Related papers: Butterfly factorization by algorithmic identificat…
Matrix factorization, one of the most popular methods in machine learning, has recently benefited from introducing non-linearity in prediction tasks using tropical semiring. The non-linearity enables a better fit to extreme values and…
We propose a way of characterizing the algorithms computing a Walsh-Hadamard transform that consist of a sequence of arrays of butterflies ($I_{2^{n-1}}\otimes \text{DFT}_2$) interleaved by linear permutations. Linear permutations are those…
Matrix factorization is a popular approach to solving matrix estimation problems based on partial observations. Existing matrix factorization is based on least squares and aims to yield a low-rank matrix to interpret the conditional sample…
Matrix factorization techniques have been widely used as a method for collaborative filtering for recommender systems. In recent times, different variants of deep learning algorithms have been explored in this setting to improve the task of…
Standard rank-revealing factorizations such as the singular value decomposition and column pivoted QR factorization are challenging to implement efficiently on a GPU. A major difficulty in this regard is the inability of standard algorithms…
Low-rank matrix factorization (MF) is an important technique in data science. The key idea of MF is that there exists latent structures in the data, by uncovering which we could obtain a compressed representation of the data. By factorizing…
In addition to recent developments in computing speed and memory, methodological advances have contributed to significant gains in the performance of stochastic simulation. In this paper, we focus on variance reduction for matrix…
We consider space-efficient single-pass estimation of the number of butterflies, a fundamental bipartite graph motif, from a massive bipartite graph stream where each edge represents a connection between entities in two different…
We propose a novel factorization of a non-singular matrix $P$, viewed as a $2\times 2$-blocked matrix. The factorization decomposes $P$ into a product of three matrices that are lower block-unitriangular, upper block-triangular, and lower…
Mining and exploring databases should provide users with knowledge and new insights. Tiles of data strive to unveil true underlying structure and distinguish valuable information from various kinds of noise. We propose a novel Boolean…
Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity…
A generalization of modularity, called block modularity, is defined. This is a quality function which evaluates a label assignment against an arbitrary block pattern. Therefore, unlike standard modularity or its variants, arbitrary network…
This paper concerns the fast evaluation of the matvec $g=Kf$ for $K\in \mathbb{C}^{N\times N}$, which is the discretization of the oscillatory integral transform $g(x) = \int K(x,\xi) f(\xi)d\xi$ with a kernel function…
We derive approximation algorithms for the nonnegative matrix factorization problem, i.e. the problem of factorizing a matrix as the product of two matrices with nonnegative coefficients. We form convex approximations of this problem which…
A robust algorithm for non-negative matrix factorization (NMF) is presented in this paper with the purpose of dealing with large-scale data, where the separability assumption is satisfied. In particular, we modify the Linear Programming…
We describe an algorithm for the application of the forward and inverse spherical harmonic transforms. It is based on a new method for rapidly computing the forward and inverse associated Legendre transforms by hierarchically applying the…
The application of binary matrices are numerous. Representing a matrix as a mixture of a small collection of latent vectors via low-rank decomposition is often seen as an advantageous method to interpret and analyze data. In this work, we…
Motivated by an application in computational biology, we consider low-rank matrix factorization with $\{0,1\}$-constraints on one of the factors and optionally convex constraints on the second one. In addition to the non-convexity shared…
Supervised matrix factorization (SMF) is a classical machine learning method that simultaneously seeks feature extraction and classification tasks, which are not necessarily a priori aligned objectives. Our goal is to use SMF to learn…
We consider multilevel low rank (MLR) matrices, defined as a row and column permutation of a sum of matrices, each one a block diagonal refinement of the previous one, with all blocks low rank given in factored form. MLR matrices extend low…