This paper focuses on metric learning with Siamese Neural Networks (SNN). Without any prior, SNNs learn to compute a non-linear metric using only similarity and dissimilarity relationships between input data. Our SNN model proposes three contributions: a tuple-based architecture, an objective function with a norm regularisation and a polar sine-based angular reformulation for cosine dissimilarity learning. Applying our SNN model for Human Action Recognition (HAR) gives very competitive results using only one accelerometer or one motion capture point on the Multimodal Human Action Dataset (MHAD). Performances and properties of our proposals in terms of accuracy, convergence and complexity are assessed, with very favourable results. Additional experiments on the ”Challenge for Multimodal Mid-Air Gesture Recognition for Close Human Computer Interaction” Dataset (ChAirGest) confirm the competitive comparison of our proposals with state-of-the-arts models.