Exemplar-based clustering methods have been extensively shown to be effective in many clustering problems. They adaptively determine the number of clusters and hold the appealing advantage of not requiring the estimation of latent parameters, which is otherwise difficult in case of complicated parametric model and high dimensionality of the data. However, modeling arbitrary underlying distribution of the data is still difficult for existing exemplar-based clustering methods. We present Pairwise Exemplar Clustering (PEC) to alleviate this problem by modeling the underlying cluster distributions more accurately with non-parametric kernel density estimation. Interpreting the clusters as classes from a supervised learning perspective, we search for an optimal partition of the data that balances two quantities: 1 the misclassification rate of the data partition for separating the clusters; 2 the sum of within-cluster dissimilarities for controlling the cluster size. The broadly used kernel form of cut turns out to be a special case of our formulation. Moreover, we optimize the corresponding objective function by a new efficient algorithm for message computation in a pairwise MRF. Experimental results on synthetic and real data demonstrate the effectiveness of our method.

Existing clustering methods can be roughly classified into two categories: generative and discriminative approaches. Generative clustering aims to explain the data and thus is adaptive to the underlying data distribution; discriminative clustering, on the other hand, emphasizes on finding partition boundaries. In this paper, we take the advantages of both models by coupling the two paradigms through feature mapping derived from linearizing Bayesian classifiers. Such the feature mapping strategy maps nonlinear boundaries of generative clustering to linear ones in the feature space where we explicitly impose the maximum entropy principle. We also propose the unified probabilistic framework, enabling solvers using standard techniques. Experiments on a variety of datasets bear out the notable benefit of our method in terms of adaptiveness and robustness.

In this paper, a new unsupervised learning algorithm, namely Nonnegative Discriminative Feature Selection (NDFS), is proposed. To exploit the discriminative information in unsupervised scenarios, we perform spectral clustering to learn the cluster labels of the input samples, during which the feature selection is performed simultaneously. The joint learning of the cluster labels and feature selection matrix enables NDFS to select the most discriminative features. To learn more accurate cluster labels, a nonnegative constraint is explicitly imposed to the class indicators. To reduce the redundant or even noisy features, l 2,1 -norm minimization constraint is added into the objective function, which guarantees the feature selection matrix sparse in rows. Our algorithm exploits the discriminative information and feature correlation simultaneously to select a better feature subset. A simple yet efficient iterative algorithm is designed to optimize the proposed objective function. Experimental results on different real world datasets demonstrate the encouraging performance of our algorithm over the state-of-the-arts.

Traditional clustering algorithms are designed to search for a single clustering solution despite the fact that multiple alternative solutions might exist for a particular dataset. For example, a set of news articles might be clustered by topic or by the author's gender or age. Similarly, book reviews might be clustered by sentiment or comprehensiveness. In this paper, we address the problem of identifying alternative clustering solutions by developing a Probabilistic Multi-Clustering (PMC) model that discovers multiple, maximally different clusterings of a data sample. Empirical results on six datasets representative of real-world applications show that our PMC model exhibits superior performance to comparable multi-clustering algorithms.

We investigate a natural generalization of the classical clustering problem, considering clustering tasks in which different instances may have different weights. We conduct the first extensive theoretical analysis on the influence of weighted data on standard clustering algorithms in both the partitional and hierarchical settings, characterizing the conditions under which algorithms react to weights. Extending a recent framework for clustering algorithm selection, we propose intuitive properties that would allow users to choose between clustering algorithms in the weighted setting and classify algorithms accordingly.

With the growing popularity of social networks and collaboration systems, people are increasingly working with or socially connected with each other. Unified messaging system provides a single interface for users to receive and process information from multiple sources. It is highly desirable to design attention management solution that can help users easily navigate and process dozens of unread messages from a unified message system. Moreover, with the proliferation of mobile devices people are now selectively consuming the most important messages on the go between different activities in their daily life. The information overload problem is especially acute for mobile users with small screen to display. In this paper, we present \PAM, an intelligent end-to-end Personalized Attention Management solution that employs analytical techniques that can learn user interests and organize and prioritize incoming messages based on user interests. For a list of unread messages, \PAM generates a concise attention report that allows users to quickly scan the important new messages from his important social connections as well as messages about his most important tasks that the user is involved with. Our solution can also be applied in other applications such as news filtering and alerts on mobile devices. Our evaluation results demonstrate the effectiveness of \PAM.

The problem of hierarchical clustering items from pairwise similarities is found across various scientific disciplines, from biology to networking. Often, applications of clustering techniques are limited by the cost of obtaining similarities between pairs of items. While prior work has been developed to reconstruct clustering using a significantly reduced set of pairwise similarities via adaptive measurements, these techniques are only applicable when choice of similarities are available to the user. In this paper, we examine reconstructing hierarchical clustering under similarity observations at-random. We derive precise bounds which show that a significant fraction of the hierarchical clustering can be recovered using fewer than all the pairwise similarities. We find that the correct hierarchical clustering down to a constant fraction of the total number of items (i.e., clusters sized O(N)) can be found using only O(N log N) randomly selected pairwise similarities in expectation.

We mathematically model Ignacio Matte Blanco's principles of symmetric and asymmetric being through use of an ultrametric topology. We use for this the highly regarded 1975 book of this Chilean psychiatrist and pyschoanalyst (born 1908, died 1995). Such an ultrametric model corresponds to hierarchical clustering in the empirical data, e.g. text. We show how an ultrametric topology can be used as a mathematical model for the structure of the logic that reflects or expresses Matte Blanco's symmetric being, and hence of the reasoning and thought processes involved in conscious reasoning or in reasoning that is lacking, perhaps entirely, in consciousness or awareness of itself. In a companion paper we study how symmetric (in the sense of Matte Blanco's) reasoning can be demarcated in a context of symmetric and asymmetric reasoning provided by narrative text.

Non-negative matrix factorization (NMF) approximates a non-negative matrix $X$ by a product of two non-negative low-rank factor matrices $W$ and $H$. NMF and its extensions minimize either the Kullback-Leibler divergence or the Euclidean distance between $X$ and $W^T H$ to model the Poisson noise or the Gaussian noise. In practice, when the noise distribution is heavy tailed, they cannot perform well. This paper presents Manhattan NMF (MahNMF) which minimizes the Manhattan distance between $X$ and $W^T H$ for modeling the heavy tailed Laplacian noise. Similar to sparse and low-rank matrix decompositions, MahNMF robustly estimates the low-rank part and the sparse part of a non-negative matrix and thus performs effectively when data are contaminated by outliers. We extend MahNMF for various practical applications by developing box-constrained MahNMF, manifold regularized MahNMF, group sparse MahNMF, elastic net inducing MahNMF, and symmetric MahNMF. The major contribution of this paper lies in two fast optimization algorithms for MahNMF and its extensions: the rank-one residual iteration (RRI) method and Nesterov's smoothing method. In particular, by approximating the residual matrix by the outer product of one row of W and one row of $H$ in MahNMF, we develop an RRI method to iteratively update each variable of $W$ and $H$ in a closed form solution. Although RRI is efficient for small scale MahNMF and some of its extensions, it is neither scalable to large scale matrices nor flexible enough to optimize all MahNMF extensions. Since the objective functions of MahNMF and its extensions are neither convex nor smooth, we apply Nesterov's smoothing method to recursively optimize one factor matrix with another matrix fixed. By setting the smoothing parameter inversely proportional to the iteration number, we improve the approximation accuracy iteratively for both MahNMF and its extensions.

An autonomous variational inference algorithm for arbitrary graphical models requires the ability to optimize variational approximations over the space of model parameters as well as over the choice of tractable families used for the variational approximation. In this paper, we present a novel combination of graph partitioning algorithms with a generalized mean field (GMF) inference algorithm. This combination optimizes over disjoint clustering of variables and performs inference using those clusters. We provide a formal analysis of the relationship between the graph cut and the GMF approximation, and explore several graph partition strategies empirically. Our empirical results provide rather clear support for a weighted version of MinCut as a useful clustering algorithm for GMF inference, which is consistent with the implications from the formal analysis.