Related papers: Iterated Function System Models in Data Analysis: …
Parallel dataflow systems are a central part of most analytic pipelines for big data. The iterative nature of many analysis and machine learning algorithms, however, is still a challenge for current systems. While certain types of bulk…
This study presents a method, along with its algorithmic and computational framework implementation, and performance verification for dynamical system identification. The approach incorporates insights from phase space structures, such as…
Iterative phase retrieval algorithms are widely used in digital optics for their efficiency and simplicity. Conventionally, these algorithms do not consider aberrations as they assume an ideal, aberration-free optical system. Here, we…
Vertical federated learning (VFL) enables a paradigm for vertically partitioned data across clients to collaboratively train machine learning models. Feature selection (FS) plays a crucial role in Vertical Federated Learning (VFL) due to…
The paper introduces a technique that decomposes the dynamics of a nonlinear system about an equilibrium into low order components, which then can be used to reconstruct the full dynamics. This is a nonlinear analogue of linear modal…
One of the key challenges of machine learning (ML) based intrusion detection system (IDS) is the expensive computational complexity which is largely due to redundant, incomplete, and irrelevant features contain in the IDS datasets. To…
The analysis of the time-frequency content of a signal is a classical problem in signal processing, with a broad number of applications in real life. Many different approaches have been developed over the decades, which provide alternative…
A variety of complex biological, natural and man-made systems exhibit non-Markovian dynamics that can be modeled through fractional order differential equations, yet, we lack sample comlexity aware system identification strategies. Towards…
A resource selection function is a model of the likelihood that an available spatial unit will be used by an animal, given its resource value. But how do we appropriately define availability? Step-selection analysis deals with this problem…
Federated learning harnesses the power of distributed optimization to train a unified machine learning model across separate clients. However, heterogeneous data distributions and computational workloads can lead to inconsistent updates and…
This paper deals with analytic families of holomorphic iterated function systems. Using real analyticity of the pressure function (which we prove), we establish a classification theorem for analytic families of holomorphic iterated function…
We extend classical basis constructions from Fourier analysis to attractors for affine iterated function systems (IFSs). This is of interest since these attractors have fractal features, e.g., measures with fractal scaling dimension.…
This paper contains four main results associated with an attractor of a projective iterated function system (IFS). The first theorem characterizes when a projective IFS has an attractor which avoids a hyperplane. The second theorem…
The majority of modern systems exhibit sophisticated concurrent behaviour, where several system components modify and observe the system state with fine-grained atomicity. Many systems (e.g., multi-core processors, real-time controllers)…
Machine learning models usually assume that a set of feature values used to obtain an output is fixed in advance. However, in many real-world problems, a cost is associated with measuring these features. To address the issue of reducing…
Dynamical systems are used to model a variety of phenomena in which the bifurcation structure is a fundamental characteristic. Here we propose a statistical machine-learning approach to derive lowdimensional models that automatically…
In collaborative filtering (CF), interaction function (IFC) plays the important role of capturing interactions among items and users. The most popular IFC is the inner product, which has been successfully used in low-rank matrix…
Iterative filtering methods were introduced around 2010 to improve definitions and measurements of structural features in signal processing. Like many applied techniques, they present considerable challenges for mathematicians to theorize…
In this paper, we study cut sets of attractors of iteration function systems (IFS) in $\mathbb{R}^d$. Under natural conditions, we show that all irreducible cut sets of these attractors are perfect sets or single points. This leads to a…
Complex dynamic systems can be investigated by fitting mechanistic stochastic dynamic models to time series data. In this context, commonly used Monte Carlo inference procedures for model selection and parameter estimation quickly become…