This work proposes an improvement of a supervised learning technique for self organizing maps. The ideas presented in This work differ from Kohonen's approach to supervision in that a.) a rejection term is used, and b.) rejection affects the training only locally. This approach produces superior results because it does not affect network weights globally, and hence, prevents the addition of noise to the learning process of remote neurons. We implemented the ideas into self-organizing maps for structured data (SOM-SD) which is a more general form of self-organizing maps capable of processing graphs. The capabilities of the proposed ideas are demonstrated by utilizing a relatively large real world learning problem from the area of image recognition. It is shown that the proposed method produces better classification performances while being more robust and flexible than other supervised approaches to SOM.