Robust Correlation Clustering

In this paper, we introduce and study the Robust-Correlation-Clustering problem: given a graph G = (V,E) where every edge is either labeled + or - (denoting similar or dissimilar pairs of vertices), and a parameter m, the goal is to delete a set D of m vertices, and partition the remaining vertices V D into clusters to minimize the cost of the clustering, which is the sum of the number of + edges with end-points in different clusters and the number of - edges with end-points in the same cluster. This generalizes the classical Correlation-Clustering problem which is the special case when m = 0. Correlation clustering is useful when we have (only) qualitative information about the similarity or dissimilarity of pairs of points, and Robust-Correlation-Clustering equips this model with the capability to handle noise in datasets. In this work, we present a constant-factor bi-criteria algorithm for Robust-Correlation-Clustering on complete graphs (where our solution is O(1)-approximate w.r.t the cost while however discarding O(1) m points as outliers), and also complement this by showing that no finite approximation is possible if we do not violate the outlier budget. Our algorithm is very simple in that it first does a simple LP-based pre-processing to delete O(m) vertices, and subsequently runs a particular Correlation-Clustering algorithm ACNAlg [Ailon et al., 2005] on the residual instance. We then consider general graphs, and show (O(log n), O(log^2 n)) bi-criteria algorithms while also showing a hardness of alpha_MC on both the cost and the outlier violation, where alpha_MC is the lower bound for the Minimum-Multicut problem

The role of human factors in stereotyping behavior and perception of digital library users: A robust clustering approach

To deliver effective personalization for digital library users, it is necessary to identify which human factors are most relevant in determining the behavior and perception of these users. This paper examines three key human factors: cognitive styles, levels of expertise and gender differences, and utilizes three individual clustering techniques: k-means, hierarchical clustering and fuzzy clustering to understand user behavior and perception. Moreover, robust clustering, capable of correcting the bias of individual clustering techniques, is used to obtain a deeper understanding. The robust clustering approach produced results that highlighted the relevance of cognitive style for user behavior, i.e., cognitive style dominates and justifies each of the robust clusters created. We also found that perception was mainly determined by the level of expertise of a user. We conclude that robust clustering is an effective technique to analyze user behavior and perception

Robust hierarchical k-center clustering

One of the most popular and widely used methods for data clustering is hierarchical clustering. This clustering technique has proved useful to reveal interesting structure in the data in several applications ranging from computational biology to computer vision. Robustness is an important feature of a clustering technique if we require the clustering to be stable against small perturbations in the input data. In most applications, getting a clustering output that is robust against adversarial outliers or stochastic noise is a necessary condition for the applicability and effectiveness of the clustering technique. This is even more critical in hierarchical clustering where a small change at the bottom of the hierarchy may propagate all the way through to the top. Despite all the previous work [2, 3, 6, 8], our theoretical understanding of robust hierarchical clustering is still limited and several hierarchical clustering algorithms are not known to satisfy such robustness properties. In this paper, we study the limits of robust hierarchical k-center clustering by introducing the concept of universal hierarchical clustering and provide (almost) tight lower and upper bounds for the robust hierarchical k-center clustering problem with outliers and variants of the stochastic clustering problem. Most importantly we present a constant-factor approximation for optimal hierarchical k-center with at most z outliers using a universal set of at most O(z2) set of outliers and show that this result is tight. Moreover we show the necessity of using a universal set of outliers in order to compute an approximately optimal hierarchical k-center with a diffierent set of outliers for each k