A Kernel-Learning Approach to Semi-supervised Clustering with Relative Distance Comparisons

• Published in: Machine Learning and Knowledge Discovery in Databases pp. 219 - 234
• Main Authors: Amid, Ehsan, Gionis, Aristides, Ukkonen, Antti
• Format: Book Chapter
• Language: English
• Published: Cham Springer International Publishing 2015
• Series: Lecture Notes in Computer Science
• Subjects: Data Item; Kernel Matrix; Pairwise Constraint; Relative Comparison; Spectral Cluster
• ISBN: 3319235273; 9783319235271
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-319-23528-8_14

We consider the problem of clustering a given dataset into k clusters subject to an additional set of constraints on relative distance comparisons between the data items. The additional constraints are meant to reflect side-information that is not expressed in the feature vectors, directly. Relative comparisons can express structures at finer level of detail than must-link (ML) and cannot-link (CL) constraints that are commonly used for semi-supervised clustering. Relative comparisons are particularly useful in settings where giving an ML or a CL constraint is difficult because the granularity of the true clustering is unknown. Our main contribution is an efficient algorithm for learning a kernel matrix using the log determinant divergence (a variant of the Bregman divergence) subject to a set of relative distance constraints. Given the learned kernel matrix, a clustering can be obtained by any suitable algorithm, such as kernel k-means. We show empirically that kernels found by our algorithm yield clusterings of higher quality than existing approaches that either use ML/CL constraints or a different means to implement the supervision using relative comparisons.