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New business models underpinned by new standards of openness, flexibility, and agility are arising in the banking sector. Therefore, banks have to establish new strategies to keep and to extend their client base, especially with the explosive growth of customers' data and interaction touch-points. Hence, banks and fintechs are in fierce competition to transform customers' data that incorporate their transactions into pertinent and significant knowledge for decision making. In this article, we present a novel system aimed toward solving a long-standing and challenging issue: obtaining classifiers to automatically categorize bank transactions for a Smart Budget Manager. We fit and test our system using real data. The strength of our system lies in the novel combination of incremental machine learning algorithms with a natural language understanding for a fine-grained categorization of bank transactions. Our system serves as a base layer for other advanced banking applications such as segmentation, next best offers and credit scoring. Our system is deployed in a real banking application of a Tunisian bank and has shown bank and customer's satisfaction.