Clustering of Data with Missing Entries using Non-convex Fusion Penalties

TL;DR

This paper introduces a novel clustering method capable of handling datasets with many missing feature values by using non-convex fusion penalties, supported by theoretical guarantees and demonstrated on real and simulated data.

Contribution

The paper presents a new clustering algorithm that manages missing data using non-convex fusion penalties, with theoretical analysis and practical validation.

Findings

Algorithm degrades gradually with more missing data

The method outperforms traditional clustering on incomplete datasets

The approach is effective on real-world datasets like MRI and Wine

Abstract

The presence of missing entries in data often creates challenges for pattern recognition algorithms. Traditional algorithms for clustering data assume that all the feature values are known for every data point. We propose a method to cluster data in the presence of missing information. Unlike conventional clustering techniques where every feature is known for each point, our algorithm can handle cases where a few feature values are unknown for every point. For this more challenging problem, we provide theoretical guarantees for clustering using a $\ell_0$ fusion penalty based optimization problem. Furthermore, we propose an algorithm to solve a relaxation of this problem using saturating non-convex fusion penalties. It is observed that this algorithm produces solutions that degrade gradually with an increase in the fraction of missing feature values. We demonstrate the utility of the proposed method using a simulated dataset, the Wine dataset and also an under-sampled cardiac MRI dataset. It is shown that the proposed method is a promising clustering technique for datasets with large fractions of missing entries.