Gradient adaptation under unit-norm constraints

We study gradient-based adaptive algorithms within parameter spaces specified by ||w||=1, where ||·|| is any vector norm. Several approximate algorithms for this task have already been developed when ||w|| is the L₂ norm. We derive general algorithm forms for arbitrary vector norms and relate them to true gradient procedures via their geometric structures. We also give algorithms that mitigate an inherent numerical instability for tangent-vector L₂-norm methods. Simulations showing the performance of the techniques for minor component analysis are provided