title: A Fast Incremental Gaussian Mixture Model.
abstract: 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 O(NKD3) for N data points, K Gaussian components and D dimensions, rendering it inadequate for high-dimensional data. In this work, we manage to reduce this complexity to O(NKD2) 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.
authors.affiliation: Instituto de Informática, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, Brazil.
authors.forename: Rafael Coimbra
authors.initials: RC
authors.lastname: Pinto
authors.affiliation: Instituto de Informática, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, Brazil.
authors.forename: Paulo Martins
authors.initials: PM
authors.lastname: Engel
mesh_terms: D000465:Algorithms; D000069550:Machine Learning; D008962:Models, Theoretical; D016011:Normal Distribution