Constrained Clustering Problems

Repeated Record Ordering for Constrained Size Clustering

One of the main techniques used in data mining is data clustering, which has many applications in computer science, biology, and social sciences. Constrained clustering is a type of clustering in which side information provided by the user is incorporated into current clustering algorithms. One of the well researched constrained clustering algorithms is called microaggregation. In a microaggreg...

Probability-one homotopy maps for tracking constrained clustering solutions

Modern machine learning problems typically have multiple criteria, but there is currently no systematic mathematical theory to guide the design of formulations and exploration of alternatives. Homotopy methods are a promising approach to characterize solution spaces by smoothly tracking solutions from one formulation (typically an “easy” problem) to another (typically a “hard” problem). New res...

Solution of Constrained Clustering Problems through Homotopy Tracking

Lagrangian Constrained Clustering

Incorporating background knowledge in clustering problems has attracted wide interest. This knowledge can be represented as pairwise instance-level constraints. Existing techniques approach satisfaction of such constraints from a soft (discretionary) perspective, yet there exist scenarios for constrained clustering where satisfying as many constraints as possible. We present a new Lagrangian Co...

Constrained fractional set programs and their application in local clustering and community detection

The (constrained) minimization of a ratio of set functions is a problem frequently occurring in clustering and community detection. As these optimization problems are typically NP-hard, one uses convex or spectral relaxations in practice. While these relaxations can be solved globally optimally, they are often too loose and thus lead to results far away from the optimum. In this paper we show t...