ABSTRACT
With the advances in sensor, storage, and networking technologies, bigger and bigger data are being generated daily in a wide range of applications. Figures 1.1 through 1.4 show some examples in computer vision, audio processing, neuroscience, remote sensing, and data mining. To succeed in this era of big data [Howe et al., 2008], it becomes more and more important to learn compact features for efficient processing. Most big data are multidimensional and they can often be represented as multidimensional arrays, which are referred to as tensors in mathematics [Kolda and Bader, 2009]. Thus, tensor-based computation is emerging, especially with the growth of mobile Internet [Lenhart et al., 2010], cloud computing [Armbrust et al., 2010], and big data such as the MapReduce model [Dean and Ghemawat, 2008; Kang et al., 2012].
