Generalized Low Rank Models

Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, the authors extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal, and other data types. This framework encompasses many well-known techniques in data analysis, such as non-negative matrix factorization, matrix completion, sparse and robust PCA, k-means, k-SVD, and maximum margin matrix factorization. The method handles heterogeneous data sets, and leads to coherent schemes for compressing, denoising, and imputing missing entries across all data types simultaneously. It also admits a number of interesting interpretations of the low rank factors, which allow clustering of examples or of features. The authors propose several parallel algorithms for fitting generalized low rank models, and describe implementations and numerical results.