Spectral clustering is one of the most popular clustering approaches. Despite its good performance, it is limited in its applicability to large-scale problems due to its high computational complexity. Recently, many approaches have been proposed to accelerate the spectral clustering. Unfortunately, these methods usually sacrifice quite a lot information of the original data, thus result in a degradation of performance. In this paper, we propose a novel approach, called Landmark-based Spectral Clustering (LSC), for large scale clustering problems. Specifically, we select $p\ (\ll n)$ representative data points as the landmarks and represent the original data points as the linear combinations of these landmarks. The spectral embedding of the data can then be efficiently computed with the landmark-based representation. The proposed algorithm scales linearly with the problem size. Extensive experiments show the effectiveness and efficiency of our approach comparing to the state-of-the-art methods.

This paper presents a novel symmetric graph regularization framework for pairwise constraint propagation. We first decompose the challenging problem of pairwise constraint propagation into a series of two-class label propagation subproblems and then deal with these subproblems by quadratic optimization with symmetric graph regularization. More importantly, we clearly show that pairwise constraint propagation is actually equivalent to solving a Lyapunov matrix equation, which is widely used in Control Theory as a standard continuous-time equation. Different from most previous constraint propagation methods that suffer from severe limitations, our method can directly be applied to multi-class problem and also can effectively exploit both must-link and cannot-link constraints. The propagated constraints are further used to adjust the similarity between data points so that they can be incorporated into subsequent clustering. The proposed method has been tested in clustering tasks on six real-life data sets and then shown to achieve significant improvements with respect to the state of the arts.

A main challenging problem for many machine learning and data mining applications is that the amount of data and features are very large, so that low-rank approximations of original data are often required for efficient computation. We propose new multi-level clustering based low-rank matrix approximations which are comparable and even more compact than Singular Value Decomposition (SVD). We utilize the cluster indicators of data clustering results to form the subspaces, hence our decomposition results are more interpretable. We further generalize our clustering based matrix decompositions to tensor decompositions that are useful in high-order data analysis. We also provide an upper bound for the approximation error of our tensor decomposition algorithm. In all experimental results, our methods significantly outperform traditional decomposition methods such as SVD and high-order SVD.

In recent years, social networks have surged in popularity as one of the main applications of the Internet. This has generated great interest in researching these networks by various fields in the scientific community. One key aspect of social network research is identifying important missing information which is not explicitly represented in the network, or is not visible to all. To date, this line of research typically focused on what connections were missing between nodes,or what is termed the "Missing Link Problem." This paper introduces a new Missing Nodes Identification problem where missing members in the social network structure must be identified. Towards solving this problem, we present an approach based on clustering algorithms combined with measures from missing link research. We show that this approach has beneficial results in the missing nodes identification process and we measure its performance in several different scenarios.

In this paper, we model the pair-wise similarities of a setof documents as a weighted network with a single cutoffparameter. Such a network can be thought of an ensemble of unweighted graphs, each consisting of edges withweights greater than the cutoff value. We look at this network ensemble as a complex system with a temperature parameter, and refer to it as a Latent Network. Ourexperiments on a number of datasets from two different domains show that certain properties of latent networks like clustering coefficient, average shortest path,and connected components exhibit patterns that are significantly divergent from randomized networks. We explain that these patterns reflect the network phase transition as well as the existence of a community structure in document collections. Using numerical analysis,we show that we can use the aforementioned networkproperties to predicts the clustering Normalized MutualInformation (NMI) with high correlation (rho > 0.9). Finally we show that our clustering method significantlyoutperforms other baseline methods (NMI > 0.5)

Strategy mining is a new area of research about discovering strategies in decision-making. In this paper, we formulate the strategy-mining problem as a clustering problem, called the latent-strategy problem. In a latent-strategy problem, a corpus of data instances is given, each of which is represented by a set of features and a decision label. The inherent dependency of the decision label on the features is governed by a latent strategy. The objective is to find clusters, each of which contains data instances governed by the same strategy. Existing clustering algorithms are inappropriate to cluster dependency because they either assume feature independency (e.g., K-means) or only consider the co-occurrence of features without explicitly modeling the special dependency of the decision label on other features (e.g., Latent Dirichlet Allocation (LDA)). In this paper, we present a baseline unsupervised learning algorithm for dependency clustering. Our model-based clustering algorithm iterates between an assignment step and a minimization step to learn a mixture of decision tree models that represent latent strategies. Similar to the Expectation Maximization algorithm, our algorithm is grounded in the statistical learning theory. Different from other clustering algorithms, our algorithm is irrelevant-feature resistant and its learned clusters (modeled by decision trees) are strongly interpretable and predictive. We systematically evaluate our algorithm using a common law dataset comprised of actual cases. Experimental results show that our algorithm significantly outperforms K-means and LDA on clustering dependency.

Multi-task learning has received increasing attention in the past decade. Many supervised multi-task learning methods have been proposed, while unsupervised multi-task learning is still a rarely studied problem. In this paper, we propose to learn a kernel for multi-task clustering. Our goal is to learn a Reproducing Kernel Hilbert Space, in which the geometric structure of the data in each task is preserved, while the data distributions of any two tasks are as close as possible. This is formulated as a unified kernel learning framework, under which we study two types of kernel learning: nonparametric kernel learning and spectral kernel design. Both types of kernel learning can be solved by linear programming. Experiments on several cross-domain text data sets demonstrate that kernel k-means on the learned kernel can achieve better clustering results than traditional single-task clustering methods. It also outperforms the newly proposed multi-task clustering method.

K-flats is a model-based linear manifold clustering algorithm which has been successfully applied in many real-world scenarios. Though some previous works have shown that K-flats doesn’t always provide good performance, little effort has been devoted to analyze its inherent deficiency. In this paper, we address this challenge by showing that the deteriorative performance of K-flats can be attributed to the usual reconstruction error measure and the infinitely extending representations of linear models. Then we propose Localized K-flats algorithm (LKF), which introduces localized representations of linear models and a new distortion measure, to remove confusion among different clusters. Experiments on both synthetic and real-world data sets demonstrate the efficiency of the proposed algorithm. Moreover, preliminary experiments show that LKF has the potential to group manifolds with nonlinear structure.

In this paper, a methodology for the automated detection and classification of Tuberculosis(TB) is presented. Tuberculosis is a disease caused by mycobacterium which spreads through the air and attacks low immune bodies easily. Our methodology is based on clustering and classification that classifies TB into two categories, Pulmonary Tuberculosis(PTB) and retroviral PTB(RPTB) that is those with Human Immunodeficiency Virus (HIV) infection. Initially K-means clustering is used to group the TB data into two clusters and assigns classes to clusters. Subsequently multiple different classification algorithms are trained on the result set to build the final classifier model based on K-fold cross validation method. This methodology is evaluated using 700 raw TB data obtained from a city hospital. The best obtained accuracy was 98.7% from support vector machine (SVM) compared to other classifiers. The proposed approach helps doctors in their diagnosis decisions and also in their treatment planning procedures for different categories.

Exploiting information induced from (query-specific) clustering of top-retrieved documents has long been proposed as a means for improving precision at the very top ranks of the returned results. We present a novel language model approach to ranking query-specific clusters by the presumed percentage of relevant documents that they contain. While most previous cluster ranking approaches focus on the cluster as a whole, our model utilizes also information induced from documents associated with the cluster. Our model substantially outperforms previous approaches for identifying clusters containing a high relevant-document percentage. Furthermore, using the model to produce document ranking yields precision-at-top-ranks performance that is consistently better than that of the initial ranking upon which clustering is performed. The performance also favorably compares with that of a state-of-the-art pseudo-feedback-based retrieval method.