Related papers: The stochastic geometry of unconstrained one-bit d…
Sketching is a probabilistic data compression technique that has been largely developed in the computer science community. Numerical operations on big datasets can be intolerably slow; sketching algorithms address this issue by generating a…
There are two main approaches in compressed sensing: the geometric approach and the combinatorial approach. In this paper we introduce an information theoretic approach and use results from the theory of Huffman codes to construct a…
Compressive Sensing, which offers exact reconstruction of sparse signal from a small number of measurements, has tremendous potential for trajectory compression. In order to optimize the compression, trajectory compression algorithms need…
Finding methods for making generalizable predictions is a fundamental problem of machine learning. By looking into similarities between the prediction problem for unknown data and the lossless compression we have found an approach that…
We show that a tessellation generated by a small number of random affine hyperplanes can be used to approximate Euclidean distances between any two points in an arbitrary bounded set $T$, where the random hyperplanes are generated by…
We investigate the Bose-Einstein Condensation on nonhomogeneous amenable networks for the model describing arrays of Josephson junctions. The resulting topological model, whose Hamiltonian is the pure hopping one given by the opposite of…
Compressed sensing is a technique for recovering a high-dimensional signal from lower-dimensional data, whose components represent partial information about the signal, utilizing prior knowledge on the sparsity of the signal. For further…
Exascale computing promises quantities of data too large to efficiently store and transfer across networks in order to be able to analyze and visualize the results. We investigate Compressive Sensing (CS) as a way to reduce the size of the…
During the last decade, the paradigm of compressed sensing has gained significant importance in the signal processing community. While the original idea was to utilize sparsity assumptions to design powerful recovery algorithms of vectors…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
In recent years, we have witnessed the presence of point cloud data in many aspects of our life, from immersive media, autonomous driving to healthcare, although at the cost of a tremendous amount of data. In this paper, we present an…
Consider a lossy compression system with $\ell$ distributed encoders and a centralized decoder. Each encoder compresses its observed source and forwards the compressed data to the decoder for joint reconstruction of the target signals under…
In 1-bit compressed sensing, the aim is to estimate a $k$-sparse unit vector $x\in S^{n-1}$ within an $\epsilon$ error (in $\ell_2$) from minimal number of linear measurements that are quantized to just their signs, i.e., from measurements…
We propose a strategy to compress and store large volumes of scientific data represented on unstructured grids. Approaches utilizing tensor decompositions for data compression have already been proposed. Here, data on a structured grid is…
The present paper suggests a new approach for geometric representation of 3D spatial models and provides a new compression algorithm for 3D meshes, which is based on mathematical theory of convex geometry. In our approach we represent a 3D…
The class of complex random vectors whose covariance matrix is linearly parameterized by a basis of Hermitian Toeplitz (HT) matrices is considered, and the maximum compression ratios that preserve all second-order information are derived…
This article considers "compressive learning," an approach to large-scale machine learning where datasets are massively compressed before learning (e.g., clustering, classification, or regression) is performed. In particular, a "sketch" is…
Motivated by the prevalent data science applications of processing large-scale graph data such as social networks and biological networks, this paper investigates lossless compression of data in the form of a labeled graph. Particularly, we…
The performance of a lossy data compression scheme for uniformly biased Boolean messages is investigated via methods of statistical mechanics. Inspired by a formal similarity to the storage capacity problem in the research of neural…
The goal of standard 1-bit compressive sensing is to accurately recover an unknown sparse vector from binary-valued measurements, each indicating the sign of a linear function of the vector. Motivated by recent advances in compressive…