Related papers: Master's thesis: Permutations With Restricted Move…
We investigate lossy compression (source coding) of data in the form of permutations. This problem has direct applications in the storage of ordinal data or rankings, and in the analysis of sorting algorithms. We analyze the rate-distortion…
Graph pattern matching is a routine process for a wide variety of applications such as social network analysis. It is typically defined in terms of subgraph isomorphism which is NP-Complete. To lower its complexity, many extensions of graph…
Embedding techniques have become essential components of large databases in the deep learning era. By encoding discrete entities, such as words, items, or graph nodes, into continuous vector spaces, embeddings facilitate more efficient…
The rapid increase in networked systems and data transmission requires advanced data compression solutions to optimize bandwidth utilization and enhance network performance. This study introduces a novel byte-level predictive model using…
Traditional compressed sensing considers sampling a 1D signal. For a multidimensional signal, if reshaped into a vector, the required size of the sensing matrix becomes dramatically large, which increases the storage and computational…
A single permutation, seen as union of disjoint cycles, represents a regular graph of degree two. Consider $d$ many independent random permutations and superimpose their graph structures. It is a common model of a random regular (multi-)…
This paper initiates a limit theory of permutation valued processes, building on the recent theory of permutons. We apply this to study the asymptotic behaviour of random sorting networks. We prove that the Archimedean path, the conjectured…
We establish a sharp estimate for a minimal number of binary digits (bits) needed to represent all bounded total generalized variation functions taking values in a general totally bounded metric space $(E,\rho)$ up to an accuracy of…
Learnable embedding vector is one of the most important applications in machine learning, and is widely used in various database-related domains. However, the high dimensionality of sparse data in recommendation tasks and the huge volume of…
Graph matching refers to finding node correspondence between graphs, such that the corresponding node and edge's affinity can be maximized. In addition with its NP-completeness nature, another important challenge is effective modeling of…
We prove inequalities relating the measures of maximal entropy of two patterns u,v where the extender set of u is contained in the extender set of v. Our main results are two generalizations of a Theorem of Meyerovitch; the first applies to…
We consider uniform random permutations in classes having a finite combinatorial specification for the substitution decomposition. These classes include (but are not limited to) all permutation classes with a finite number of simple…
In machine learning, graph embedding algorithms seek low-dimensional representations of the input network data, thereby allowing for downstream tasks on compressed encodings. Recently, within the framework of network renormalization,…
Symmetry breaking for graphs and other combinatorial objects is notoriously hard. On the one hand, complete symmetry breaks are exponential in size. On the other hand, current, state-of-the-art, partial symmetry breaks are often considered…
This work develops compressive sampling strategies for computing the dynamic mode decomposition (DMD) from heavily subsampled or output-projected data. The resulting DMD eigenvalues are equal to DMD eigenvalues from the full-state data. It…
Given two independent point processes and a certain rule for matching points between them, what is the fraction of matched points over infinitely long streams? In many application contexts, e.g., secure networking, a meaningful matching…
In this paper, we propose an efficient numerical implementation of Network Embedding based on commute times, using sparse approximation of a diffusion process on the network obtained by a modified version of the diffusion wavelet algorithm.…
Entropy metrics (for example, permutation entropy) are nonlinear measures of irregularity in time series (one-dimensional data). Some of these entropy metrics can be generalised to data on periodic structures such as a grid or lattice…
This paper demonstrates how new principles of compressed sensing, namely asymptotic incoherence, asymptotic sparsity and multilevel sampling, can be utilised to better understand underlying phenomena in practical compressed sensing and…
We begin with pervasive ultrametricity due to high dimensionality and/or spatial sparsity. How extent or degree of ultrametricity can be quantified leads us to the discussion of varied practical cases when ultrametricity can be partially or…