Simplicial Mixture Models

A simplicial mixture model is a parametric probability distribution which is used to fit topological structure to data.

Prerequisites

• numpy > 1.16.2
• numba > 0.43.1

Minimal example

from smm import SimplicialMM, GLEMM_Parameters, MCMC_Integrator
from smm.helpfulfunctions import initialise_V
import matplotlib.pyplot as plt

% Generate some data, a noisy circle
N = 100
t = 2.0 * np.pi * np.random.rand(N)
X = np.vstack([np.cos(t), np.sin(t)]).T + \
      0.1 * np.random.randn(N, 2)
plt.scatter(X[:,0], X[:,1])

% Setup the model with 5 feature vectors and 1-dimensional simplices
m, n, k = 5, 2, 1
L = SimplicialMM(m, n, k)

% Initialise parameters for the model
TH = GLEMM_Parameters(initialise_V(m, X),  % initial vertex positions
                      L.M,                 % number of simplices
                      covar_type='spherical',
                      covar=0.1)

% Markov-Chain Monte-Carlo integrator
M = MCMC_Integrator(L, TH, X)

% Stochastic EM-algorithm to fit the model
per_step = "CUq" * 10 + "m"
M.perform(per_step * 100)

% Plot points sampled from the model using the fitted parameters M.TH
Y, _ = L.sample(M.TH, 1000)
plt.scatter(Y[:,0], Y[:,1], c='r', s=1)
plt.show()

Installation

To install run:

python setup.py sdist
pip install dist/SMM-*.*.*.tar.gz

Documentation

I use Sphinx for the documentation.

On Windows in a cmd shell in the docs/ directory I run:

make.bat html

to make the documentation.

Testing

I use pytest for testing, run:

pytest

from the project folder, to examine coverage I run:

pytest --cov=smm --cov-report html smm/test/

which requires pytest-cov to be installed.