Related papers: Dictionary Learning and Sparse Coding for Third-or…
Symmetric tensor operations arise in a wide variety of computations. However, the benefits of exploiting symmetry in order to reduce storage and computation is in conflict with a desire to simplify memory access patterns. In this paper, we…
Sparse representations using data dictionaries provide an efficient model particularly for signals that do not enjoy alternate analytic sparsifying transformations. However, solving inverse problems with sparsifying dictionaries can be…
Interpretability benefits the theoretical understanding of representations. Existing word embeddings are generally dense representations. Hence, the meaning of latent dimensions is difficult to interpret. This makes word embeddings like a…
The efficient sparse coding and reconstruction of signal vectors via linear observations has received a tremendous amount of attention over the last decade. In this context, the automated learning of a suitable basis or overcomplete…
Deep learning techniques have been successfully applied in many areas of computer vision, including low-level image restoration problems. For image super-resolution, several models based on deep neural networks have been recently proposed…
This chapter discusses the importance of incorporating three-dimensional symmetries in the context of statistical learning models geared towards the interpolation of the tensorial properties of atomic-scale structures. We focus on Gaussian…
Sparse document representations have been widely used to retrieve relevant documents via exact lexical matching. Owing to the pre-computed inverted index, it supports fast ad-hoc search but incurs the vocabulary mismatch problem. Although…
Supervised Dictionary Learning has gained much interest in the recent decade and has shown significant performance improvements in image classification. However, in general, supervised learning needs a large number of labelled samples per…
We propose a new approach for metric learning by framing it as learning a sparse combination of locally discriminative metrics that are inexpensive to generate from the training data. This flexible framework allows us to naturally derive…
Sparse coding, which refers to modeling a signal as sparse linear combinations of the elements of a learned dictionary, has proven to be a successful (and interpretable) approach in applications such as signal processing, computer vision,…
Automated code generation and performance enhancements for sparse tensor algebra have become essential in many real-world applications, such as quantum computing, physical simulations, computational chemistry, and machine learning. General…
This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…
Deep neural networks employ specialized architectures for vision, sequential and language tasks, yet this proliferation obscures their underlying commonalities. We introduce a unified matrix-order framework that casts convolutional,…
Tensor rank and low-rank tensor decompositions have many applications in learning and complexity theory. Most known algorithms use unfoldings of tensors and can only handle rank up to $n^{\lfloor p/2 \rfloor}$ for a $p$-th order tensor in…
Convolutional Sparse Coding (CSC) is an increasingly popular model in the signal and image processing communities, tackling some of the limitations of traditional patch-based sparse representations. Although several works have addressed the…
High-dimensional sparse data emerge in many critical application domains such as healthcare and cybersecurity. To extract meaningful insights from massive volumes of these multi-dimensional data, scientists employ unsupervised analysis…
Dictionary learning is the task of determining a data-dependent transform that yields a sparse representation of some observed data. The dictionary learning problem is non-convex, and usually solved via computationally complex iterative…
Sparse coding is a class of unsupervised methods for learning a sparse representation of the input data in the form of a linear combination of a dictionary and a sparse code. This learning framework has led to state-of-the-art results in…
In this work, we propose a novel information theoretic framework for dictionary learning (DL) and sparse coding (SC) on a statistical manifold (the manifold of probability distributions). Unlike the traditional DL and SC framework, our new…
We propose an algorithm for rotational sparse coding along with an efficient implementation using steerability. Sparse coding (also called dictionary learning) is an important technique in image processing, useful in inverse problems,…