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Associative memory operating in a real environment must perform well in online incremental learning and be robust to noisy data because noisy associative patterns are presented sequentially in a real environment. We propose a novel associative memory that satisfies these requirements. Using the proposed method, new associative pairs that are presented sequentially can be learned accurately without forgetting previously learned patterns. The memory size of the proposed method increases adaptively with learning patterns. Therefore, it suffers neither redundancy nor insufficiency of memory size, even in an environment in which the maximum number of associative pairs to be presented is unknown before learning. Noisy inputs in real environments are classifiable into two types: noise-added original patterns and faultily presented random patterns. The proposed method deals with two types of noise. To our knowledge, no conventional associative memory addresses noise of both types. The proposed associative memory performs as a bidirectional one-to-many or many-to-one associative memory and deals not only with bipolar data, but also with real-valued data. Results demonstrate that the proposed method's features are important for application to an intelligent robot operating in a real environment. The originality of our work consists of two points: employing a growing self-organizing network for an associative memory, and discussing what features are necessary for an associative memory for an intelligent robot and proposing an associative memory that satisfies those requirements.