scholarly journals Predicting tipping points in mutualistic networks through dimension reduction

2018 ◽  
Vol 115 (4) ◽  
pp. E639-E647 ◽  
Author(s):  
Junjie Jiang ◽  
Zi-Gang Huang ◽  
Thomas P. Seager ◽  
Wei Lin ◽  
Celso Grebogi ◽  
...  
Keyword(s):  
Dimension Reduction ◽  
Reduction Process ◽  
Real Data ◽  
Tipping Point ◽  
Networked Systems ◽  
Weighted Averaging ◽  
Dynamical Mechanism ◽  
Point Of No Return ◽  
2D System ◽  
Mutualistic Networks

Complex networked systems ranging from ecosystems and the climate to economic, social, and infrastructure systems can exhibit a tipping point (a “point of no return”) at which a total collapse of the system occurs. To understand the dynamical mechanism of a tipping point and to predict its occurrence as a system parameter varies are of uttermost importance, tasks that are hindered by the often extremely high dimensionality of the underlying system. Using complex mutualistic networks in ecology as a prototype class of systems, we carry out a dimension reduction process to arrive at an effective 2D system with the two dynamical variables corresponding to the average pollinator and plant abundances. We show, using 59 empirical mutualistic networks extracted from real data, that our 2D model can accurately predict the occurrence of a tipping point, even in the presence of stochastic disturbances. We also find that, because of the lack of sufficient randomness in the structure of the real networks, weighted averaging is necessary in the dimension reduction process. Our reduced model can serve as a paradigm for understanding and predicting the tipping point dynamics in real world mutualistic networks for safeguarding pollinators, and the general principle can be extended to a broad range of disciplines to address the issues of resilience and sustainability.

scholarly journals Tipping point and noise-induced transients in ecological networks

2020 ◽  
Vol 17 (171) ◽  
pp. 20200645
Author(s):  
Yu Meng ◽  
Ying-Cheng Lai ◽  
Celso Grebogi
Keyword(s):  
Steady State ◽  
Scaling Laws ◽  
First Passage Time ◽  
Gaussian White Noise ◽  
Tipping Point ◽  
High Dimensional ◽  
Stable Steady State ◽  
Dynamical Mechanism ◽  
Mutualistic Networks ◽  
Demographic Noise

A challenging and outstanding problem in interdisciplinary research is to understand the interplay between transients and stochasticity in high-dimensional dynamical systems. Focusing on the tipping-point dynamics in complex mutualistic networks in ecology constructed from empirical data, we investigate the phenomena of noise-induced collapse and noise-induced recovery. Two types of noise are studied: environmental (Gaussian white) noise and state-dependent demographic noise. The dynamical mechanism responsible for both phenomena is a transition from one stable steady state to another driven by stochastic forcing, mediated by an unstable steady state. Exploiting a generic and effective two-dimensional reduced model for real-world mutualistic networks, we find that the average transient lifetime scales algebraically with the noise amplitude, for both environmental and demographic noise. We develop a physical understanding of the scaling laws through an analysis of the mean first passage time from one steady state to another. The phenomena of noise-induced collapse and recovery and the associated scaling laws have implications for managing high-dimensional ecological systems.

scholarly journals Cumulative Median Estimation for Sufficient Dimension Reduction

Stats ◽  
2021 ◽  
Vol 4 (1) ◽  
pp. 138-145
Author(s):  
Stephen Babos ◽  
Andreas Artemiou
Keyword(s):  
Dimension Reduction ◽  
Real Data ◽  
Sufficient Dimension Reduction

In this paper, we present the Cumulative Median Estimation (CUMed) algorithm for robust sufficient dimension reduction. Compared with non-robust competitors, this algorithm performs better when there are outliers present in the data and comparably when outliers are not present. This is demonstrated in simulated and real data experiments.

scholarly journals New coronavirus outbreak. Lessons learned from the severe acute respiratory syndrome epidemic

2015 ◽  
Vol 143 (13) ◽  
pp. 2882-2893 ◽  
Author(s):  
E. ÁLVAREZ ◽  
J. DONADO-CAMPOS ◽  
F. MORILLA
Keyword(s):  
Severe Acute Respiratory Syndrome ◽  
System Dynamics ◽  
Iterative Process ◽  
Emerging Infectious Diseases ◽  
Real Data ◽  
Lessons Learned ◽  
Networked Systems ◽  
Sensitivity Analyses ◽  
Algebraic Equations ◽  
Auxiliary Variables

SUMMARYSystem dynamics approach offers great potential for addressing how intervention policies can affect the spread of emerging infectious diseases in complex and highly networked systems. Here, we develop a model that explains the severe acute respiratory syndrome coronavirus (SARS-CoV) epidemic that occurred in Hong Kong in 2003. The dynamic model developed with system dynamics methodology included 23 variables (five states, four flows, eight auxiliary variables, six parameters), five differential equations and 12 algebraic equations. The parameters were optimized following an iterative process of simulation to fit the real data from the epidemics. Univariate and multivariate sensitivity analyses were performed to determine the reliability of the model. In addition, we discuss how further testing using this model can inform community interventions to reduce the risk in current and future outbreaks, such as the recently Middle East respiratory syndrome coronavirus (MERS-CoV) epidemic.

scholarly journals Generalized penalty for circular coordinate representation

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Hengrui Luo ◽  
Alice Patania ◽  
Jisu Kim ◽  
Mikael Vejdemo-Johansson
Keyword(s):  
Dimension Reduction ◽  
Real Data ◽  
Topological Data Analysis ◽  
High Dimensional ◽  
Topological Structures ◽  
Sampling Schemes ◽  
Coordinate Representation ◽  
Geometrical Shapes ◽  
Persistent Cohomology ◽  
High Dimensional Datasets

<p style='text-indent:20px;'>Topological Data Analysis (TDA) provides novel approaches that allow us to analyze the geometrical shapes and topological structures of a dataset. As one important application, TDA can be used for data visualization and dimension reduction. We follow the framework of circular coordinate representation, which allows us to perform dimension reduction and visualization for high-dimensional datasets on a torus using persistent cohomology. In this paper, we propose a method to adapt the circular coordinate framework to take into account the roughness of circular coordinates in change-point and high-dimensional applications. To do that, we use a generalized penalty function instead of an <inline-formula><tex-math id="M1">\begin{document}$ L_{2} $\end{document}</tex-math></inline-formula> penalty in the traditional circular coordinate algorithm. We provide simulation experiments and real data analyses to support our claim that circular coordinates with generalized penalty will detect the change in high-dimensional datasets under different sampling schemes while preserving the topological structures.</p>

Dimension Selection for Feature Selection and Dimension Reduction with Principal and Independent Component Analysis

2007 ◽  
Vol 19 (2) ◽  
pp. 513-545 ◽  
Author(s):  
Inge Koch ◽  
Kanta Naito
Keyword(s):  
Independent Component Analysis ◽  
Dimension Reduction ◽  
Dimensional Space ◽  
Principal Component ◽  
Real Data ◽  
Component Analysis ◽  
Independent Component ◽  
Data Sets ◽  
Optimal Dimension ◽  
Lower Dimensional Space

This letter is concerned with the problem of selecting the best or most informative dimension for dimension reduction and feature extraction in high-dimensional data. The dimension of the data is reduced by principal component analysis; subsequent application of independent component analysis to the principal component scores determines the most nongaussian directions in the lower-dimensional space. A criterion for choosing the optimal dimension based on bias-adjusted skewness and kurtosis is proposed. This new dimension selector is applied to real data sets and compared to existing methods. Simulation studies for a range of densities show that the proposed method performs well and is more appropriate for nongaussian data than existing methods.

scholarly journals Kernel Sliced Inverse Regression: Regularization and Consistency

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Qiang Wu ◽  
Feng Liang ◽  
Sayan Mukherjee
Keyword(s):  
Dimension Reduction ◽  
Real Data ◽  
Sliced Inverse Regression ◽  
Inverse Regression ◽  
Computational Stability ◽  
Generalization Performance ◽  
Nonlinear Dimension Reduction ◽  
Nonlinear Dimension

Kernel sliced inverse regression (KSIR) is a natural framework for nonlinear dimension reduction using the mapping induced by kernels. However, there are numeric, algorithmic, and conceptual subtleties in making the method robust and consistent. We apply two types of regularization in this framework to address computational stability and generalization performance. We also provide an interpretation of the algorithm and prove consistency. The utility of this approach is illustrated on simulated and real data.

scholarly journals Amalgams: data-driven amalgamation for the reference-free dimensionality reduction of zero-laden compositional data

2020 ◽  
Author(s):  
Thomas P. Quinn ◽  
Ionas Erb
Keyword(s):  
Dimension Reduction ◽  
Domain Knowledge ◽  
Compositional Data ◽  
Real Data ◽  
R Package ◽  
Data Driven ◽  
Alternative Methods ◽  
Compositional Data Analysis ◽  
Data Sets ◽  
Log Ratio

AbstractIn the health sciences, many data sets produced by next-generation sequencing (NGS) only contain relative information because of biological and technical factors that limit the total number of nucleotides observed for a given sample. As mutually dependent elements, it is not possible to interpret any component in isolation, at least without normalization. The field of compositional data analysis (CoDA) has emerged with alternative methods for relative data based on log-ratio transforms. However, NGS data often contain many more features than samples, and thus require creative new ways to reduce the dimensionality of the data without sacrificing interpretability. The summation of parts, called amalgamation, is a practical way of reducing dimensionality, but can introduce a non-linear distortion to the data. We exploit this non-linearity to propose a powerful yet interpretable dimension reduction method. In this report, we present data-driven amalgamation as a new method and conceptual framework for reducing the dimensionality of compositional data. Unlike expert-driven amalgamation which requires prior domain knowledge, our data-driven amalgamation method uses a genetic algorithm to answer the question, “What is the best way to amalgamate the data to achieve the user-defined objective?”. We present a user-friendly R package, called amalgam, that can quickly find the optimal amalgamation to (a) preserve the distance between samples, or (b) classify samples as diseased or not. Our benchmark on 13 real data sets confirm that these amalgamations compete with the state-of-the-art unsupervised and supervised dimension reduction methods in terms of performance, but result in new variables that are much easier to understand: they are groups of features added together.

scholarly journals GENERATION ALGORITHM OF DISCRETE LINE IN MULTI-DIMENSIONAL GRIDS

2017 ◽  
Vol XLII-2/W7 ◽  
pp. 11-15
Author(s):  
L. Du ◽  
J. Ben ◽  
Y. Li ◽  
R. Wang
Keyword(s):  
Dimension Reduction ◽  
Spatial Data ◽  
Reference Model ◽  
Three Dimensional ◽  
Reduction Process ◽  
Mathematic Model ◽  
Combination Method ◽  
Two Dimensional ◽  
Rectangular Grid ◽  
Discrete Line

Discrete Global Grids System (DGGS) is a kind of digital multi-resolution earth reference model, in terms of structure, it is conducive to the geographical spatial big data integration and mining. Vector is one of the important types of spatial data, only by discretization, can it be applied in grids system to make process and analysis. Based on the some constraint conditions, this paper put forward a strict definition of discrete lines, building a mathematic model of the discrete lines by base vectors combination method. Transforming mesh discrete lines issue in n-dimensional grids into the issue of optimal deviated path in n-minus-one dimension using hyperplane, which, therefore realizing dimension reduction process in the expression of mesh discrete lines. On this basis, we designed a simple and efficient algorithm for dimension reduction and generation of the discrete lines. The experimental results show that our algorithm not only can be applied in the two-dimensional rectangular grid, also can be applied in the two-dimensional hexagonal grid and the three-dimensional cubic grid. Meanwhile, when our algorithm is applied in two-dimensional rectangular grid, it can get a discrete line which is more similar to the line in the Euclidean space.

Sparse sufficient dimension reduction with heteroscedasticity

2021 ◽  
pp. 2150037
Author(s):  
Haoyang Cheng ◽  
Wenquan Cui
Keyword(s):  
Data Analysis ◽  
Dimension Reduction ◽  
High Dimensional Data ◽  
Real Data ◽  
Dimensional Subspace ◽  
High Dimensional ◽  
Sufficient Dimension Reduction ◽  
Lasso Regression ◽  
High Dimension Data ◽  
Reduction Problem

Heteroscedasticity often appears in the high-dimensional data analysis. In order to achieve a sparse dimension reduction direction for high-dimensional data with heteroscedasticity, we propose a new sparse sufficient dimension reduction method, called Lasso-PQR. From the candidate matrix derived from the principal quantile regression (PQR) method, we construct a new artificial response variable which is made up from top eigenvectors of the candidate matrix. Then we apply a Lasso regression to obtain sparse dimension reduction directions. While for the “large [Formula: see text] small [Formula: see text]” case that [Formula: see text], we use principal projection to solve the dimension reduction problem in a lower-dimensional subspace and projection back to the original dimension reduction problem. Theoretical properties of the methodology are established. Compared with several existing methods in the simulations and real data analysis, we demonstrate the advantages of our method in the high dimension data with heteroscedasticity.

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