Comparing Singular Value Decomposition and Non-negative Matrix Factorization Applied to Dimensionality Reduction of Precipitation in Japan

Abstract

Dimensionality reduction methods such as singular value decomposition (SVD) have been widely applied in the earth science field. On the other hand, non-negative matrix factorization (NMF), one of the other dimensionality reduction methods based on matrix decomposition, has been used only to limited applications in the earth science. This study applies the two dimensionality reduction methods, SVD and NMF, to the Radar-AMeDAS precipitation, and compares the extracted features by these decomposition methods. The extracted features are used to reconstruct the original precipitation fields from limited amount of data at AMeDAS observation locations. We compare the two decomposition methods through evaluating errors in reconstructed precipitation fields. For further comparison, this study succeeds in visualizing the features extracted by the two decomposition methods. Through these comparisons, we found that NMF is more robust to reconstruct precipitation fields than SVD. In addition, NMF provided more physically interpretable features than SVD.