Related papers: The Sparse Manifold Transform

This work presents an innovative method for point set self-embedding, that encodes the structural information of a dense point set into its sparser version in a visual but imperceptible form. The self-embedded point set can function as the…

We establish a general form of explicit, input-dependent, measure-valued warpings for learning nonstationary kernels. While stationary kernels are ubiquitous and simple to use, they struggle to adapt to functions that vary in smoothness…

We use spatially-sparse two, three and four dimensional convolutional autoencoder networks to model sparse structures in 2D space, 3D space, and 3+1=4 dimensional space-time. We evaluate the resulting latent spaces by testing their…

Parsimony in signal representation is a topic of active research. Sparse signal processing and representation is the outcome of this line of research which has many applications in information processing and has shown significant…

Multiscale phenomena that evolve on multiple distinct timescales are prevalent throughout the sciences. It is often the case that the governing equations of the persistent and approximately periodic fast scales are prescribed, while the…

The analysis of data sets arising from multiple sensors has drawn significant research attention over the years. Traditional methods, including kernel-based methods, are typically incapable of capturing nonlinear geometric structures. We…

Signal models formed as linear combinations of few atoms from an over-complete dictionary or few frame vectors from a redundant frame have become central to many applications in high dimensional signal processing and data analysis. A core…

Many applications in signal processing benefit from the sparsity of signals in a certain transform domain or dictionary. Synthesis sparsifying dictionaries that are directly adapted to data have been popular in applications such as image…

Compressed Neural Networks have the potential to enable deep learning across new applications and smaller computational environments. However, understanding the range of learning tasks in which such models can succeed is not well studied.…

The representation of images in the brain is known to be sparse. That is, as neural activity is recorded in a visual area ---for instance the primary visual cortex of primates--- only a few neurons are active at a given time with respect to…

This paper presents a novel yet intuitive approach to unsupervised feature learning. Inspired by the human visual system, we explore whether low-level motion-based grouping cues can be used to learn an effective visual representation.…

Autoencoders represent an effective approach for computing the underlying factors characterizing datasets of different types. The latent representation of autoencoders have been studied in the context of enabling interpolation between data…

In this paper we state the basics for a signal processing framework on quiver representations. A quiver is a directed graph and a quiver representation is an assignment of vector spaces to the nodes of the graph and of linear maps between…

Statistical neurodynamics studies macroscopic behaviors of randomly connected neural networks. We consider a deep layered feedforward network where input signals are processed layer by layer. The manifold of input signals is embedded in a…

The role of sparse representations in the context of structured noise filtering is discussed. A strategy, especially conceived so as to address problems of an ill posed nature, is presented. The proposed approach revises and extends the…

We propose an end-to-end learned image data hiding framework that embeds and extracts secrets in the latent representations of a generic neural compressor. By leveraging a perceptual loss function in conjunction with our proposed message…

Recent advances in representation learning have demonstrated an ability to represent information from different modalities such as video, text, and audio in a single high-level embedding vector. In this work we present a self-supervised…

The recently proposed multi-layer sparse model has raised insightful connections between sparse representations and convolutional neural networks (CNN). In its original conception, this model was restricted to a cascade of convolutional…

Graph-based representations play a key role in machine learning. The fundamental step in these representations is the association of a graph structure to a dataset. In this paper, we propose a method that aims at finding a block sparse…

Compressed sensing is a relatively new mathematical paradigm that shows a small number of linear measurements are enough to efficiently reconstruct a large dimensional signal under the assumption the signal is sparse. Applications for this…