# Cluster Quilting: Spectral Clustering for Patchwork Learning

arXiv: https://arxiv.org/abs/2406.13833 · HTML: https://mlsanity.com/paper/2406.13833/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 59 references that are in the map.
- First posted on arXiv 19 Jun 2024.

## Builds on (most cited first, 16 of 16)

- [Consistency of spectral clustering in stochastic block models](https://mlsanity.com/paper/1312.2050/) (2013)
- [Spectral Methods for Data Science: A Statistical Perspective](https://mlsanity.com/paper/2012.08496/) (2020)
- [Optimality of Spectral Clustering in the Gaussian Mixture Model](https://mlsanity.com/paper/1911.00538/) (2019)
- [Doubly Aligned Incomplete Multi-view Clustering](https://mlsanity.com/paper/1903.02785/) (2019)
- [A Survey on Incomplete Multi-view Clustering](https://mlsanity.com/paper/2208.08040/) (2022)
- [One-Pass Incomplete Multi-view Clustering](https://mlsanity.com/paper/1903.00637/) (2019)
- [k-POD: A Method for k-Means Clustering of Missing Data](https://mlsanity.com/paper/1411.7013/) (2014)
- [Optimal High-order Tensor SVD via Tensor-Train Orthogonal Iteration](https://mlsanity.com/paper/2010.02482/) (2020)
- [Bayesian Consensus Clustering](https://mlsanity.com/paper/1302.7280/) (2013)
- [Integrative Generalized Convex Clustering Optimization and Feature Selection for Mixed Multi-View Data](https://mlsanity.com/paper/1912.05449/) (2019)
- [Matrix Completion When Missing Is Not at Random and Its Applications in Causal Panel Data Models](https://mlsanity.com/paper/2308.02364/) (2023)
- [Entrywise Inference for Missing Panel Data: A Simple and Instance-Optimal Approach](https://mlsanity.com/paper/2401.13665/) (2024)
- [Low-Rank Covariance Completion for Graph Quilting with Applications to Functional Connectivity](https://mlsanity.com/paper/2209.08273/) (2022)
- [Optimal Clustering with Missing Values](https://mlsanity.com/paper/1902.09694/) (2019)
- [Heteroskedastic Tensor Clustering](https://mlsanity.com/paper/2311.02306/) (2023)
- [Clustering of Data with Missing Entries using Non-convex Fusion Penalties](https://mlsanity.com/paper/1709.01870/) (2017)

## Abstract (arXiv)

Patchwork learning arises as a new and challenging data collection paradigm where both samples and features are observed in fragmented subsets. Due to technological limits, measurement expense, or multimodal data integration, such patchwork data structures are frequently seen in neuroscience, healthcare, and genomics, among others. Instead of analyzing each data patch separately, it is highly desirable to extract comprehensive knowledge from the whole data set. In this work, we focus on the clustering problem in patchwork learning, aiming at discovering clusters amongst all samples even when some are never jointly observed for any feature. We propose a novel spectral clustering method called Cluster Quilting, consisting of (i) patch ordering that exploits the overlapping structure amongst all patches, (ii) patchwise SVD, (iii) sequential linear mapping of top singular vectors for patch overlaps, followed by (iv) k-means on the combined and weighted singular vectors. Under a sub-Gaussian mixture model, we establish theoretical guarantees via a non-asymptotic misclustering rate bound that reflects both properties of the patch-wise observation regime as well as the clustering signal and noise dependencies. We also validate our Cluster Quilting algorithm through extensive empirical studies on both simulated and real data sets in neuroscience and genomics, where it discovers more accurate and scientifically more plausible clusters than other approaches.