Fast, stealthy, and cheap--autonomous, semisubmersible drone boats carrying tons of cocaine could be international law enforcement's nightmare scenario. A big one just came ashore. Colombian military officials intercepted this 40-foot-long uncrewed fiberglass "narco sub" in the ocean just off Tayrona National Park. On a bright morning last April, a surveillance plane operated by the Colombian military spotted a 40-foot-long shark-like silhouette idling in the ocean just off Tayrona National Park. It was, unmistakably, a "narco sub," a stealthy fiberglass vessel that sails with its hull almost entirely underwater, used by drug cartels to move cocaine north. The plane's crew radioed it in, and eventually nearby coast guard boats got the order, routine but urgent: Intercept. In Cartagena, about 150 miles from the action, Captain Jaime González Zamudio, commander of the regional coast guard group, sat down at his desk to watch what happened next.

Greedy optimization methods such as Matching Pursuit (MP) and Frank-Wolfe (FW) algorithms regained popularity in recent years due to their simplicity, effectiveness and theoretical guarantees. MP and FW address optimization over the linear span and the convex hull of a set of atoms, respectively. In this paper, we consider the intermediate case of optimization over the convex cone, parametrized as the conic hull of a generic atom set, leading to the first principled definitions of non-negative MP algorithms for which we give explicit convergence rates and demonstrate excellent empirical performance. In particular, we derive sublinear (O(1/t)) convergence on general smooth and convex objectives, and linear convergence (O(e^{-t})) on strongly convex objectives, in both cases for general sets of atoms. Furthermore, we establish a clear correspondence of our algorithms to known algorithms from the MP and FW literature. Our novel algorithms and analyses target general atom sets and general objective functions, and hence are directly applicable to a large variety of learning settings.

Neural Information Processing Systems http://nips.cc/

In this paper, we address the graph matching problem.

In this paper, we address the graph matching problem.

The flexibility of these methods is often limited by the requirement that the cuts be axis aligned.

This assumption is used, for example, by biologists on gene similarity networks [Zhou et al., 2002] and cancer-related protein-protein-interaction networks [Li et al., 2012, 2013].

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The paper presents a novel approach for column sampling when the data point clusters comprise of non-convex hulls. Column sampling is important in selecting a small subset of data that represents the properties of the original dataset. The presented approach is based upon the computation of Zeta hulls. The authors model the graph cycles by means of the sum-product rule and integrate them using the Zeta function. The authors set up the optimization problem as finding the subset of points with the strongest point extremenesses.

Selecting a small informative subset from a given dataset, also called column sampling, has drawn much attention in machine learning. For incorporating structured data information into column sampling, research efforts were devoted to the cases where data points are fitted with clusters, simplices, or general convex hulls. This paper aims to study nonconvex hull learning which has rarely been investigated in the literature. In order to learn data-adaptive nonconvex hulls, a novel approach is proposed based on a graph-theoretic measure that leverages graph cycles to characterize the structural complexities of input data points. Employing this measure, we present a greedy algorithmic framework, dubbed Zeta Hulls, to perform structured column sampling. The process of pursuing a Zeta hull involves the computation of matrix inverse. To accelerate the matrix inversion computation and reduce its space complexity as well, we exploit a low-rank approximation to the graph adjacency matrix by using an efficient anchor graph technique. Extensive experimental results show that data representation learned by Zeta Hulls can achieve state-of-the-art accuracy in text and image classification tasks.