advanced-algorithmic-trading

310
Figure 22.2: K-Means Algorithm on Simulated Data with k = 3 and k = 4
distributions with differing means and variances. It is immediately apparent that the choice of
K when carrying out the K-Means algorithm is important for the interpretation of results.
In the left subplot the algorithm is forced to choose three clusters. It has largely captured
the three separate Gaussian clusters, assigning blue, red and green colours to each. Although
it clearly has difficulty in selecting the closest clusters for the "outlying" points of each cluster
that lie in the neighbourhood of x 1 = 5, x 2 = 8. This is a difficult situation for any clustering
algorithm that involves overlapping data.
Recall that the K-Means algorithm is a hard clustering tool. That is, it creates a distinct
hard boundary between cluster membership, rather than probabalistically assigning membership
as in a soft cluster algorithm.
In the right subplot the algorithm is forced to choose four clusters and has divided the
grouping on the left hand side of the plot into two separate regions (yellow and red). However
it is known that this particular cluster was generated from a single Gaussian distribution and
hence the algorithm has incorrectly clustered the data. The remaining clusters on the right hand
side are correctly identified however.
The choice of K has significant implications for the usefulness of the algorithm–particularly
with regard to quantitative trading applications.
22.1.4 OHLC Clustering
In this section K-Means Clustering will be used on daily Open-High-Low-Close (OHLC) data,
also known as bars or candles. Such analysis is interesting because it considers extra dimensions
to daily data that are often ignored, in favour of making sole use of adjusted closing prices.
Because it is important to compare each candle on a "like-for-like" basis, each of the High, Low
and Close dimensions will be normalised by the corresponding Open price. This has the added
benefit that stock splits, dividends and other "discrete" price-affecting corporate actions will
automatically be accounted for. By normalising each candle in this manner, the dimensionality
is reduced from four (Open, High, Low, Close) to three: High/Open, Low/Open, Close/Open.
In the following code two years of S&P500 data will be downloaded. The bars will then
be plotted using Matplotlib. The data will then be normalised in the manner described above,