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Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
In this paper, we propose a computationally efficient iterative algorithm for proper orthogonal decomposition (POD) using random sampling based techniques. In this algorithm, additional rows and columns are sampled and a merging technique…
In this paper, we propose a computationally efficient iterative algorithm for proper orthogonal decomposition (POD) using random sampling based techniques. In this algorithm, additional rows and columns are sampled and a merging technique…
Most high-level computer vision tasks rely on low-level image operations as their initial processes. Operations such as edge detection, image enhancement, and super-resolution, provide the foundations for higher level image analysis. In…
Quantum-inspired singular value decomposition (SVD) is a technique to perform SVD in logarithmic time with respect to the dimension of a matrix, given access to the matrix embedded in a segment-tree data structure. The speedup is possible…
Smart grids extremely rely on Information and Communications Technology (ICT) and smart meters to control and manage numerous parameters of the network. However, using these infrastructures make smart grids more vulnerable to cyber threats…
Divide-and-conquer is a central paradigm for the design of algorithms, through which some fundamental computational problems, such as sorting arrays and computing convex hulls, are solved in optimal time within $\Theta(n\log{n})$ in the…
We extend the randomized singular value decomposition (SVD) algorithm \citep{Halko2011finding} to estimate the SVD of a shifted data matrix without explicitly constructing the matrix in the memory. With no loss in the accuracy of the…
We propose an efficient, distributed, out-of-memory implementation of the truncated singular value decomposition (t-SVD) for heterogeneous (CPU+GPU) high performance computing (HPC) systems. Various implementations of SVD have been…
Edge-preserving smoothing (EPS) can be formulated as minimizing an objective function that consists of data and prior terms. This global EPS approach shows better smoothing performance than a local one that typically has a form of weighted…
Distributed optimization is an essential paradigm to solve large-scale optimization problems in modern applications where big-data and high-dimensionality creates a computational bottleneck. Distributed optimization algorithms that exhibit…
The regularized D-bar method is a popular method for solving Electrical Impedance Tomography (EIT) problems due to its efficiency and simplicity. It utilizes the low-pass truncated scattering data in the non-linear Fourier domain to solve…
The capacitated arc routing problem is a very important problem with many practical applications. This paper focuses on the large scale capacitated arc routing problem. Traditional solution optimization approaches usually fail because of…
Traditional low-rank approximation is a powerful tool to compress the huge data matrices that arise in simulations of partial differential equations (PDE), but suffers from high computational cost and requires several passes over the PDE…
Motivation: Cellular Electron CryoTomography (CECT) enables 3D visualization of cellular organization at near-native state and in sub-molecular resolution, making it a powerful tool for analyzing structures of macromolecular complexes and…
The singular value decomposition (SVD) of large-scale matrices is a key tool in data analytics and scientific computing. The rapid growth in the size of matrices further increases the need for developing efficient large-scale SVD…
The sparse factorization of a large matrix is fundamental in modern statistical learning. In particular, the sparse singular value decomposition and its variants have been utilized in multivariate regression, factor analysis, biclustering,…
Efficient exploitation of exascale architectures requires rethinking of the numerical algorithms used in many large-scale applications. These architectures favor algorithms that expose ultra fine-grain parallelism and maximize the ratio of…
Embedding-based retrieval (EBR) methods are widely used in modern recommender systems thanks to its simplicity and effectiveness. However, along the journey of deploying and iterating on EBR in production, we still identify some fundamental…
Motion Estimation (ME) is one of the most time-consuming parts in video coding. The use of multiple partition sizes in H.264/AVC makes it even more complicated when compared to ME in conventional video coding standards. It is important to…