Research Online at MacEwan :: Browsing by Author "Anton, Cristina"

Browsing by Author "Anton, Cristina"

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Cluster weighted models for functional data
(2025) Anton, Cristina; Smith, Iain
We propose a method, funWeightClust, based on a family of parsimonious models for clustering heterogeneous functional linear regression data. These models extend cluster weighted models to functional data, and they allow for multi-variate functional responses and predictors. The proposed methodology follows the approach used by the functional high dimensional data clustering (funHDDC) method. We construct an expectation maximization (EM) algorithm for parameter estimation. Using simulated and benchmark data we show that funWeightClust outperforms funHDDC and several two-steps clustering methods. We also use funWeightClust to analyze traffic patterns in Edmonton, Canada.
Clustering of time series cytotoxicity data
(2020) Richard, Dan; Anton, Cristina
To study the effect of various toxicants on cells’ growth, the Alberta Centre for Toxicology did several in-vitro experiments, and concentration response curves (TCRCs) were generated. Each TCRC represents a time series that gives the temporal evolution of the number of cells, after exposure to a chemical with a certain concentration. Here we use the wavelet transform to extract important features from the original TCRC data, and we apply self organizing maps to classify the toxicants according to their adverse biological response.
Explicit pseudo-symplectic methods based on generating functions for stochastic Hamiltonian systems
(2020) Anton, Cristina
We propose a systematic approach to construct explicit pseudo-symplectic schemes for stochastic Hamiltonian systems. This method is based on generating functions, so it is an extension of the techniques used for constructing high-order symplectic schemes for stochastic Hamiltonian systems. We study the order of convergence of the proposed explicit pseudo-symplectic schemes. The excellent long term performance of the pseudo-symplectic schemes is verified numerically.
Explicit pseudo-symplectic Runge-Kutta methods for stochastic Hamiltonian systems
(2023) Anton, Cristina
We give conditions for stochastic Runge-Kutta methods to near preserve quadratic invariants, and we discuss the associated simpli ed order conditions. For stochastic Hamiltonian systems we propose a systematic approach to construct explicit stochastic Runge-Kutta pseudo-symplectic schemes. Our approach is based on colored trees and B-series. We construct some pseudosymplectic stochastic Runge-Kutta methods with strong convergence order, and we illustrate numerically the long term performance of the proposed schemes.
Exponential bounds for the density of the law of the solution of a SDE with locally Lipschitz coefficients
(2024) Anton, Cristina
Under the uniform Hörmander’s hypothesis we study smoothness and exponential bounds of the density of the law of the solution of a stochastic differential equation (SDE) with locally Lipschitz drift that satisfy a monotonicity condition. To obtain estimates for the Malliavin covariance matrix and its inverse, we extend the approach in to SDEs with non-globally Lipschitz coefficients. As in, to avoid non-integrability problems we use results about Malliavin differentiability based on the concepts of Ray Absolute Continuity and Stochastic Gateâux differentiability.
Exponential bounds for the density of the law of the solution of an SDE with locally Lipschitz coefficients
(2025) Anton, Cristina
Under the uniform Hörmander hypothesis, we study the smoothness and exponential bounds of the density of the law of the solution of a stochastic differential equation (SDE) with locally Lipschitz drift that satisfies a monotonicity condition. We extend the approach used for SDEs with globally Lipschitz coefficients and obtain estimates for the Malliavin covariance matrix and its inverse. Based on these estimates and using the Malliavin differentiability of any order of the solution of the SDE, we prove exponential bounds of the solution’s density law. These results can be used to study the convergence of implicit numerical schemes for SDEs.
Forecasting CAD/USD exchange rate
(2023) Wu, Joyce; Anton, Cristina
The exchange rate of Canadian dollars was closely bound up with the US dollars for the past decades. The last time that the Canadian dollar was worth more than the US dollar was in July 2011. It then experienced its fastest decline in modern-day history as commodity prices rapidly deteriorated. We use time series analysis to study the variation of CAD/USD exchange rate since 2010. We fit an ARIMA model and analyze how different economic and social policies in both countries affect the exchange rate.
Functional non-parametric mixed effects models for cytotoxicity assessment and clustering
(2023) Ma, Tiantian; Richard, Dan; Yang, Yongqing Betty; Kashlak, Adam B.; Anton, Cristina
A multitude of natural and synthetic chemicals are present in our environment. Through the study of a compound’s cytotoxicity, researchers can carefully set regulations regarding how much of a certain chemical in the ambient environment is tolerable. In the past, research has focused on point measurements such as the LD50. Instead, we consider entire time-dependent cellular response curves through the application of functional mixed effects models. We identify differences in such curves corresponding to the chemical’s mode of action—i.e. how the compound attacks human cells. Through such analysis, we identify curve features to be used for cluster analysis via application of both k-means and self organizing maps. The data is analyzed by making use of functional principal components as a data driven basis and separately by considering B-splines for identifying local-time features. Our analysis can be used to drastically speed up future cytotoxicity research.
The influence of noise in cytoxicity assessment
(2016) Yong, Alan; Anton, Cristina
Industrial activity produces many chemicals that may be hazardous to human health or the environment. Traditionally, experiments can be carried out on live subjects (in vivo), but this is both expensive and raises significant ethical concerns. Rather than conducting these assays, we might try using mathematical or computational models to assess the effect of these toxicants (1). With in vitro assays at the Alberta Centre of Toxicology using the xCelligence Real-Time Cell Analysis HT system, time-dependent response curves (TCRCs) were generated. These experimentally-derived curves reflect the response of human cells to these toxicants. The goal was to find a mathematical model that could accurately reproduce these curves (2). Depending on the value of various parameters of the toxicant – such as its toxicity and how fast cells absorb it – there are generally two possible equilibria dependent on the toxicant's initial external concentration: a cell line may persevere and survive; or the concentration may be large enough to cause extinction of the cell population. Data from the TCRCs were used to generate a deterministic model. That is, a given set of parameter values will always generate the same cell fate. However, there is inherently uncertainty in the value of these parameters. To assess the influence of this noise on the external concentration of toxicant at which some population of cells would reach survival or extinction equilibria, a new model was created with additional variables for this uncertainty. Several simulations were run with this extended model. The information generated will be useful for planning further experiments regarding cytotoxicity, and for numerically generating TCRCs for clustering and classification.
MacEwan University WiFi analysis
(2016) Prince, James; Yong, Alan; Anton, Cristina
One of the worst feelings in the world is waiting for a slow Internet connection. While this may be more a reflection of our impaired society than a faulty modem, this study will shed some light as to soothe these pains while on MacEwan University Campus. MacEwan University has recently undergone a "WiFi Renovation", with many new WiFi units installed all throughout the school. The goal of this experiment is to find where in the school are the strongest and weakest connections. This will be an interesting reflection on the new system effectiveness and coverage. The factors that will be tested for are the Location in the school, Time of Day, Day of the Week and Type of Device used, and blocking will be done on the last four factors. To measure the connection quality, a file of a pre-determined size will be downloaded and the time taken will be recorded. Alan will be using an Apple Iphone, and James will be using a Samsung Galaxy S3, which will eliminate the chance of a newer device being different than an older one, or an Apple device vs an Android. This study will determine which factors are significant, and which factor combination yields the best results in terms of WiFi connectivity. This method of mapping a WiFi system will be useful to students and to the IT management of the University because the results of this study will provide the school with information which will help plan for future changes to WiFi layout. An easy extension of the methodology of this experiment could be developed and used to assess any WiFi or cellular device service. The results from this experiment alone will be interesting, but a larger application of the method could be groundbreaking.
Mining COVID-19 data to predict the effect of policies on severity of outbreaks
(2023) El-Hajj, Mohamad; Anton, Calin; Anton, Cristina; Dobosz, Dominic; Smith, Iain; Deiab, Fattima; Saleh, Nagam
During the years 2020, 2021, and partially 2022, the COVID-19 virus ran rampant across the globe, causing devastating effects on the masses. Using data mining techniques, we explored factors linked to severe cases of COVID-19 and tried to identify the effect of different government policies on the evolution of the severity of infections. Four countries were selected with a date range of the year 2021 to investigate each region’s efforts regarding vaccine distribution and specific policies enacted for COVID-19 suppression. Pearson’s Correlation Coefficients were used to help establish initially relationships between the policies, vaccines, and severe cases. We used the identified factors to predict the number of new COVID-19 cases and hospital ICU admissions. We included all the country data from Our World in Data (OWID) for this phase. Our investigation indicates that, given enough data, long-range trend predictions can be obtained using Random Forest Regressors. A trained Random Forest model can readily explain factors that effectively slow the spread of COVID-19. With proposed policies given as input, the model can return the expected number of cases, thus informing policies without spending multiple weeks tracking results.
Model based clustering of functional data with mild outliers
(2023) Anton, Cristina; Smith, Iain; Brito, Paula; Dias, José G.; Lausen, Berthold; Montanari, Angela; Nugent, Rebecca
We propose a procedure, called CFunHDDC, for clustering functional data with mild outliers which combines two existing clustering methods: the functional high dimensional data clustering (FunHDDC) [1] and the contaminated normal mixture (CNmixt) [3] method for multivariate data. We adapt the FunHDDC approach to data with mild outliers by considering a mixture of multivariate contaminated normal distributions. To fit the functional data in group-specific functional subspaces we extend the parsimonious models considered in FunHDDC, and we estimate the model parameters using an expectation-conditional maximization algorithm (ECM). The performance of the proposed method is illustrated for simulated and real-world functional data, and CFunHDDC outperforms FunHDDC when applied to functional data with outliers.
Model-based clustering of functional data via mixtures of t distributions
(2023) Anton, Cristina; Smith, Iain
We propose a procedure, called T-funHDDC, for clustering multivariate functional data with outliers which extends the functional high dimensional data clustering (funHDDC) method (Schmutz et al, 2020) by considering a mixture of multivariate t distributions. We de ne a family of latent mixture models following the approach used for the parsimonious models considered in funHDDC and also constraining or not the degrees of freedom of the multivariate t distributions to be equal across the mixture components. The parameters of these models are estimated using an expectation maximization (EM) algorithm. In addition to proposing the T-funHDDC method, we add a family of parsimonious models to C-funHDDC, which is an alternative method for clustering multivariate functional data with outliers based on a mixture of contaminated normal distributions (Amovin-Assagba et al, 2022). We compare T-funHDDC, C-funHDDC, and other existing methods on simulated functional data with outliers and for real-world data. T-funHDDC out-performs funHDDC when applied to functional data with outliers, and its good performance makes it an alternative to C-funHDDC. We also apply the T-funHDDC method to the analysis of traffic flow in Edmonton, Canada.
Moving limit cycles model of an economic system
(2017) Kryuchkov, Vladimir; Solomonovich, Mark; Anton, Cristina
We consider a model explaining the dependence between the productivity of labor (PL) and the fixed capital per worker (FC) in an economic system. The core of the model is a nonlinear oscillator with a limit cycle as an attractor. We run numerical simulations of the dynamics specific to this non-autonomous model to compare with the actual data recorded for the years 1987–2001 for the enterprise Omsk Bacon. Based on the numerical analysis we can conclude that the interior dynamics is not affected by exterior perturbations. The numerical simulations can help the managers of the enterprise to take the right steps to avoid stagnation.
A multivariate functional data clustering method using parsimonious cluster weighted models
(2025) Anton, Cristina; Smith, Iain
We propose a method for clustering multivariate functional linear regression data. Our approach extends multivariate cluster weighted models to functional data with multivariate functional response and predictors, based on the ideas used by the funHDDC method. To add model flexibility, we consider several two-component parsimonious models by combining the parsimonious models used for funHDDC with the Gaussian parsimonious clustering models family in. Parameter estimation is carried out within the expectation maximization (EM) algorithm framework. The proposed method outperforms funHDDC on simulated and real-world data.
A new class of symplectic methods for stochastic Hamiltonian systems
(2025) Anton, Cristina
We propose a systematic approach to construct a new family of stochastic symplectic schemes for the strong approximation of the solution of stochastic Hamiltonian systems. Our approach is based both on B-series and generating functions. The proposed schemes are a generalization of the implicit midpoint rule, they require derivatives of the Hamiltonian functions of at most order two, and are constructed by defining a generating function. We construct some schemes with strong convergence order one and a half, and we illustrate numerically their long term performance.
Parameter estimation and prediction for time-dependent concentration response curves for cytotoxicity assessment
(2016) Anton, Cristina
We propose a model based on the logistic equation and linear kinetics to study the effect of toxicants with various initial concentrations on a cells' population. To efficiently estimate the model's parameters, we design an Expectation Maximization algorithm. The model is validated by showing that it accurately represents the information provided by in-vitro experiments.
Preliminary results on using clustering of functional data to identify patients with alzheimer’s disease by analyzing brain MRI scans
(2025) Anton, Calin; Anton, Cristina; El-Hajj, Mohamad; Craner, Matthew; Lui, Richard
This study delves into the effectiveness of funWeightClust, a sophisticated model-based clustering technique that leverages functional linear regression models to pinpoint patients diagnosed with Alzheimer’s Disease. Our research entailed a thorough analysis of voxelwise fractional anisotropy data derived from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) dataset, with a particular emphasis on the Cingulum and Corpus Callosum, which are critical regions of interest in understanding the disease’s impact on brain structure. Through a series of experiments, we established that funWeightClust is efficient at distinguishing between patients with Alzheimer’s Disease and healthy control subjects. Notably, the clustering model yielded even more pronounced and accurate results when we focused our analysis on specific brain regions, such as the Left Hippocampus and the Splenium. We postulate that integrating additional biomarkers could significantly enhance the accuracy and reliability of funWeightClust in identifying patients who exhibit signs of Alzheimer’s Disease.
Pseudo-symplectic methods for stochastic Hamiltonian systems
(2018) Anton, Cristina
We propose a systematic approach to construct explicit pseudo-symplectic schemes for stochastic Hamiltonian systems. This method is based on generating functions, so it is an extension of the techniques used for constructing high-order symplectic schemes for stochastic Hamiltonian systems. We study the order of convergence of the proposed explicit pseudo-symplectic schemes. The excellent long term performance of the pseudo-symplectic schemes is verified numerically.
Research recast(ed): Dreaming big through research in mathematics and statistics and shaping the minds of young mathematicians with Cristina Anton
(2023) Miskiman, Megan; Schabert, Reinette; Anton, Cristina
In today's episode, Cristina Anton, professor of Mathematics and Statistics at MacEwan University, discusses her research on clustering functional data with outliers and toxicity assessments. Cristina discusses involvement in youth math competitions and math labs, encouraging students to dream big. With special thanks to Cristina's research partners and students. Machine learning project for clustering functional data with outliers Iain Smith Malcolm Nielsen. Time Series Project Sandy Julian and Joyce Wu.

Browsing by Author "Anton, Cristina"

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