This includes a test of the new GMM routines in https://github.com/bthirion/scikit-learn/tree/gmm-fixes
By changing the line
GMM = mixture.GMM
at the top of the file, we can plot the BIC and AIC for each variant of GMM. Standard GMM works beautifully: it settles in on 3 components, which are a good description of the data. DPGMM and VBGMM produce some unexpected results.
| import pylab as pl | |
| import numpy as np | |
| from sklearn import mixture | |
| GMM = mixture.GMM | |
| #GMM = mixture.DPGMM | |
| #GMM = mixture.VBGMM | |
| # make some data | |
| Npts = 100 | |
| np.random.seed(0) | |
| centers = np.array([[0.25, 0.75], | |
| [0.75, 0.75], | |
| [0.75, 0.25]]) | |
| covars = 0.1 | |
| X = np.random.normal(centers, covars, size=(Npts, 3, 2)) * 10 | |
| X = X.reshape(-1, 2) | |
| colors = (np.ones((Npts,1)) * np.arange(3)).reshape(-1) | |
| pl.figure() | |
| pl.scatter(X[:, 0], X[:, 1], c=colors, s=16, lw=0) | |
| pl.title('input data') | |
| n_components = np.arange(1, 16) | |
| BIC = np.zeros(n_components.shape) | |
| AIC = np.zeros(n_components.shape) | |
| for i, n in enumerate(n_components): | |
| clf = GMM(n_components=n, | |
| covariance_type='diag') | |
| clf.fit(X) | |
| if isinstance(GMM, mixture.VBGMM) or isinstance(GMM, mixture.DPGMM): | |
| BIC[i] = - 2 * clf.eval(X)[0].sum() | |
| else: | |
| BIC[i] = clf.bic(X) | |
| pl.figure() | |
| pl.plot(n_components, AIC, label='AIC') | |
| pl.plot(n_components, BIC, label='BIC') | |
| pl.legend(loc=0) | |
| pl.xlabel('n_components') | |
| pl.ylabel('AIC / BIC') | |
| i_n = np.argmin(BIC) | |
| clf = GMM(n_components[i_n]) | |
| clf.fit(X) | |
| label = clf.predict(X) | |
| pl.figure() | |
| pl.scatter(X[:, 0], X[:, 1], c=label, s=16, lw=0) | |
| pl.title('classification at min(BIC)') | |
| pl.show() |