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The goal of compressive sensing is efficient reconstruction of data from few measurements, sometimes leading to a categorical decision. If only classification is required, reconstruction can be circumvented and the measurements needed are…

Compressed sensing is a technique for finding sparse solutions to underdetermined linear systems. This technique relies on properties of the sensing matrix such as the restricted isometry property. Sensing matrices that satisfy the…

How many measurements are fundamentally required to capture a signal. Shannon's information theory established the bedrock of this question in 1948, the Nyquist Shannon theorem set the first answer, and compressed sensing (CS) rewrote it in…

This paper presents a novel centroid-based heuristic algorithm, termed Kempe Swap K-Means, for constrained clustering under rigid must-link (ML) and cannot-link (CL) constraints. The algorithm employs a dual-phase iterative process: an…

This paper considers the problem of compressive sensing over a finite alphabet, where the finite alphabet may be inherent to the nature of the data or a result of quantization. There are multiple examples of finite alphabet based static as…

Though mostly used as a clustering algorithm, k-means are originally designed as a quantization algorithm. Namely, it aims at providing a compression of a probability distribution with k points. Building upon [21, 33], we try to investigate…

Compressed sensing (CS) shows that a signal having a sparse or compressible representation can be recovered from a small set of linear measurements. In classical CS theory, the sampling matrix and representation matrix are assumed to be…

A traditional assumption underlying most data converters is that the signal should be sampled at a rate exceeding twice the highest frequency. This statement is based on a worst-case scenario in which the signal occupies the entire…

The joint optimization of the integer matrix $\mathbf{A}$ and the power scaling matrix $\mathbf{D}$ is central to achieving the capacity-approaching performance of Integer-Forcing (IF) precoding. This problem, however, is known to be…

Compressed sensing is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper we present a theoretical analysis of the iterative hard thresholding…

Quantum sensing is commonly described as a constrained optimization problem: maximize the information gained about an unknown quantity using a limited number of particles. Important sensors including gravitational-wave interferometers and…

The submodular knapsack problem (SKP), which seeks to maximize a submodular set function by selecting a subset of elements within a given budget, is an important discrete optimization problem. The majority of existing approaches to solving…

This paper proposes a novel algorithm for signal classification problems. We consider a non-stationary random signal, where samples can be classified into several different classes, and samples in each class are identically independently…

We study the theoretical and practical runtime limits of k-means and k-median clustering on large datasets. Since effectively all clustering methods are slower than the time it takes to read the dataset, the fastest approach is to quickly…

$k-$means Clustering requires as input the exact value of $k$, the number of clusters. Two challenges are open: (i) Is there a data-determined definition of $k$ which is provably correct and (ii) Is there a polynomial time algorithm to find…

Many large-scale Web applications that require ranked top-k retrieval such as Web search and online advertising are implemented using inverted indices. An inverted index represents a sparse term-document matrix, where non-zero elements…

Clustering is an important technique for identifying structural information in large-scale data analysis, where the underlying dataset may be too large to store. In many applications, recent data can provide more accurate information and…

In this work, we aim to solve a practical use-case of unsupervised clustering which has applications in predictive maintenance in the energy operations sector using quantum computers. Using only cloud access to quantum computers, we…

The compressed indexing problem is to preprocess a string $S$ of length $n$ into a compressed representation that supports pattern matching queries. That is, given a string $P$ of length $m$ report all occurrences of $P$ in $S$. We present…

We study community detection in the \emph{symmetric $k$-stochastic block model}, where $n$ nodes are evenly partitioned into $k$ clusters with intra- and inter-cluster connection probabilities $p$ and $q$, respectively. Our main result is a…