A Fast Incremental Gaussian Mixture Model

This work builds upon previous efforts in online incremental learning, namely the Incremental Gaussian Mixture Network (IGMN). The IGMN is capable of learning from data streams in a single-pass by improving its model after analyzing each data point and discarding it thereafter. Nevertheless, it suffers from the scalability point-of-view, due to its asymptotic time complexity of $\operatorname{O}\bigl(NKD^3\bigr)$ for $N$ data points, $K$ Gaussian components and $D$ dimensions, rendering it inadequate for high-dimensional data. In this paper, we manage to reduce this complexity to $\operatorname{O}\bigl(NKD^2\bigr)$ by deriving formulas for working directly with precision matrices instead of covariance matrices. The final result is a much faster and scalable algorithm which can be applied to high dimensional tasks. This is confirmed by applying the modified algorithm to high-dimensional classification datasets.