Anticipated hand movements of amputee subjects are considered difficult to classify using only Electromyogram (EMG) signals and machine learning techniques. For a long time, classifying such s-EMG signals have been considered as a non-linear problem, and the problem of signal sparsity has not been given detailed attention in a large set of action classes. For addressing these problems, this paper is proposing a linear-time classifier termed as Random Fourier Mapped Collaborative Representation with distance weighted Tikhonov regularization matrix (RFMCRT). RFMCRT attempts to tackle the non-linear problem via Random Fourier Features and sparsity issue with collaborative representation. The projection error of Random Fourier Features is reduced by projecting to the same dimension as the original feature space and later finding the collaborative representation, with an optional non-negative constraint (RFMNNCRT). The proposed two classifiers were tested with time-domain features computed from the EMG signals obtained from NINAPRO databases using a non-overlapping sliding window size of 256 ms. Due to the random nature of our proposed classifiers, this paper has computed the average and worst-case performance for 50 trials and compared them with other reported classifiers. The results show that RFMNNCRT (average case) outperformed state-of-the-art classifiers with the accuracy of 93.44% for intact subjects and 55.67% for amputee subjects. In the worst-case situation, RFMCRT achieves considerable performance for the same, with the reported accuracy of 91.55% and 50.27% respectively. Our proposed classifier guarantees acceptable levels of accuracy for large classes of hand movements and also maintains good computational efficiency in comparison to LDA and SVM.