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Estimation of Locally Stationary Graph Processes from Incomplete Realizations
2022 IEEE 32nd International Workshop on Machine Learning for Signal Processing (MLSP)
Year: 2022 | Conference Paper |
Cited by: Papers (3)
Stationarity is a well-studied concept in signal processing and the concept of stationary random processes has been extended to graph domains in several recent works. Meanwhile, in many scenarios a globally stationary process model may fail to accurately represent the correlation patterns of the data on the whole graph, e.g. when data is acquired on big graphs or when the behavior of the process v...Show More
An Approach to Simulation of Stationary and Non-stationary Processes in the Harmonic Basis
2021 IEEE Conference of Russian Young Researchers in Electrical and Electronic Engineering (ElConRus)
Year: 2021 | Conference Paper |
Cited by: Papers (2)
Environment simulation is a part of the development and research of various real-time systems. Environmental influences are modeled as stationary and non-stationary processes. Useful signals are commonly simulated as stationary processes. Simulation of non-stationary processes is required to represent signal-noise mixtures, fluctuations, turbulence. The authors propose to simulate a non-stationary...Show More
Reduced Stationary Subspace Analysis for Anomaly Detection in Nonstationary Industrial Processes
2020 Chinese Automation Congress (CAC)
Year: 2020 | Conference Paper |
Anomaly detection is significant to ensure production efficiency and system safety of industrial processes. Complex processes generally show nonstationary properties, so nonstationary process monitoring has become a research hotspot recently. As two major methods, adaptive methods are difficult to model significant nonstationary trends, and cointegration analysis-based approaches are insensitive t...Show More
On Rate of Convergence of Statistical Estimation of Stationary Ergodic Processes
Stationary ergodic processes with finite alphabets are approximated by finite memory processes based on an n-length realization of the process. Under the assumptions of summable continuity rate and non-nullness, a rate of convergence in d̅-distance is obtained, with explicit constants. Asymptotically, as n → ∞, the result is near the optimum.Show More
Stationary graph process models are commonly used in the analysis and inference of data sets collected on irregular network topologies. While most of the existing methods represent graph signals with a single stationary process model that is globally valid on the entire graph, in many practical problems, the characteristics of the process may be subject to local variations in different regions of ...Show More
Python-Based Simulation of Non-Gaussian Stationary Random Process with Arbitrary Auto-Correlation Function
2023 International Conference on Electrical, Computer and Energy Technologies (ICECET)
Year: 2023 | Conference Paper |
Simulation of stationary random processes (time series) is an essential engineering tool for system prototyping, design, and optimization. To create a simulation, a randomly generated time series must have a pre-defined distribution and autocorrelation function (ACF). It is challenging to model non-Gaussian distributions as using a linear filter can alter the target distribution. To address this i...Show More
Asymptotic Generalized Eigenvalue Distribution of Block Multilevel Toeplitz Matrices
In many detection and estimation problems associated with processing of second-order stationary random processes, the observation data are the sum of two zero-mean second-order stationary processes: the process of interest and the noise process. In particular, the main performance criterion is the signal-to-noise ratio (SNR). After linear filtering, the optimal SNR corresponds to the maximal value...Show More
Fast Algorithms for the Schur- Type Nonlinear Parametrization of Higher-Order Stochastic Processes
2018 26th European Signal Processing Conference (EUSIPCO)
Year: 2018 | Conference Paper |
Cited by: Papers (1)
We propose a class of fast algorithms, efficiently performing nonlinear Schur parametrization of higher-order and non-Gaussian stochastic processes, following from consideration of (weak) higher-order stationarity of the underlying signals and resulting in essential nonlinear complexity reduction, allowing for their practical implementations.Show More
The main result is a universal pointwise test that, when presented with a set of words S on a finite or countable alphabet X that purports to be a set of memory words for a stationary process, will eventually almost surely return the value YES precisely when all positive probability words in S are memory words. For example, if S consists of all of the single letters in X, then the test will eventu...Show More
Learning Parametric Time-Vertex Graph Processes from Incomplete Realizations
2021 IEEE 31st International Workshop on Machine Learning for Signal Processing (MLSP)
Year: 2021 | Conference Paper |
Cited by: Papers (2)
We consider the problem of estimating time-varying graph signals with missing observations, which is of interest in many applications involving data acquisition on irregular topologies. We model time-varying graph signals as jointly stationary time-vertex ARMA graph processes. We formulate the learning of ARMA process parameters as an optimization problem where the joint power spectral density of ...Show More
Extreme Value Theory for Univariate Stationary Processes
2016 Global Summit on Computer & Information Technology (GSCIT)
Year: 2016 | Conference Paper |
Cited by: Papers (1)
Extreme value theory assumes that random variables are independent and identically distributed. This assumption cannot occur in time series analysis. In this paper, we investigate the extremal behavior of a stationary Gaussian autoregressive model. The Kolmogorov-Smirnov goodness of fit test shows that block maxima data converges in probability to a Gumbel distribution, so the introduction of depe...Show More
Spectral methods for stationary harmonizable alpha-stable processes
9th European Signal Processing Conference (EUSIPCO 1998)
Year: 1998 | Conference Paper |
We address the problem of estimation of the fractional-power spectrum of certain classes of symmetric, alpha-stable (SαS) processes. We start with a summary of the key definitions and results from the theory of stationary, harmonizable SαS processes and proceed to discuss the performance of fractional-power periodograms. Next, we present a high resolution fractional-power spectrum estimation algor...Show More
A class of second-order stationary self-similar processes for 1/f phenomena
We propose a class of statistically self-similar processes and outline an alternative mathematical framework for the modeling and analysis of 1/f phenomena. The foundation of the proposed class is based on the extensions of the basic concepts of classical time series analysis, in particular, on the notion of stationarity. We consider a class of stochastic processes whose second-order structure is ...Show More
Phase-Rectified Signal Variance Series and its Values for a Stationary Gaussian Process
2024 13th Conference of the European Study Group on Cardiovascular Oscillations (ESGCO)
Year: 2024 | Conference Paper |
Phase-Rectified Signal Averaging (PRSA) computes the average of portions of a time series aligned at a given anchor point. In this study we explored the variance of such samples around the PRSA, or “Phase-Rectified Signal Variance” series (PRSV), and derived its analytical formulation for a stationary Gaussian process. The mathematical prediction was compared with estimates obtained from a set of ...Show More
Learning Graph ARMA Processes From Time-Vertex Spectra
Eylem Tuğçe Güneyi;Berkay Yaldız;Abdullah Canbolat;Elif Vural
The modeling of time-varying graph signals as stationary time-vertex stochastic processes permits the inference of missing signal values by efficiently employing the correlation patterns of the process across different graph nodes and time instants. In this study, we propose an algorithm for computing graph autoregressive moving average (graph ARMA) processes based on learning the joint time-verte...Show More
Methodology for Identifying Critical Vulnerabilities in Distributed Systems
2018 International Scientific-Practical Conference Problems of Infocommunications. Science and Technology (PIC S&T)
Year: 2018 | Conference Paper |
The urgency of using modern mathematical methods in analyzing the reliability and fault tolerance of distributed system elements is not in doubt at this time. The trend of using the theory of stationary processes as a basis for methodologies for analysis and decision making has become global. To ensure the reliability and fault tolerance of distributed systems, modern analyzes include a mathematic...Show More
Assessment of Texture Stationarity Using the Asymptotic Behavior of the Empirical Mean and Variance
RÉmy Blanc;Jean-Pierre Da Costa;Youssef Stitou;Pierre Baylou;Christian Germain
Given textured images considered as realizations of 2-D stochastic processes, a framework is proposed to evaluate the stationarity of their mean and variance. Existing strategies focus on the asymptotic behavior of the empirical mean and variance (respectively EM and EV), known for some types of nondeterministic processes. In this paper, the theoretical asymptotic behaviors of the EM and EV are st...Show More
Conventional reliability models seldom consider the times of load action. The reliability calculated by these models is actually the reliability when random load acts for specified times. For general components and systems, these models can't reflect the effect of times of load action on reliability explicitly. In this paper different types of load models and the methodology for solving the time i...Show More
Some common misconceptions about the modeling of repairable components
2009 IEEE Power & Energy Society General Meeting
Year: 2009 | Conference Paper |
Cited by: Papers (8)
Although stochastic point process theory has been successfully applied in many fields of knowledge, in power systems reliability it has not received so much attention what is reflected in the low number of reported applications. This may be due to some common misconceptions about the modeling of repairable components which falsely show this method is the same than other popular ones. All these mis...Show More
Event-Based Control and Scheduling Codesign: Stochastic and Robust Approaches
With the advent of networked embedded control systems (NECSs) new opportunities and challenges have arisen. Among others, the challenges result mostly from variable communication delays, access constraints, and resource constraints. An event-based control and scheduling (EBCS) codesign strategy for NECSs involving a set of continuous-time LTI plants is proposed in this paper addressing all aforeme...Show More
Spectral Relations for Multidimensional Complex Improper Stationary and (Almost) Cyclostationary Processes
We study continuous-time multidimensional wide- sense stationary (WSS) and (almost) cyclostationary processes in the frequency domain. Under the assumption that the correlation function is uniformly continuous, we prove the existence of a unique sequence of spectral measures, which coincide with the restrictions to certain subdiagonals of the spectral measure in the strongly harmonizable case. Mor...Show More
Octahedral Transforms for 3-D Image Processing
The octahedral group is one of the finite subgroups of the rotation group in 3-D Euclidean space and a symmetry group of the cubic grid. Compression and filtering of 3-D volumes are given as application examples of its representation theory. We give an overview over the finite subgroups of the 3-D rotation group and their classification. We summarize properties of the octahedral group and basic re...Show More
The exact Cramer-Rao bound for Gaussian autoregressive processes
An explicit expression is derived for the Cramer-Rao bound (CRB) on unbiased estimates of the parameters of autoregressive (AR) processes, given a finite number of measurements. The expression converges to the well-known asymptotic form of the CRB when the number of measurements tends to infinity. The behavior of the bound is illustrated by some numerical examples.<>
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Show MoreOn the Properties of Time-Varying SNR Process in Cellular-Enabled UAV Networks
Siva Duggireddy;Pranava C. Stanam;Praful D. Mankar;Harpreet S. Dhillon
ICC 2022 - IEEE International Conference on Communications
Year: 2022 | Conference Paper |
Cited by: Papers (1)
The unmanned aerial vehicle (UAV) based communication is expected to play an important role in enabling a variety of applications in future cellular networks. However, because of the mobility of the UAVs, the communications links involving UAVs undergo large-scale temporal variations in the received signal quality, which may affect the quality-of-service of the underlying application. Therefore, i...Show More
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