In this paper, we present HAMEX, a new public dataset that contains mathematical expressions available in their on-line handwritten form and in their audio spoken form. We have designed this dataset so that, given a mathematical expression, its handwritten signal and its audio signal can be used jointly to design multimodal recognition systems. Here, we describe the different steps that allowed us to acquire this dataset, from the creation of the mathematical expression corpora (including expressions from Wikipedia pages) to the segmentation and the transcription of the collected data, via the data collection process itself. Currently, the dataset contains 4 350 on-line handwritten mathematical expressions written by 58 writers, and the corresponding audio expressions (in French) spoken by 58 speakers. The ground truth is also provided both for the handwritten expressions (as INKML files with the digital ink, the symbol segmentation, and the MATHML structure) and for the audio expressions (as XML files with the transcriptions of the spoken expressions).

In this paper, we present a new method to design customizable self-evolving fuzzy rule-based classifiers. The presented approach combines an incremental clustering algorithm with a fuzzy adaptation method in order to learn and maintain the model. We use this method to build an evolving handwritten gesture recognition system, that can be integrated into an application to provide personalization capabilities. Experiments on an on-line gesture database were performed by considering various user personalization scenarios. The experiments show that the proposed evolving gesture recognition system continuously adapts and evolve according to new data of learned classes, and remains robust when introducing new unseen classes, at any moment during the lifelong learning process.

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