Generalized Low Rank Models

TL;DR

This paper introduces a unified framework called Generalized Low Rank Models that extends PCA to handle diverse data types, enabling simultaneous compression, denoising, and missing data imputation across heterogeneous datasets.

Contribution

The paper develops a flexible, unified approach that generalizes PCA to various data types and integrates multiple matrix factorization techniques within a single framework.

Findings

Handles heterogeneous data types simultaneously

Enables effective data compression and denoising

Provides scalable parallel algorithms for model fitting

Abstract

Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we 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 nonnegative 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. We propose several parallel algorithms for fitting generalized low rank models, and describe implementations and numerical results.