advanced-algorithmic-trading

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22.1.3 Simulated Data
In this section K-Means Clustering will be applied to a set of simulated data in order to provide
familiarisation with the specific Scikit-Learn implementation of the algorithm. It will also be
shown how the choice of K in the algorithm is extremely important in order to achieve good
results.
The task will involve sampling three separate two-dimensional Gaussian distributions to create
a selection of observation data. The K-Means Algorithm will then be used, with various
choices of the parameter K, to infer cluster membership. A comparison of two separate choices
for K will be plotted along with inferred cluster membership by colour.
Similar simulated data exercises have been carried out throughout the book. They help identify
the potential flaws in models on synthetic data, the statistical properties of which are easily
controlled. This provides strong insight into the limitation of such models prior to their application
on real financial data, where we most certainly cannot control the statistical properties!
The first step is to import the necessary libraries. The Python itertools library is used to
chain lists of lists together when generating the random sample data. Itertools is an extremely
useful library, which can save a significant amount of development time. Reading through the
documentation is a good exercise for any budding quant developer or trader.
The remaining imports are NumPy, Matplotlib and the KMeans class from Scikit-Learn, which
lives in the cluster module:
# simulated_data.py
import itertools
import numpy as np
import matplotlib.pyplot as plt
from sklearn.cluster import KMeans
The first task within the __main__ function is to set the random seed so that the code
below is completely reproducible. Subsequently the number of samples for each cluster is set
(samples=100), as well as the two-dimensional means and covariance matrices of each Gaussian
cluster (one per element in each list).
The norm_dists list contains three separate two-dimensional lists of observations, one for
each cluster, generated using a list comprehension. Finally the observational data X is generated
by chaining each of these sublists using the itertools library:
np.random.seed(1)
# Set the number of samples, the means and
# variances of each of the three simulated clusters
samples = 100
mu = [(7, 5), (8, 12), (1, 10)]
cov = [
[[0.5, 0], [0, 1.0]],
[[2.0, 0], [0, 3.5]],
[[3, 0], [0, 5]],