Integrated Principal Components Analysis

Abstract

Data integration, or the strategic analysis of multiple sources of data simultaneously, can often lead to discoveries that may be hidden in individualistic analyses of a single data source. We develop a new unsupervised data integration method named Integrated Principal Components Analysis (iPCA), which is a model-based generalization of PCA and serves as a practical tool to find and visualize common patterns that occur in multiple data sets. The key idea driving iPCA is the matrix-variate normal model, whose Kronecker product covariance structure captures both individual patterns within each data set and joint patterns shared by multiple data sets. Building upon this model, we develop several penalized (sparse and non-sparse) covariance estimators for iPCA, and using geodesic convexity, we prove that our non-sparse iPCA estimator converges to the global solution of a non-convex problem. We also demonstrate the practical advantages of iPCA through extensive simulations and a case study application to integrative genomics for Alzheimer's disease. In particular, we show that the joint patterns extracted via iPCA are highly predictive of a patient's cognition and Alzheimer's diagnosis.

References in corpus (7)

• Joint and individual variation explained (JIVE) for integrated analysis of multiple data types
• Sparse Inverse Covariance Matrix Estimation Using Quadratic Approximation
• Convergence Properties of Kronecker Graphical Lasso Algorithms
• Orthogonal Sparse PCA and Covariance Estimation via Procrustes Reformulation
• Geodesic Convex Optimization: Differentiation on Manifolds, Geodesics, and Convexity
• Robust Kronecker Product PCA for Spatio-Temporal Covariance Estimation
• Distributed Estimation of Principal Eigenspaces

Cited by in corpus (4)

• Integrative Generalized Convex Clustering Optimization and Feature Selection for Mixed Multi-View Data
• No-go Theorem for Acceleration in the Hyperbolic Plane
• RaJIVE: Robust Angle Based JIVE for Integrating Noisy Multi-Source Data
• Near optimal sample complexity for matrix and tensor normal models via geodesic convexity