Block Tensor Decomposition for Source Apportionment of Air Pollution
  The ambient particulate chemical composition data with three particle diameter sizes (2.5mm<D< 1.15mm, 1.15mm<D<0.34mm and 0.34mm<D<0.1mm) collected at a major industrial center in Allen Park in Detroit, MI is examined. Standard multiway (tensor) methods like PARAFAC and Tucker tensor decompositions have been applied extensively to many chemical data. However, for multiple particle sizes, the source apportionment analysis calls for a novel multiway factor analysis. We apply the regularized block tensor decomposition to the collected air sample data. In particular, we use the Block Term Decomposition (BTD) in rank-(L;L;1) form to identify nine pollution sources (Fe+Zn, Sulfur with Dust, Road Dust, two types of Metal Works, Road Salt, Local Sulfate, and Homogeneous and Cloud Sulfate). 
Philip K. Hopke, Maggie Leung, Na Li and Carmeliza Navasca
math.NA