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Abstract
c The Author(s) 2015. This article is published with open access at Springerlink.com Abstract As a kind of weaker supervisory information, pairwise constraints can be exploited to guide the data analysis process, such as data clustering. This paper formulates pairwise constraint propagation, which aims to predict the large quantity of unknown constraints from scarce known constraints, as a low-rank matrix recovery (LMR) problem. Although recent advances in transductive learning based on matrix completion can be directly adopted to solve this problem, our work intends to develop a more general low-rank matrix recovery solution for pairwise constraint propagation, which not only completes the unknown entries in the constraint matrix but also removes the noise from the data matrix. The problem can be eectively solved using an augmented Lagrange multiplier method. Experimental results on constrained clustering tasks based on the propagated pairwise constraints have shown that our method can obtain more stable results than state-of-the-art algorithms, and outperform them.
Highlights
Pairwise constraints provide prior knowledge as to whether two data points belong to the same class or not, known as must-link constraints and cannot-link constraints, respectively
The effectiveness of our propagation method is verified by the fact that our low-rank matrix recovery based pairwise constraint propagation (LMRPCP) consistently obtains better results in the constrained clustering task
LMRPCP performs better and more stably than the other three constraint propagation methods. This is because LMRPCP can consider the global low-rank structure and remove the influence of the data noise
Summary
Pairwise constraints provide prior knowledge as to whether two data points belong to the same class or not, known as must-link constraints and cannot-link constraints, respectively. We cannot infer instance labels from only pairwise constraints, especially for multi-class data. Manuscript received: 2014-12-05; accepted: 2015-03-18 means that pairwise constraints are weaker and more general than explicit labels on data. Pairwise constrains have been widely used in the context of clustering with side information, called semi-supervised clustering or constrained clustering, where it has been shown that the presence of appropriate pairwise constraints can often improve the performance [1,2,3,4,5]. While it is possible to infer pairwise constraints from domain knowledge or user feedback, in practice, the availability of such constraints is scarce. Pairwise constraint propagation aims to produce a large quantity of pairwise constraints from scarce known constraints
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