Related papers: On some deterministic dictionaries supporting spar…
Current distributed representations of words show little resemblance to theories of lexical semantics. The former are dense and uninterpretable, the latter largely based on familiar, discrete classes (e.g., supersenses) and relations (e.g.,…
In this survey a novel system, called the oscillator system, consisting of order of p^3 functions (signals) on the finite field F_{p}, is described and studied. The new functions are proved to satisfy good auto-correlation,…
In an incoherent dictionary, most signals that admit a sparse representation admit a unique sparse representation. In other words, there is no way to express the signal without using strictly more atoms. This work demonstrates that sparse…
A finite oscillator dictionary which has important applications in sequences designs and the compressive sensing was introduced by Gurevich, Hadani and Sochen. In this paper, we first revisit closed formulae of the finite split oscillator…
A new method presented for design of incoherent dictionaries.
Many natural signals exhibit a sparse representation, whenever a suitable describing model is given. Here, a linear generative model is considered, where many sparsity-based signal processing techniques rely on such a simplified model. As…
We recall the definition of the $\epsilon$-distortion complexity of a set defined in \cite{bcc} and the results obtained in this paper for Cantor sets of the interval defined by iterated function systems. We state an analogous definition…
A novel system, called the oscillator system, consisting of order of p^3 functions (signals) on the finite field F_p; with p an odd prime, is described and studied. The new functions are proved to satisfy good auto-correlation,…
Dictionaries are collections of vectors used for representations of random vectors in Euclidean spaces. Recent research on optimal dictionaries is focused on constructing dictionaries that offer sparse representations, i.e.,…
A popular approach within the signal processing and machine learning communities consists in modelling signals as sparse linear combinations of atoms selected from a learned dictionary. While this paradigm has led to numerous empirical…
Known sparsity thresholds for basis pursuit to deliver the maximally sparse solution of the compressed sensing recovery problem typically depend on the dictionary's coherence. While the coherence is easy to compute, it can lead to rather…
In dictionary learning, also known as sparse coding, the algorithm is given samples of the form $y = Ax$ where $x\in \mathbb{R}^m$ is an unknown random sparse vector and $A$ is an unknown dictionary matrix in $\mathbb{R}^{n\times m}$…
Data-driven representation learning for words is a technique of central importance in NLP. While indisputably useful as a source of features in downstream tasks, such vectors tend to consist of uninterpretable components whose relationship…
Convolutional sparse representations are a form of sparse representation with a dictionary that has a structure that is equivalent to convolution with a set of linear filters. While effective algorithms have recently been developed for the…
We study the Dictionary Learning (aka Sparse Coding) problem of obtaining a sparse representation of data points, by learning \emph{dictionary vectors} upon which the data points can be written as sparse linear combinations. We view this…
This work addresses the problem of learning sparse representations of tensor data using structured dictionary learning. It proposes learning a mixture of separable dictionaries to better capture the structure of tensor data by generalizing…
Rank/Select dictionaries are data structures for an ordered set $S \subset \{0,1,...,n-1\}$ to compute $\rank(x,S)$ (the number of elements in $S$ which are no greater than $x$), and $\select(i,S)$ (the $i$-th smallest element in $S$),…
Compositionality is at the heart of computer science and several other areas of applied category theory such as computational linguistics, categorical quantum mechanics, interpretable AI, dynamical systems, compositional game theory, and…
Mixed dictionaries generated by cosine and B-spline functions are considered. It is shown that, by highly nonlinear approaches such as Orthogonal Matching Pursuit, the discrete version of the proposed dictionaries yields a significant gain…
An oscillator group $G$ is a semidirect product of a Heisenberg group with a one-parameter group. In this article we construct Olshanski semigroups for infinite-dimensional oscillator groups. These are complex involutive semigroups which…