# Angle-Based Joint and Individual Variation Explained

## TL;DR

This paper introduces a new angle-based method for integrative analysis of multiple data blocks, effectively capturing joint and individual variations without normalization, demonstrated on cancer and mortality datasets.

## Contribution

It presents a novel angle-based approach that improves understanding of data heterogeneity and offers a fast, normalization-free analysis of joint and individual variation.

## Key findings

- Revealed distinct behaviors of signals in tumor subtypes
- Uncovered historical insights from mortality data
- Method is insensitive to data heterogeneity

## Abstract

Integrative analysis of disparate data blocks measured on a common set of experimental subjects is a major challenge in modern data analysis. This data structure naturally motivates the simultaneous exploration of the joint and individual variation within each data block resulting in new insights. For instance, there is a strong desire to integrate the multiple genomic data sets in The Cancer Genome Atlas to characterize the common and also the unique aspects of cancer genetics and cell biology for each source. In this paper we introduce Angle-Based Joint and Individual Variation Explained capturing both joint and individual variation within each data block. This is a major improvement over earlier approaches to this challenge in terms of a new conceptual understanding, much better adaption to data heterogeneity and a fast linear algebra computation. Important mathematical contributions are the use of score subspaces as the principal descriptors of variation structure and the use of perturbation theory as the guide for variation segmentation. This leads to an exploratory data analysis method which is insensitive to the heterogeneity among data blocks and does not require separate normalization. An application to cancer data reveals different behaviors of each type of signal in characterizing tumor subtypes. An application to a mortality data set reveals interesting historical lessons. Software and data are available at GitHub <https://github.com/MeileiJiang/AJIVE_Project>.