In many clustering problems, we have access to multiple views of the data each of which could be individually used for clustering. Exploiting information from multiple views, one can hope to find a clustering that is more accurate than the ones obtained using the individual views. Since the true clustering would assign a point to the same cluster irrespective of the view, we can approach this problem by looking for clusterings that are consistent across the views, i.e., corresponding data points in each view should have same cluster membership. We propose a spectral clustering framework that achieves this goal by co-regularizing the clustering hypotheses, and propose two co-regularization schemes to accomplish this. Experimental comparisons with a number of baselines on two synthetic and three real-world datasets establish the efficacy of our proposed approaches.

We consider the problem of estimating neural spikes from extracellular voltage recordings. Most current methods are based on clustering, which requires substantial human supervision and produces systematic errors by failing to properly handle temporally overlapping spikes. We formulate the problem as one of statistical inference, in which the recorded voltage is a noisy sum of the spike trains of each neuron convolved with its associated spike waveform. Joint maximum-a-posteriori (MAP) estimation of the waveforms and spikes is then a blind deconvolution problem in which the coefficients are sparse. We develop a block-coordinate descent method for approximating the MAP solution. We validate our method on data simulated according to the generative model, as well as on real data for which ground truth is available via simultaneous intracellular recordings. In both cases, our method substantially reduces the number of missed spikes and false positives when compared to a standard clustering algorithm, primarily by recovering temporally overlapping spikes. The method offers a fully automated alternative to clustering methods that is less susceptible to systematic errors.

Many clustering techniques aim at optimizing empirical criteria that are of the form of a U-statistic of degree two. Given a measure of dissimilarity between pairs of observations, the goal is to minimize the within cluster point scatter over a class of partitions of the feature space. It is the purpose of this paper to define a general statistical framework, relying on the theory of U-processes, for studying the performance of such clustering methods. In this setup, under adequate assumptions on the complexity of the subsets forming the partition candidates, the excess of clustering risk is proved to be of the order O(1/\sqrt{n}). Based on recent results related to the tail behavior of degenerate U-processes, it is also shown how to establish tighter rate bounds. Model selection issues, related to the number of clusters forming the data partition in particular, are also considered.

Clustering is a popular problem with many applications. We consider the k-means problem in the situation where the data is too large to be stored in main memory and must be accessed sequentially, such as from a disk, and where we must use as little memory as possible. Our algorithm is based on recent theoretical results, with significant improvements to make it practical. Our approach greatly simplifies arecently developed algorithm, both in design and in analysis, and eliminates large constant factors in the approximation guarantee, the memory requirements, and the running time. We then incorporate approximate nearest neighbor search to compute k-means in o(nk) (where n is the number of data points; note that computing thecost, given a solution, takes 8(nk) time). We show that our algorithm compares favorably to existing algorithms - both theoretically and experimentally, thus providing state-of-the-art performance in both theory and practice.

Many machine learning and signal processing problems can be formulated as linearly constrained convex programs, which could be efficiently solved by the alternating direction method (ADM). However, usually the subproblems in ADM are easily solvable only when the linear mappings in the constraints are identities. To address this issue, we propose a linearized ADM (LADM) method by linearizing the quadratic penalty term and adding a proximal term when solving the subproblems. For fast convergence, we also allow the penalty to change adaptively according a novel update rule. We prove the global convergence of LADM with adaptive penalty (LADMAP). As an example, we apply LADMAP to solve low-rank representation (LRR), which is an important subspace clustering technique yet suffers from high computation cost. By combining LADMAP with a skinny SVD representation technique, we are able to reduce the complexity $O(n^3)$ of the original ADM based method to $O(rn^2)$, where $r$ and $n$ are the rank and size of the representation matrix, respectively, hence making LRR possible for large scale applications. Numerical experiments verify that for LRR our LADMAP based methods are much faster than state-of-the-art algorithms.

Spectral clustering is based on the spectral relaxation of the normalized/ratio graph cut criterion. While the spectral relaxation is known to be loose, it has been shown recently that a non-linear eigenproblem yields a tight relaxation of the Cheeger cut. In this paper, we extend this result considerably by providing a characterization of all balanced graph cuts which allow for a tight relaxation. Although the resulting optimization problems are non-convex and non-smooth, we provide an efficient first-order scheme which scales to large graphs. Moreover, our approach comes with the quality guarantee that given any partition as initialization the algorithm either outputs a better partition or it stops immediately.

In this paper, we consider the 'Precis' problem of sampling K representative yet diverse data points from a large dataset. This problem arises frequently in applications such as video and document summarization, exploratory data analysis, and pre-filtering. We formulate a general theory which encompasses not just traditional techniques devised for vector spaces, but also non-Euclidean manifolds, thereby enabling these techniques to shapes, human activities, textures and many other image and video based datasets. We propose intrinsic manifold measures for measuring the quality of a selection of points with respect to their representative power, and their diversity. We then propose efficient algorithms to optimize the cost function using a novel annealing-based iterative alternation algorithm. The proposed formulation is applicable to manifolds of known geometry as well as to manifolds whose geometry needs to be estimated from samples. Experimental results show the strength and generality of the proposed approach.

An agglomerative clustering algorithm merges the most similar pair of clusters at every iteration. The function that evaluates similarity is traditionally hand- designed, but there has been recent interest in supervised or semisupervised settings in which ground-truth clustered data is available for training. Here we show how to train a similarity function by regarding it as the action-value function of a reinforcement learning problem. We apply this general method to segment images by clustering superpixels, an application that we call Learning to Agglomerate Superpixel Hierarchies (LASH). When applied to a challenging dataset of brain images from serial electron microscopy, LASH dramatically improved segmentation accuracy when clustering supervoxels generated by state of the boundary detection algorithms. The naive strategy of directly training only supervoxel similarities and applying single linkage clustering produced less improvement.

This paper presents an approach that predicts the effectiveness of HIV combination therapies by simultaneously addressing several problems affecting the available HIV clinical data sets: the different treatment backgrounds of the samples, the uneven representation of the levels of therapy experience, the missing treatment history information, the uneven therapy representation and the unbalanced therapy outcome representation. The computational validation on clinical data shows that, compared to the most commonly used approach that does not account for the issues mentioned above, our model has significantly higher predictive power. This is especially true for samples stemming from patients with longer treatment history and samples associated with rare therapies. Furthermore, our approach is at least as powerful for the remaining samples.

Importance of document clustering is now widely acknowledged by researchers for better management, smart navigation, efficient filtering, and concise summarization of large collection of documents like World Wide Web (WWW). The next challenge lies in semantically performing clustering based on the semantic contents of the document. The problem of document clustering has two main components: (1) to represent the document in such a form that inherently captures semantics of the text. This may also help to reduce dimensionality of the document, and (2) to define a similarity measure based on the semantic representation such that it assigns higher numerical values to document pairs which have higher semantic relationship. Feature space of the documents can be very challenging for document clustering. A document may contain multiple topics, it may contain a large set of class-independent general-words, and a handful class-specific core-words. With these features in mind, traditional agglomerative clustering algorithms, which are based on either Document Vector model (DVM) or Suffix Tree model (STC), are less efficient in producing results with high cluster quality. This paper introduces a new approach for document clustering based on the Topic Map representation of the documents. The document is being transformed into a compact form. A similarity measure is proposed based upon the inferred information through topic maps data and structures. The suggested method is implemented using agglomerative hierarchal clustering and tested on standard Information retrieval (IR) datasets. The comparative experiment reveals that the proposed approach is effective in improving the cluster quality.