A novel sparse encoding algorithm is developed to detect and study plasma instabilities automatically. This algorithm, called Elastic Random Mode Decomposition, is applied to the Mirnov coil signals of a dataset of 1291 discharges of the TJ-II stellarator, enabling the identification of the Alfvénic activity. In the presented approach, each signal is encoded as a collection of basic waveforms called atoms, drawn from a signal’s dictionary. Then the modes are identified using clustering and correlations with other plasma signals. The performance of the proposed algorithm is dramatically increased by using elastic net regularization and taking advantage of GPU architectures, hence the signal size and the number of dictionary elements are no longer limiting factors for encoding complex signals. Once the modes are retrieved from the shots, they can be easily analyzed with standard clustering techniques, thereby describing the physical mode characteristics of this subset of TJ-II shots. The clustering features consider the relationship with the plasma current Ip, the diamagnetic energy W, and inverse squared root electronic density 1/√n, profiling different subtypes of Alfvénic activity. The proposed algorithm can potentially create large databases of labeled modes with unprecedented detail.