The development of automatic sleep based abnormality detection in patient for sleep related problem is a key field in the recent research. However the sleep signals are obtained as long-time recordings and inhibit complex characteristics, making their analysis computationally challenging. As a result, recognition methods that facilitate efficient dimensionality reduction are developed to suit different applications. In recent years sparse representation schemes provide an effective means for achieving best possible data reduction by comparing the input with pre-formulated dictionaries, especially for huge datasets. Recent research proves the usability of these methods for signal classification. In this paper, a robust technique is provided for sparse representation of small dataset signal types. Here, the signal decomposition is obtained using the l(1)-minimization technique, following which a generalization based on the leave-one-out (LOO) is performed. The dependency of the proposed algorithm is analyzed, using a sparsity measure, in order to verify the dependency between the input data and extracted feature space. Performance measures obtained using long-term sleep data shows an average classification accuracy of 80% and further validates the usefulness of the technique for long term biomedical signal analysis.