advanced-algorithmic-trading

Chapter 22
Clustering Methods
In this chapter the concept of unsupervised clustering will be considered. In quantitative finance
finding groups of similar assets, or regimes in asset price series, is extremely useful. For instance,
it can aid in the development of entry and exit rule filters.
Clustering is an unsupervised learning method that attempts to partition observational data
into separate subgroups or clusters. The desired outcome of clustering is to ensure observations
within clusters are similar to each other but different to observations in other clusters.
Clustering is a vast area of academic research and it would be difficult to provide a full
taxonomy of clustering algorithms in this chapter. Instead a common, but very useful, algorithm
will be considered called K-Means Clustering. Resources will be outlined that allow further study
of more advanced algorithms if so desired.
K-Means Clustering will be applied to daily OHLC bar data in order to identify separate
price action clusters. These clusters can then be used to determine if certain market regimes
exist, as with Hidden Markov Models.
22.1 K-Means Clustering
K-Means Clustering is a particular technique for identifying subgroups or clusters within a set
of observations. It is a hard clustering technique, which means that each observation is forced
to have a unique cluster assignment. This is in contrast to a soft, or probabilistic, clustering
technique, which assigns probabilites for cluster membership.
To use K-Means Clustering it is necessary to specify a parameter K, which is the number
of desired clusters to partition the data into. These K clusters do not overlap and have "hard"
boundaries between membership (see Figure 22.1). The task is to assign each of the N observations
into one of the K clusters, where each observation belongs to a cluster with the closest
mean feature/observation vector.
Mathematically we can define sets S k , k ∈ {1, . . . , K}, each of which contains the indices
of the subset of the N observations that lie in each cluster. These sets exhaustively cover all
indices, that is each observation belongs to at least one of the sets S k and the clusters are
mutually exclusive with "hard" boundaries:
• S = ⋃ K
k=1 S k = {1, . . . , N}
• S k ∩ S k ′ = φ, ∀k ≠ k ′ 305