Scalable diagnostics for global atmospheric chemistry using Ristretto library (version 1.0)

We introduce a new set of algorithmic tools capable of producing scalable, low-rank decompositions of global spatiotemporal atmospheric chemistry data. By exploiting emerging randomized linear algebra algorithms, a suite of decompositions are proposed that extract the dominant features from big data sets (i.e., global atmospheric chemistry at longitude, latitude, and elevation) with improved interpretability. Importantly, our proposed algorithms scale with the intrinsic rank of the global chemistry space rather than the ever increasing spatiotemporal measurement space, thus allowing for the efficient representation and compression of the data. In addition to scalability, two additional innovations are proposed for improved interpretability: (i) a nonnegative decomposition of the data for improved interpretability by constraining the chemical space to have only positive expression values (unlike PCA analysis); and (ii) sparse matrix decompositions, which threshold small weights to zero, thus highlighting the dominant, localized spatial activity (again unlike PCA analysis). Our methods are demonstrated on a full year of global chemistry dynamics data, showing the significant improvement in computational speed and interpretability. We show that the decomposition methods presented here successfully extract known major features of atmospheric chemistry, such as summertime surface pollution and biomass burning activities.

Relationship Matrix Nonnegative Decomposition for Clustering

Nonnegative matrix factorization (NMF) is a popular tool for analyzing the latent structure of nonnegative data. For a positive pairwise similarity matrix, symmetric NMF (SNMF) and weighted NMF (WNMF) can be used to cluster the data. However, both of them are not very efficient for the ill-structured pairwise similarity matrix. In this paper, a novel model, called relationship matrix nonnegative decomposition (RMND), is proposed to discover the latent clustering structure from the pairwise similarity matrix. The RMND model is derived from the nonlinear NMF algorithm. RMND decomposes a pairwise similarity matrix into a product of three low rank nonnegative matrices. The pairwise similarity matrix is represented as a transformation of a positive semidefinite matrix which pops out the latent clustering structure. We develop a learning procedure based on multiplicative update rules and steepest descent method to calculate the nonnegative solution of RMND. Experimental results in four different databases show that the proposed RMND approach achieves higher clustering accuracy.