Dimension Reduction for Model-based Clustering via Mixtures of ...

• Then update the set of currently included variables such that s j = s ′ j ∪ {i j }.4. Set j = j + 1 and iterate the previous step until a stopping rule is met. Our algorithmterminates when the BIC difference for the inclusion of a variable becomesnegative.At each step, the search over the model space is performed with respect to the modelparametrization and the number of clusters.As mentioned before, the greedy search will likely discard the tMMDR variableswhich are associated with small eigenvalues as they do not carry any clustering information.Then a tMM can be fitted on the selected set of tMMDR variables and thecorresponding tMMDR directions will be estimated. The feature selection step is thenrepeated until no directions can be dropped. This entire process is summarized in thealgorithm below.Algorithm: tMMDR estimation and feature selection1. Fit a t-distribution mixture model (tMM) to the data.2. Estimate the tMMDR directions using the method in Section 3.2.2.3. Perform feature selection using the greedy algorithm in Section 3.2.3.4. Fit a tMM on the selected tMMDR variables and return to step 2.5. Repeat steps 2 − 4 until none of the features can be dropped.22