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A wide variety of distortion functions, such as squared Euclidean distance, Mahalanobis distance, Itakura-Saito distance and relative entropy, have been used for clustering. In this paper, we propose and analyze parametric hard and soft clustering algorithms based on a large class of distortion functions known as Bregman divergences. The proposed algorithms… (More)

Anomaly detection is an important problem that has been researched within diverse research areas and application domains. Many anomaly detection techniques have been specifically developed for certain application domains, while others are more generic. This survey tries to provide a structured and comprehensive overview of the research on anomaly detection.… (More)

Semi-supervised clustering uses a small amount of supervised data to aid unsupervised learning. One typical approach specifies a limited number of must-link and cannot-link constraints between pairs of examples. This paper presents a pairwise constrained clustering framework and a new method for actively selecting informative pairwise constraints to get… (More)

Several large scale data mining applications, such as text categorization and gene expression analysis, involve high-dimensional data that is also inherently directional in nature. Often such data is L 2 normalized so that it lies on the surface of a unit hypersphere. Popular models such as (mixtures of) multi-variate Gaussians are inadequate for… (More)

Co-clustering is a powerful data mining technique with varied applications such as text clustering, microarray analysis and recommender systems. Recently, an information-theoretic co-clustering approach applicable to empirical joint probability distributions was proposed. In many situations, co-clustering of more general matrices is desired. In this paper,… (More)

Online optimization has emerged as powerful tool in large scale optimization. In this paper , we introduce efficient online optimization algorithms based on the alternating direction method (ADM), which can solve online convex optimization under linear constraints where the objective could be non-smooth. We introduce new proof techniques for ADM in the… (More)

The mirror descent algorithm (MDA) generalizes gradient descent by using a Bregman divergence to replace squared Euclidean distance. In this paper, we similarly generalize the alternating direction method of multipliers (ADMM) to Bregman ADMM (BADMM), which allows the choice of different Bregman divergences to exploit the structure of problems. BADMM… (More)

Given a probability space (Ω, F , P), a F-measurable random variable X, and a sub-σ-algebra G ⊂ F , it is well known that the conditional expectation E[X|G] is the optimal L 2-predictor (also known as " the least mean square error " predictor) of X among all the G-measurable random variables [8, 11]. In this paper, we provide necessary and sufficient… (More)

We propose a new matrix completion algorithm— Kernelized Probabilistic Matrix Factorization (KPMF), which effectively incorporates external side information into the matrix factorization process. Unlike Probabilis-tic Matrix Factorization (PMF) [14], which assumes an independent latent vector for each row (and each column) with Gaussian priors, KMPF works… (More)