Heart sound classification is still suffered from the challenge of achieving high accuracy in the case of small samples. Dimension reduction attempts to extract low-dimensional features with more discriminability from the high-dimensional spaces or raw data, which is popular for learning predictive models targeting small sample problem. However, it can also be harmful to classification because any reduction has the potential to lose information containing category attributes. For this, a novel SNMFNet classifier is designed to directly associate the dimension reduction process with the classification procedure for promoting features dimension reduction to follow the way that's beneficial for classification, thus to make the low-dimensional features more distinguishable and address the challenge of heart sound classification under small samples. We evaluated our method and representative ones on the public heart sound dataset. The experiment results demonstrate that our method outperforms all comparative models with an obvious improvement for small samples. Furthermore, even if with relatively sufficient samples, our method is at least as well as the baseline that uses the same high-dimensional features. The proposed SNMFNet classifier is significant to improve the small samples problem in the heart sound classification.