Related papers: Discrete Signal Processing on Meet/Join Lattices
A lattice is a set of all the integer linear combinations of certain linearly independent vectors. One of the most important concepts on lattice is the successive minima which is of vital importance from both theoretical and practical…
Representing and exploiting multivariate signals requires capturing relations between variables, which we can represent by graphs. Graph dictionaries allow to describe complex relational information as a sparse sum of simpler structures,…
Systems whose entities interact with each other are common. In many interacting systems, it is difficult to observe the relations between entities which is the key information for analyzing the system. In recent years, there has been…
In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be…
Transportation processes, which play a prominent role in the life and social sciences, are typically described by discrete models on lattices. For studying their dynamics a continuous formulation of the problem via partial differential…
In this paper we study ideas which have proved useful in topological network theory in the context of lattices of numbers. A number lattice $L_S$ is a collection of row vectors, over $\mathbb{Q}$ on a finite column set $S,$ generated by…
Graphs are irregular structures which naturally account for data integrity, however, traditional approaches have been established outside Signal Processing, and largely focus on analyzing the underlying graphs rather than signals on graphs.…
The collaborative filtering (CF) problem with only user-item interaction information can be solved by graph signal processing (GSP), which uses low-pass filters to smooth the observed interaction signals on the similarity graph to obtain…
To analyze data supported by arbitrary graphs G, DSP has been extended to Graph Signal Processing (GSP) by redefining traditional DSP concepts like shift, filtering, and Fourier transform among others. This paper revisits modulation,…
Natural language sentence matching is the task of comparing two sentences and identifying the relationship between them.It has a wide range of applications in natural language processing tasks such as reading comprehension, question and…
The Discrete Gabor Transform (DGT) is the most commonly used transform for signal analysis and synthesis using a linear frequency scale. It turns out that the involved operators are rich in structure if one samples the discrete phase space…
Images are composed as a hierarchy of object parts. We use this insight to create a generative graphical model that defines a hierarchical distribution over image parts. Typically, this leads to intractable inference due to loops in the…
This paper proposes spatial lattice modulation (SLM), a spatial modulation method for multipleinput-multiple-output (MIMO) systems. The key idea of SLM is to jointly exploit spatial, in-phase, and quadrature dimensions to modulate…
Laplacian regularized stratified models (LRSM) are models that utilize the explicit or implicit network structure of the sub-problems as defined by the categorical features called strata (e.g., age, region, time, forecast horizon, etc.),…
Recently, MLP-based vision backbones have achieved promising performance in several visual recognition tasks. However, the existing MLP-based methods directly aggregate tokens with static weights, leaving the adaptability to different…
Graph signal processing (GSP) is a framework to analyze and process graph-structured data. Many research works focus on developing tools such as Graph Fourier transforms (GFT), filters, and neural network models to handle graph signals.…
We present a network architecture for processing point clouds that directly operates on a collection of points represented as a sparse set of samples in a high-dimensional lattice. Naively applying convolutions on this lattice scales…
Data-driven artificial intelligence (AI) techniques are becoming prominent for learning in support of data compression, but are focused on standard problems such as text compression. To instead address the emerging problem of semantic…
Neural networks and other machine learning models compute continuous representations, while humans communicate with discrete symbols. Reconciling these two forms of communication is desirable to generate human-readable interpretations or to…
There is increasing focus on analyzing data represented as hypergraphs, which are better able to express complex relationships amongst entities than are graphs. Much of the critical information about hypergraph structure is available only…