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Many tasks in data mining and related fields can be formalized as matching between objects in two heterogeneous domains, including collaborative filtering, link prediction, image tagging, and web search. Machine learning techniques,…
Let X[0..n-1] and Y[0..m-1] be two sorted arrays, and define the mxn matrix A by A[j][i]=X[i]+Y[j]. Frederickson and Johnson gave an efficient algorithm for selecting the k-th smallest element from A. We show how to make this algorithm…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
This paper introduces an Enhanced Boolean version of the Correlation Matrix Memory (CMM), which is useful to work with binary memories. A novel Boolean Orthonormalization Process (BOP) is presented to convert a non-orthonormal Boolean…
We present new algorithms to detect and correct errors in the lower-upper factorization of a matrix, or the triangular linear system solution, over an arbitrary field. Our main algorithms do not require any additional information or…
Matrix-vector multiplication is one of the most fundamental computing primitives. Given a matrix $A\in\mathbb{F}^{N\times N}$ and a vector $b$, it is known that in the worst case $\Theta(N^2)$ operations over $\mathbb{F}$ are needed to…
The CUR matrix decomposition is an important extension of Nystr\"{o}m approximation to a general matrix. It approximates any data matrix in terms of a small number of its columns and rows. In this paper we propose a novel randomized CUR…
The approximate minimum degree algorithm is widely used before numerical factorization to reduce fill-in for sparse matrices. While considerable attention has been given to the numerical factorization process, less focus has been placed on…
Factorization and multiplication of dense matrices and tensors are critical, yet extremely expensive pieces of the scientific toolbox. Careful use of low rank approximation can drastically reduce the computation and memory requirements of…
This work explores fundamental modeling and algorithmic issues arising in the well-established MapReduce framework. First, we formally specify a computational model for MapReduce which captures the functional flavor of the paradigm by…
We present a sub-matrix update algorithm for the continuous-time auxiliary field method that allows the simulation of large lattice and impurity problems. The algorithm takes optimal advantage of modern CPU architectures by consistently…
Data movement is becoming the dominant contributor to the time and energy costs of computation across a wide range of application domains. However, time complexity is inadequate to analyze data movement. This work expands upon Data Movement…
In this paper we consider a general matrix factorization model which covers a large class of existing models with many applications in areas such as machine learning and imaging sciences. To solve this possibly nonconvex, nonsmooth and…
In this paper we describe a parallel Gaussian elimination algorithm for matrices with entries in a finite field. Unlike previous approaches, our algorithm subdivides a very large input matrix into smaller submatrices by subdividing both…
Hierarchical matrix computations have attracted significant attention in the science and engineering community as exploiting data-sparse structures can significantly reduce the computational complexity of many important kernels. One…
As one of the most important basic operations, matrix multiplication computation (MMC) has varieties of applications in the scientific and engineering community such as linear regression, k-nearest neighbor classification and biometric…
Multiresolution Matrix Factorization (MMF) was recently introduced as a method for finding multiscale structure and defining wavelets on graphs/matrices. In this paper we derive pMMF, a parallel algorithm for computing the MMF…
We present factorization and solution phases for a new linear complexity direct solver designed for concurrent batch operations on fine-grained parallel architectures, for matrices amenable to hierarchical representation. We focus on the…
The extremum graph is a succinct representation of the Morse decomposition of a scalar field. It has increasingly become a useful data structure that supports topological feature directed visualization of 2D / 3D scalar fields, and enables…
Mapping is essential in robotics and autonomous systems because it provides the spatial foundation for path planning. Efficient mapping enables planning algorithms to generate reliable paths while ensuring safety and adapting in real time…