management tool. We will be studying
clustering techniques for assets in the following chapter.
21.4 Bibliographic Note
An introduction to unsupervised learning, and its difficulties, can be found in James et al
(2013)[59]. It is accessible to those without a strong mathematical background or those coming
from other areas of science.
A significantly more advanced mathematical discussion, at the graduate level, can be found
in Hastie et al (2009)[51]. The book discusses many unsupervised techniques, although it is
primarily about supervised methods.
Barber (2012)[20] discusses high-dimensionality and the problems it causes at a reasonable
mathematical level, concentrating primarily on PCA and clustering, while Murphy (2012)[71]
considers unsupervised learning through the probabilistic density estimation approach at a gentler
mathematical level of rigour.