# Linked Component Analysis from Matrices to High Order Tensors: Applications to Biomedical Data

arXiv: https://arxiv.org/abs/1508.07416 · HTML: https://mlsanity.com/paper/1508.07416/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Aug 2015.

## Built on by (most cited first, 16 of 16)

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- [Intelligently Augmented Contrastive Tensor Factorization: Empowering Multi-dimensional Time Series Classification in Low-Data Environments](https://mlsanity.com/paper/2505.03825/) (2025)
- [sparseGeoHOPCA: A Geometric Solution to Sparse Higher-Order PCA Without Covariance Estimation](https://mlsanity.com/paper/2506.08670/) (2025)
- [Normalized Iterative Hard Thresholding for Tensor Recovery](https://mlsanity.com/paper/2507.04228/) (2025)
- [Motor Imagery EEG Signal Classification Using Minimally Random Convolutional Kernel Transform and Hybrid Deep Learning](https://mlsanity.com/paper/2508.16179/) (2025)
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## Abstract (arXiv)

With the increasing availability of various sensor technologies, we now have access to large amounts of multi-block (also called multi-set, multi-relational, or multi-view) data that need to be jointly analyzed to explore their latent connections. Various component analysis methods have played an increasingly important role for the analysis of such coupled data. In this paper, we first provide a brief review of existing matrix-based (two-way) component analysis methods for the joint analysis of such data with a focus on biomedical applications. Then, we discuss their important extensions and generalization to multi-block multiway (tensor) data. We show how constrained multi-block tensor decomposition methods are able to extract similar or statistically dependent common features that are shared by all blocks, by incorporating the multiway nature of data. Special emphasis is given to the flexible common and individual feature analysis of multi-block data with the aim to simultaneously extract common and individual latent components with desired properties and types of diversity. Illustrative examples are given to demonstrate their effectiveness for biomedical data analysis.