The methods of geometrical regularization in data learning theory have caused wide public concern. In the
background of seismic data processing based on independent component analysis, a problem of two-class clustering on unit
hypersphere is studied for the unit norm constraint. The Riemannian gradient is formulated based on the induced metric from
Euclidean space, which realizes the construction of a fixed-point algorithm for two-class clustering and data averaging on
unit hypersphere. Finally, the simulation result shows the effectiveness and superiority of this algorithm.