Related papers: Lossless Compression and Complexity of Chaotic Seq…
Data compression algorithms are generally perceived as being of interest for data communication and storage purposes only. However, their use in the field of data classification and analysis is also of equal importance. Automatic data…
We argue that Non-sequential Recursive Pair Substitution (NSRPS) as suggested by Jim\'enez-Monta\~no and Ebeling can indeed be used as a basis for an optimal data compression algorithm. In particular, we prove for Markov sequences that…
We present rigorous results on some open questions on NSRPS, non sequential recursive pairs substitution method (see Grassberger in \cite{G}). In particular, starting from the action of NSRPS on finite strings we define a corresponding…
A new framework is introduced for examining and evaluating the fundamental limits of lossless data compression, that emphasizes genuinely non-asymptotic results. The {\em sample complexity} of compressing a given source is defined as the…
A new run length encoding algorithm for lossless data compression that exploits positional redundancy by representing data in a two-dimensional model of concentric circles is presented. This visual transform enables detection of runs (each…
This article describes lossless compression algorithms for multisets of sequences, taking advantage of the multiset's unordered structure. Multisets are a generalisation of sets where members are allowed to occur multiple times. A multiset…
We propose a novel classification framework grounded in symbolic dynamics and data compression using chaotic maps. The core idea is to model each class by generating symbolic sequences from thresholded real-valued training data, which are…
We numerically test the method of non-sequential recursive pair substitutions to estimate the entropy of an ergodic source. We compare its performance with other classical methods to estimate the entropy (empirical frequencies, return…
This paper is dedicated to lossless data compression with probability estimation using neural networks. First, we propose a probability estimation architecture based on a chain of neural predictors, so that each unit of the chain is defined…
In this paper, we developed a novel method of nonparametric relative entropy (RlEn) for modelling loss of complexity in intermittent time series. The method consists of two steps. We first fit a nonlinear autoregressive model to each…
A lossy compression algorithm for binary redundant memoryless sources is presented. The proposed scheme is based on sparse graph codes. By introducing a nonlinear function, redundant memoryless sequences can be compressed. We propose a…
We study the sample complexity of the Sign-Perturbed Sums (SPS) method, which constructs exact, non-asymptotic confidence regions for the true system parameters under mild statistical assumptions, such as independent and symmetric noise…
Equations governing the nonlinear dynamics of complex systems are usually unknown and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences…
This thesis deals with the problem of communicating and storing non-sequential data. We investigate this problem through the lens of lossless source coding, also sometimes referred to as lossless compression, from both an algorithmic and…
The paper introduces a new lossless, highly robust compression algorithm that similar with LZW algorithm, yet the algorithm discards dictionary processing and uses irregular sequences with massive, random information instead. Then the paper…
In-context learning has established itself as an important learning paradigm for Large Language Models (LLMs). In this paper, we demonstrate that LLMs can learn encoding keys in-context and perform analysis directly on encoded…
We propose a framework for joint entropy coding and encryption using Chaotic maps. We begin by observing that the message symbols can be treated as the symbolic sequence of a discrete dynamical system. For an appropriate choice of the…
Learning-based lossless image compression employs pixel-based or subimage-based auto-regression for probability estimation, which achieves desirable performances. However, the existing works only consider context dependencies in one…
The problem of variable-rate lossless data compression is considered, for codes with and without prefix constraints. Sharp bounds are derived for the best achievable compression rate of memoryless sources, when the excess-rate probability…
Entropy measures are effective features for time series classification problems. Traditional entropy measures, such as Shannon entropy, use probability distribution function. However, for the effective separation of time series, new entropy…