k-medoids algorithm is a partitional, centroid-based clustering algorithm which uses pairwise distances of data points and tries to directly decompose the dataset with @math points into a set of @math disjoint clusters. However, k-medoids itself requires all distances between data points that are not so easy to get in many applications. In this paper, we introduce a new method which requires only a small proportion of the whole set of distances and makes an effort to estimate an upper-bound for unknown distances using the inquired ones. This algorithm makes use of the triangle inequality to calculate an upper-bound estimation of the unknown distances. Our method is built upon a recursive approach to cluster objects and to choose some points actively from each bunch of data and acquire the distances between these prominent points from oracle. Experimental results show that the proposed method using only a small subset of the distances can find proper clustering on many real-world and synthetic datasets.
In @cite_26 @cite_3 , distance-based algorithms are presented for active spectral clustering in which a perturbation theory approach is used to select queries. A constraint-based algorithm has also been presented in @cite_14 for active spectral clustering that uses an approach based on maximum expected error reduction to select queries.
@cite_14 @cite_26 @cite_3
2134342006 1508464538 2003293138 2068935349
The technique of spectral clustering is widely used to segment a range of data from graphs to images. Our work marks a natural progression of spectral clustering from the original passive unsupervised formulation to our active semi-supervised formulation. We follow the widely used area of constrained clustering and allow supervision in the form of pair wise relations between two nodes: Must-Link and Cannot-Link. Unlike most previous constrained clustering work, our constraints are specified incrementally by querying an oracle (domain expert). Since in practice, each query comes with a cost, our goal is to maximally improve the result with as few queries as possible. The advantages of our approach include: 1) it is principled by querying the constraints which maximally reduce the expected error, 2) it can incorporate both hard and soft constraints which are prevalent in practice. We empirically show that our method significantly outperforms the baseline approach, namely constrained spectral clustering with randomly selected constraints, on UCI benchmark data sets. This work focuses on the active selection of pairwise constraints for spectral clustering. We develop and analyze a technique for Active Constrained Clustering by Examining Spectral eigenvectorS (ACCESS) derived from a similarity matrix. The ACCESS method uses an analysis based on the theoretical properties of spectral decomposition to identify data items that are likely to be located on the boundaries of clusters, and for which providing constraints can resolve ambiguity in the cluster descriptions. Empirical results on three synthetic and five real data sets show that ACCESS significantly outperforms constrained spectral clustering using randomly selected constraints. While spectral clustering is usually an unsupervised operation, there are circumstances in which we have prior belief that pairs of samples should (or should not) be assigned with the same cluster. Constrained spectral clustering aims to exploit this prior belief as constraint (or weak supervision) to influence the cluster formation so as to obtain a structure more closely resembling human perception. Two important issues remain open: (1) how to propagate sparse constraints effectively, (2) how to handle ill-conditioned noisy constraints generated by imperfect oracles. In this paper we present a unified framework to address the above issues. Specifically, in contrast to existing constrained spectral clustering approaches that blindly rely on all features for constructing the spectral, our approach searches for neighbours driven by discriminative feature selection for more effective constraint diffusion. Crucially, we formulate a novel data-driven filtering approach to handle the noisy constraint problem, which has been unrealistically ignored in constrained spectral clustering literature. We present an image set classification algorithm based on unsupervised clustering of labeled training and unlabeled test data where labels are only used in the stopping criterion. The probability distribution of each class over the set of clusters is used to define a true set based similarity measure. To this end, we propose an iterative sparse spectral clustering algorithm. In each iteration, a proximity matrix is efficiently recomputed to better represent the local subspace structure. Initial clusters capture the global data structure and finer clusters at the later stages capture the subtle class differences not visible at the global scale. Image sets are compactly represented with multiple Grassmannian manifolds which are subsequently embedded in Euclidean space with the proposed spectral clustering algorithm. We also propose an efficient eigenvector solver which not only reduces the computational cost of spectral clustering by many folds but also improves the clustering quality and final classification results. Experiments on five standard datasets and comparison with seven existing techniques show the efficacy of our algorithm.