The classification of high-dimensional data with too few labeled samples is a major challenge which is difficult to meet unless some special characteristics of the data can be exploited. In remote sensing, the problem is particularly serious because of the difficulty and cost factors involved in assignment of labels to high-dimensional samples. In this paper, we exploit certain special properties of hyperspectral data and propose an l1-minimization -based sparse representation classification approach to overcome this difficulty in hyperspectral data classification. We assume that the data within each hyperspectral data class lies in a very low-dimensional subspace. Unlike traditional supervised methods, the proposed method does not have separate training and testing phases and, therefore, does not need a training procedure for model creation. Further, to prove the sparsity of hyperspectral data and handle the computational intensiveness and time demand of general-purpose linear programming (LP) solvers, we propose a Homotopy-based sparse classification approach, which works efficiently when data is highly sparse. The approach is not only time efficient, but it also produces results, which are comparable to the traditional methods. The proposed approaches are tested for our difficult classification problem of hyperspectral data with few labeled samples. Extensive experiments on four real hyperspectral data sets prove that hyperspectral data is highly sparse in nature, and the proposed approaches are robust across different databases, offer more classification accuracy, and are more efficient than state-of-the-art methods.