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A natural and important generalization of submodularity -- $k$-submodularity -- applies to set functions with $k$ arguments and appears in a broad range of applications, such as infrastructure design, machine learning, and healthcare. In…
We introduce the natural notion of a matching frame in a $2$-dimensional string. A matching frame in a $2$-dimensional $n\times m$ string $M$, is a rectangle such that the strings written on the horizontal sides of the rectangle are…
Real-world data typically contain repeated and periodic patterns. This suggests that they can be effectively represented and compressed using only a few coefficients of an appropriate basis (e.g., Fourier, Wavelets, etc.). However, distance…
Nonlinear dimensionality reduction or, equivalently, the approximation of high-dimensional data using a low-dimensional nonlinear manifold is an active area of research. In this paper, we will present a thematically different approach to…
The problem of biclustering consists of the simultaneous clustering of rows and columns of a matrix such that each of the submatrices induced by a pair of row and column clusters is as uniform as possible. In this paper we approximate the…
Large scale parameter estimation problems are among some of the most computationally demanding problems in numerical analysis. An academic researcher's domain-specific knowledge often precludes that of software design, which results in…
Image search engines enable the retrieval of images relevant to a query image. In this work, we consider the setting where a query for similar images is derived from a collection of images. For visual search, the similarity measurements may…
Image super-resolution remains an important research topic to overcome the limitations of physical acquisition systems, and to support the development of high resolution displays. Previous example-based super-resolution approaches mainly…
Embedding image features into a binary Hamming space can improve both the speed and accuracy of large-scale query-by-example image retrieval systems. Supervised hashing aims to map the original features to compact binary codes in a manner…
Finding a maximum independent set is a fundamental NP-hard problem that is used in many real-world applications. Given an unweighted graph, this problem asks for a maximum cardinality set of pairwise non-adjacent vertices. Some of the most…
Convolutional Neural Networks (CNNs) have achieved superior performance on object image retrieval, while Bag-of-Words (BoW) models with handcrafted local features still dominate the retrieval of overlapping images in 3D reconstruction. In…
While deep learning methods have achieved state-of-the-art performance in many challenging inverse problems like image inpainting and super-resolution, they invariably involve problem-specific training of the networks. Under this approach,…
A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a…
Sub-image search with high accuracy in natural images still remains a challenging problem. This paper proposes a new feature vector called profile for a keypoint in a bag of visual words model of an image. The profile of a keypoint captures…
The problem that we consider is the following: given an $n \times n$ array $A$ of positive numbers, find a tiling using at most $p$ rectangles (which means that each array element must be covered by some rectangle and no two rectangles must…
Given a set R of n red points and a set B of m blue points, we study the problem of finding a rectangle that contains all the red points, the minimum number of blue points and has the largest area. We call such rectangle a maximum…
In this paper, we present a new image segmentation method based on the concept of sparse subset selection. Starting with an over-segmentation, we adopt local spectral histogram features to encode the visual information of the small segments…
Multipoint polynomial evaluation and interpolation are fundamental for modern symbolic and numerical computing. The known algorithms solve both problems over any field of constants in nearly linear arithmetic time, but the cost grows to…
A novel artificial neural network method is proposed for solving Cauchy inverse problems. It allows multiple hidden layers with arbitrary width and depth, which theoretically yields better approximations to the inverse problems. In this…
Sublinear time complexity is required by the massively parallel computation (MPC) model. Breaking dynamic programs into a set of sparse dynamic programs that can be divided, solved, and merged in sublinear time. The rectangle escape problem…