Subspace Clustering when Data is Missing

Grouping data points that follow the same linear pattern. The challenge is that data is highly incomplete.

Subspace clustering aims to sort mixed data by uncovering their hidden linear patterns — like sorting fabrics by the weave hidden beneath their colors and designs.

Unfortunately, missing data is ubiquitous in modern applications. For example, medical records often have incomplete test results, sensors in engineering systems can fail to record measurements, and surveys or social science studies frequently contain unanswered questions.

The challenge with missing data is that many linear patterns may fit — like sorting fabrics by weave when you only have a few loose threads from each one.

We investigate the theoretical limits that determine when this type of clustering is possible — how many threads we need — and we design practical algorithms that can cluster efficiently.