In this paper, we propose quality function for an unsupervised neural classification. The function is based on the third order polynomials. The objective of the quality function is to find a place of the input space sparse in data points. By maximising the quality function, we find decision boundary between data clusters instead of centres of the clusters. The shape and place of the decision boundary are rather insensitive to the magnitude of the weight vector established during the maximisation process. A superiority of the proposed quality function over other similar functions as well as conventional clustering algorithms tested has been observed in the experiments. The proposed quality function has been successfully used for colour image segmentation.