Spectral clustering is a flexible clustering technique that finds data clusters in the spectral embedding space of the data. It doesn’t assume convexity of the shape of clusters, and is able to find non-linear cluster boundaries. Constrained spectral clustering aims at incorporating user-defined pairwise constraints in to spectral clustering. Typically, there are two kinds of pairwise constrain...

Distance-based learning methods, like clustering and SVMs, are dependent on good distance metrics. This paper does unsupervised metric learning in the context of clustering. We seek transformations of data which give clean and well separated clusters where clean clusters are those for which membership can be accurately predicted. The transformation (hence distance metric) is obtained by minimiz...

Distance metric learning provides an approach to transfer knowledge from sparse labeled data to unlabeled data. The learned metric is more proper to measure the similarity of semantics among instances. The main idea of the algorithm is to create an objective function using the equivalence constraints and in-equivalence constraints and pose the problem as an optimization problem. In this paper, ...

In order to improve the computational efficiency of conformal predictor, distance metric learning methods were used in the algorithm. The process of learning was divided into two stages: offline learning and online learning. Firstly, part of the training data was used in distance metric learning to get a space transformation matrix in the offline learning stage; Secondly, standard CP-KNN was co...

In large scale machine learning and data mining problems with high feature dimensionality, the Euclidean distance between data points can be uninformative, and Distance Metric Learning (DML) is often desired to learn a proper similarity measure (using side information such as example data pairs being similar or dissimilar). However, high dimensionality and large volume of pairwise constraints i...

Y. Huang acknowledges partial support from a UCF Graduate College Presidential Fellowship and National Science Foundation (NS F) grant No. 1200566. C. Li acknowledges partial support from NSF grants No. 0806931 and No. 0963146. M. Georgiopoulos acknowledges partial support from NSF grants No. 1161228 and No. 0525429. G. G. Anagnostopoulos acknowledges partial support from NSF grant No. 1263011....

We present a survey of recent work on the problem of learning a distance metric in the framework of semidefinite programming (SDP). Along with a brief theoretical background on convex optimization and distance metrics, we present various methods developed in this context under different approaches and provide theoretical analysis for a subset of them. A gradient ascent projection algorithm (Xin...

We consider the problem of learning a measure of distance among vectors in a feature space and propose a hybrid method that simultaneously learns from similarity ratings assigned to pairs of vectors and class labels assigned to individual vectors. Our method is based on a generative model in which class labels can provide information that is not encoded in feature vectors but yet relates to per...

In this paper, we propose a new multi-manifold metric learning (MMML) method for the task of face recognition based on image sets. Different from most existing metric learning algorithms that learn the distance metric for measuring single images, our method aims to learn distance metrics to measure the similarity between manifold pairs. In our method, each image set is modeled as a manifold and...