The ability of Deep Neural Networks (DNNs) to provide very high accuracy in classification and recognition problems makes them the major tool for developments in such problems. It is, however, known that DNNs are currently used in a 'black box' manner, lacking transparency and interpretability of their decision-making process. Moreover, DNNs should use prior information on data classes, or object categories, so as to provide efficient classification of new data, or objects, without forgetting their previous knowledge. In this paper, we propose a novel class of systems that are able to adapt and contextualize the structure of trained DNNs, providing ways for handling the above-mentioned problems. A hierarchical and distributed system memory is generated and used for this purpose. The main memory is composed of the trained DNN architecture for classification/prediction, i.e., its structure and weights, as well as of an extracted - equivalent - Clustered Representation Set (CRS) generated by the DNN during training at its final - before the output - hidden layer. The latter includes centroids - 'points of attraction' - which link the extracted representation to a specific area in the existing system memory. Drift detection, occurring, for example, in personalized data analysis, can be accomplished by comparing the distances of new data from the centroids, taking into account the intra-cluster distances. Moreover, using the generated CRS, the system is able to contextualize its decision-making process, when new data become available. A new public medical database on Parkinson's disease is used as testbed to illustrate the capabilities of the proposed architecture.