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Many scientific areas are faced with the challenge of extracting information from large, complex, and highly structured data sets. A great deal of modern statistical work focuses on developing tools for handling such data. This paper…

In this paper we propose a novel texture descriptor called Fractal Weighted Local Binary Pattern (FWLBP). The fractal dimension (FD) measure is relatively invariant to scale-changes, and presents a good correlation with human viewpoint of…

Functional data analysis (FDA) is a part of modern multivariate statistics that analyses data providing information about curves, surfaces or anything else varying over a certain continuum. In economics and empirical finance we often have…

Multifractal detrended fluctuation analysis (MFDFA) has become a central method to characterise the variability and uncertainty in empiric time series. Extracting the fluctuations on different temporal scales allows quantifying the strength…

The purpose of this paper is to study the fractal phenomena in large data sets and the associated questions of dimension reduction. We examine situations where the classical Principal Component Analysis is not effective in identifying the…

This work presents a methodology to the morphology analysis and characterization of nanostructured material images acquired from FEG-SEM (Field Emission Gun-Scanning Electron Microscopy) technique. The metrics were extracted from the image…

Many conventional statistical and machine learning methods face challenges when applied directly to high dimensional temporal observations. In recent decades, Functional Data Analysis (FDA) has gained widespread popularity as a framework…

Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and,…

With the advance of modern technology, more and more data are being recorded continuously during a time interval or intermittently at several discrete time points. They are both examples of "functional data", which have become a prevailing…

This paper analyzes the performance of the Fractal Decomposition Algorithm (FDA) metaheuristic applied to low-dimensional continuous optimization problems. This algorithm was originally developed specifically to deal efficiently with…

Restructuring compilers use dependence analysis to prove that the meaning of a program is not changed by a transformation. A well-known limitation of dependence analysis is that it examines only the memory locations read and written by a…

The abundance of functional observations in scientific endeavors has led to a significant development in tools for functional data analysis (FDA). This kind of data comes with several challenges: infinite-dimensionality of function spaces,…

Most of the known methods for estimating the fractal dimension of fractal sets are based on the evaluation of a single geometric characteristic, e.g. the volume of its parallel sets. We propose a method involving the evaluation of several…

Methodology is proposed to uncover structural breaks in functional data that is "fully functional" in the sense that it does not rely on dimension reduction techniques. A thorough asymptotic theory is developed for a fully functional break…

Interpretability is becoming an active research topic as machine learning (ML) models are more widely used to make critical decisions. Tabular data is one of the most commonly used modes of data in diverse applications such as healthcare…

In this work, we explore data augmentations for knowledge distillation on semantic segmentation. To avoid over-fitting to the noise in the teacher network, a large number of training examples is essential for knowledge distillation.…

To address the issue of feature descriptors being ineffective in representing grayscale feature information when images undergo high affine transformations, leading to a rapid decline in feature matching accuracy, this paper proposes a…

Functional integrals are defined in terms of locally compact topological groups and their associated Banach-valued Haar integrals. This approach generalizes the functional integral scheme of Cartier and DeWitt-Morette. The definition allows…

We present some work relating to fractal transformations on masked iterated function systems and demonstrate how well known algorithms for generating fractal transformations can be modifed for these systems. We also demonstrate that these…

The advent of big data has raised significant challenges in analysing high-dimensional datasets across various domains such as medicine, ecology, and economics. Functional Data Analysis (FDA) has proven to be a robust framework for…