A unified least-square kernel (ULK)framework is formulated for both process modeling and fault diagnosis issues. As a specific algorithmic implementation of the ULK method, an adaptive kernel learning (AKL) network classifier is developed for process diagnosis, which is a two-stage online learning algorithm with a fixed-memory strategy. A new concept of space angle index is proposed to structure the growth of node and actively control the complexity of the network. The AKL network performs a backward decreasing for forgetting an old pattern and a forward increasing for incorporating a new online pattern. The recursive algorithms for both stages are derived for quick online updating. Applications of the AKL network to two numerical cases and the Tennessee Eastman process show good performance in comparison to other established methods, and new insights on the pattern recognition for fault diagnosis arising from this flexible classifier are highlighted. (c) 2006 American Institute of Chemical Engineers.