Multidimensional optimization holds a central role in many machine learning problems. When a model quality functional is measured with an almost arbitrary external noise, it makes sense to use randomized optimization techniques. This paper deals with the problem of clustering of a Gaussian mixture model under unknown but bounded disturbances. We introduce a stochastic approximation algorithm with randomly perturbed input (like SPSA) to solve this problem. The proposed method is appropriate for the online learning with streaming data, and it has a high speed of convergence. We study the conditions of the SPSA clustering algorithm applicability and show illustrative examples.