Related papers: Dictionary Learning and Sparse Coding for Third-or…
Higher-order tensors have received increased attention across science and engineering. While most tensor decomposition methods are developed for a single tensor observation, scientific studies often collect side information, in the form of…
Machine Learning approaches like clustering methods deal with massive datasets that present an increasing challenge. We devise parallel algorithms to compute the Multi-Slice Clustering (MSC) for 3rd-order tensors. The MSC method is based on…
We consider the problem of designing sparse sampling strategies for multidomain signals, which can be represented using tensors that admit a known multilinear decomposition. We leverage the multidomain structure of tensor signals and…
Many approaches to transform classification problems from non-linear to linear by feature transformation have been recently presented in the literature. These notably include sparse coding methods and deep neural networks. However, many of…
Deep dictionary learning seeks multiple dictionaries at different image scales to capture complementary coherent characteristics. We propose a method for learning a hierarchy of synthesis dictionaries with an image classification goal. The…
The widespread use of multisensor technology and the emergence of big data sets have brought the necessity to develop more versatile tools to represent higher-order data with multiple aspects and high dimensionality. Data in the form of…
Statistical inference on large-dimensional tensor data has been extensively studied in the literature and widely used in economics, biology, machine learning, and other fields, but how to generate a structured tensor with a target…
The T-product for third-order tensors has been used extensively in the literature. In this paper, we first introduce the first-order and second-order T-derivatives for the multi-vector real-valued function with the tensor T-product; and…
Learned Sparse Retrieval (LSR) has traditionally focused on small-scale encoder-only transformer architectures. With the advent of large-scale pre-trained language models, their capability to generate sparse representations for retrieval…
Convolutional sparse coding (CSC) improves sparse coding by learning a shift-invariant dictionary from the data. However, existing CSC algorithms operate in the batch mode and are expensive, in terms of both space and time, on large…
A tensor is a multidimensional array of numbers that can be used to store data, encode a computational relation and represent quantum entanglement. In this sense a tensor can be viewed as valuable resource whose transformation can lead to…
This document describes an attempt to develop a compiler-based approach for computations with symmetric tensors. Given a computation and the symmetries of its input tensors, we derive formulas for random access under a storage scheme that…
Statistical learning algorithms are finding more and more applications in science and technology. Atomic-scale modeling is no exception, with machine learning becoming commonplace as a tool to predict energy, forces and properties of…
In many real-world problems, we are dealing with collections of high-dimensional data, such as images, videos, text and web documents, DNA microarray data, and more. Often, high-dimensional data lie close to low-dimensional structures…
Sparse coding is an unsupervised learning algorithm that learns a succinct high-level representation of the inputs given only unlabeled data; it represents each input as a sparse linear combination of a set of basis functions. Originally…
Sparse coding is a proven principle for learning compact representations of images. However, sparse coding by itself often leads to very redundant dictionaries. With images, this often takes the form of similar edge detectors which are…
Word embeddings are a powerful natural language processing technique, but they are extremely difficult to interpret. To enable interpretable NLP models, we create vectors where each dimension is inherently interpretable. By inherently…
In many practical applications such as direction-of-arrival (DOA) estimation and line spectral estimation, the sparsifying dictionary is usually characterized by a set of unknown parameters in a continuous domain. To apply the conventional…
Large tensors are frequently encountered in various fields such as computer vision, scientific simulations, sensor networks, and data mining. However, these tensors are often too large for convenient processing, transfer, or storage.…
The sparse modeling is an evident manifestation capturing the parsimony principle just described, and sparse models are widespread in statistics, physics, information sciences, neuroscience, computational mathematics, and so on. In…