An important and well-studied problem in hyperspectral image data applications is to identify materials present in the object or scene being imaged and to quantify their abundance in the mixture. Due to the increasing quantity of data usually encountered in hyperspectral datasets, effective data compression is also an important consideration. In this paper, we develop novel methods based on tensor analysis that focus on all three of these goals: material identification, material abundance estimation, and data compression. Test results are reported in all three perspectives.