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We introduce a general tensor model suitable for data analytic tasks for {\em heterogeneous} datasets, wherein there are joint low-rank structures within groups of observations, but also discriminative structures across different groups. To…
Despite the outstanding performance of deep neural networks in different applications, they are still computationally extensive and require a great number of memories. This motivates more research on reducing the resources required for…
Matrix factorization is an important mathematical problem encountered in the context of dictionary learning, recommendation systems and machine learning. We introduce a new `decimation' scheme that maps it to neural network models of…
It has been an important approach of using matrix completion to perform image restoration. Most previous works on matrix completion focus on the low-rank property by imposing explicit constraints on the recovered matrix, such as the…
General-purpose multiprocessors (as, in our case, Intel IvyBridge and Intel Haswell) increasingly add GPU computing power to the former multicore architectures. When used for embedded applications (for us, Synthetic aperture radar) with…
Matrix completion is one of the key problems in signal processing and machine learning. In recent years, deep-learning-based models have achieved state-of-the-art results in matrix completion. Nevertheless, they suffer from two drawbacks:…
Fast Fourier Transform (FFT) is an efficient algorithm to compute the Discrete Fourier Transform (DFT) and its inverse. In this paper, we pay special attention to the description of complex-data FFT. We analyze two common descriptions of…
In recent years, a new kind of accelerated hardware has gained popularity in the Artificial Intelligence (AI) and Machine Learning (ML) communities which enables extremely high-performance tensor contractions in reduced precision for deep…
For most problems in science and engineering we can obtain data sets that describe the observed system from various perspectives and record the behavior of its individual components. Heterogeneous data sets can be collectively mined by data…
Diffusion Transformer (DiT) has driven significant progress in image generation tasks. However, DiT inferencing is notoriously compute-intensive and incurs long latency even on datacenter-scale GPUs, primarily due to its iterative nature…
This paper shows that it is possible to improve the computational cost, the memory requirements and the accuracy of Quick Fourier Transform (QFT) algorithm for power-of-two FFT (Fast Fourier Transform) just introducing a slight modification…
Generalised matrix-matrix multiplication forms the kernel of many mathematical algorithms. A faster matrix-matrix multiply immediately benefits these algorithms. In this paper we implement efficient matrix multiplication for large matrices…
We describe a graph-based neural acceleration technique for nonnegative matrix factorization that builds upon a connection between matrices and bipartite graphs that is well-known in certain fields, e.g., sparse linear algebra, but has not…
Multiresolution Matrix Factorization (MMF) is unusual amongst fast matrix factorization algorithms in that it does not make a low rank assumption. This makes MMF especially well suited to modeling certain types of graphs with complex…
Matrix completion is a class of machine learning methods that concerns the prediction of missing entries in a partially observed matrix. This paper studies matrix completion for mixed data, i.e., data involving mixed types of variables…
We study categories of matrix factorizations. These categories are defined for any regular function on a suitable regular scheme. Our paper has two parts. In the first part we develop the foundations; for example we discuss derived direct…
Nonnegative matrix factorization (NMF) is an emerging technique with a wide spectrum of potential applications in data analysis. Mathematically, NMF can be formulated as a minimization problem with nonnegative constraints. This problem is…
Matrix factorization is a popular framework for modeling low-rank data matrices. Motivated by manifold learning problems, this paper proposes a quadratic matrix factorization (QMF) framework to learn the curved manifold on which the dataset…
Edge devices are being deployed at increasing volumes to sense and act on information from the physical world. The discrete Fourier transform (DFT) is often necessary to make this sensed data suitable for further processing -- such as by…
A new class of matrices based on a parametrization of the Feig-Winograd factorization of 8-point DCT is proposed. Such parametrization induces a matrix subspace, which unifies a number of existing methods for DCT approximation. By solving a…