Reconstructing Plant Connectivity using Directed Spectral Decomposition
TL;DR: In this article, the authors developed a methodology for reconstruction of plant connectivity from dynamic data using directional spectral analysis, a novel adaptation of ideas from neurosciences and econometrics.
About: This article is published in IFAC Proceedings Volumes.The article was published on 2012-01-01. It has received 9 citations till now.
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Posted Content•
TL;DR: The problem of reconstructing or identifying the network topology from steady state flux measurements using steady-state flow rate measurements is solved through a sequence of steps including estimating approximate linear relationships between variables using Principal Component Analysis (PCA), obtaining fundamental cut-sets from the model estimated by PCA, and graph realization from f-cut-sets.
Abstract: In this paper, we solve the problem of reconstructing or identifying the network topology from steady state flux measurements. Specifically, given a data matrix $\mathbf{X}$, where each column contains measurements corresponding to a distinct steady state configuration, we wish to estimate a model $\mathbf{A}$ which captures the approximate linear relationships between different variables comprising $\mathbf{X}$ (i.e. of the form $\mathbf{AX \approx 0}$) such that $\mathbf{A}$ is full rank (highest possible) and consistent with a network incidence structure. Hence the network topology can be obtained just by looking at this estimated model. The problem is solved through a sequence of steps including estimating approximate linear relationships between variables using Principal Component Analysis (PCA), obtaining fundamental cut-sets from the model estimated by PCA, and graph realization from f-cut-sets (or equivalently f-circuits). Each step and the overall process is polynomial time. The method is illustrated using an example of water network reconstruction using steady-state flow rate measurements. We also establish hard limits on what can be, and cannot be done with steady-state data.
3 citations
Cites background from "Reconstructing Plant Connectivity u..."
...Relevant examples include identifying plant topology or connectivity from time series measurements [4], reconstruction of chemical reaction networks from data [5] etc....
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TL;DR: This work studies the problem of obtaining efficient estimates of network connectivity strengths and shows that the parametric models used in estimating connectivity strengths should be commensurate with the dynamics of the process as characterized by the newly introduced VACF and VPACF.
2 citations
01 Jan 2013
TL;DR: The EAUDI method is further extended to detect causality from process data, and it can also provide models of all connecting paths simultaneously, and hypothesis testing is proposed to verify the results of this approach (by testing cross-regressive coefficients).
Abstract: To the best of our knowledge, there are few methods which can determine both causality and models from process data, although both of them are crucial in practical applications. The extended augmented UD identification (EAUDI) is an identification approach which does not need a priori causal relationship between variables in advance. In this method, however, the information contained in the augmented information matrix (AIM) is still not fully utilized and yet helpful for causality analysis, namely, whether the values of cross-regressive coefficients are sufficiently weak to be considered as insignificant. Based on this, the EAUDI method is further extended to detect causality from process data, and it can also provide models of all connecting paths simultaneously. Moreover, hypothesis testing (F-distribution) is proposed to verify the results of this approach (by testing cross-regressive coefficients). The effectiveness of the proposed method is demonstrated by numerical examples. I. INTRODUCTION In industry, we often encounter with vast amount of process data, which is usually rich in information content (1). With careful mathematical analysis of the data, we can extract much more useful information. Some important tasks are the detection of causality from process data and furthermore, the determination of models from the data. The causality information is crucial in practical applications, particularly in chemical processes. The data set from chemical processes is multivariate in nature and characterized by serial correlation which is caused by the interconnected operations (heating, cooling, pumping, and mixing) and inertial units (reactors, tanks, and recycle streams). For chemical processes, the knowledge of causality and models is of great help for the control design. Therefore, it is imperative to find methods to automatically determine the causality and models from vast amount of data.
1 citations
Dissertation•
01 Jan 2015
References
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TL;DR: In this article, the cross spectrum between two variables can be decomposed into two parts, each relating to a single causal arm of a feedback situation, and measures of causal lag and causal strength can then be constructed.
Abstract: There occurs on some occasions a difficulty in deciding the direction of causality between two related variables and also whether or not feedback is occurring. Testable definitions of causality and feedback are proposed and illustrated by use of simple two-variable models. The important problem of apparent instantaneous causality is discussed and it is suggested that the problem often arises due to slowness in recording information or because a sufficiently wide class of possible causal variables has not been used. It can be shown that the cross spectrum between two variables can be decomposed into two parts, each relating to a single causal arm of a feedback situation. Measures of causal lag and causal strength can then be constructed. A generalisation of this result with the partial cross spectrum is suggested.
16,349 citations
"Reconstructing Plant Connectivity u..." refers methods in this paper
...Connectivity analysis using Granger causality [Granger, 1969] has emerged as a major tool for examining information flow between brain regions [Smith et al., 2011, Baccala and Sameshima, 2001]....
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...Granger [1969] adopted Wiener’s ideas to give rise to a practically implementable definition of causality, now known as Granger causality [Granger, 1969]....
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01 Jan 2001
TL;DR: In this article, it is shown that the cross spectrum between two variables can be decomposed into two parts, each relating to a single causal arm of a feedback situation, and measures of causal lag and causal strength can then be constructed.
Abstract: There occurs on some occasions a difficulty in deciding the direction of causality between two related variables and also whether or not feedback is occurring. Testable definitions of causality and feedback are proposed and illustrated by use of simple two-variable models. The important problem of apparent instantaneous causality is discussed and it is suggested that the problem often arises due to slowness in recordhag information or because a sufficiently wide class of possible causal variables has not been used. It can be shown that the cross spectrum between two variables can be decomposed into two parts, each relating to a single causal arm of a feedback situation. Measures of causal lag and causal strength can then be constructed. A generalization of this result with the partial cross spectrum is suggested.The object of this paper is to throw light on the relationships between certain classes of econometric models involving feedback and the functions arising in spectral analysis, particularly the cross spectrum and the partial cross spectrum. Causality and feedback are here defined in an explicit and testable fashion. It is shown that in the two-variable case the feedback mechanism can be broken down into two causal relations and that the cross spectrum can be considered as the sum of two cross spectra, each closely connected with one of the causations. The next three sections of the paper briefly introduce those aspects of spectral methods, model building, and causality which are required later. Section IV presents the results for the two-variable case and Section V generalizes these results for three variables.
11,896 citations
"Reconstructing Plant Connectivity u..." refers methods in this paper
...Connectivity analysis using Granger causality [Granger, 1969] has emerged as a major tool for examining information flow between brain regions [Smith et al....
[...]
...Connectivity analysis using Granger causality [Granger, 1969] has emerged as a major tool for examining information flow between brain regions [Smith et al., 2011, Baccala and Sameshima, 2001]....
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...Granger [1969] adopted Wiener’s ideas to give rise to a practically implementable definition of causality, now known as Granger causality [Granger, 1969]....
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04 Oct 2007
TL;DR: This reference work and graduate level textbook considers a wide range of models and methods for analyzing and forecasting multiple time series, which include vector autoregressive, cointegrated, vector Autoregressive moving average, multivariate ARCH and periodic processes as well as dynamic simultaneous equations and state space models.
Abstract: This reference work and graduate level textbook considers a wide range of models and methods for analyzing and forecasting multiple time series. The models covered include vector autoregressive, cointegrated, vector autoregressive moving average, multivariate ARCH and periodic processes as well as dynamic simultaneous equations and state space models. Least squares, maximum likelihood, and Bayesian methods are considered for estimating these models. Different procedures for model selection and model specification are treated and a wide range of tests and criteria for model checking are introduced. Causality analysis, impulse response analysis and innovation accounting are presented as tools for structural analysis. The book is accessible to graduate students in business and economics. In addition, multiple time series courses in other fields such as statistics and engineering may be based on it. Applied researchers involved in analyzing multiple time series may benefit from the book as it provides the background and tools for their tasks. It bridges the gap to the difficult technical literature on the topic.
5,244 citations
Journal Article•
21 Mar 1991
TL;DR: In this article, the authors introduce the concept of Stationary Random Processes and Spectral Analysis in the Time Domain and Frequency Domain, and present an analysis of Processes with Mixed Spectra.
Abstract: Preface. Preface to Volume 2. Contents of Volume 2. List of Main Notation. Basic Concepts. Elements of Probability Theory. Stationary Random Processes. Spectral Analysis. Estimation in the Time Domain. Estimation in the Frequency Domain. Spectral Analysis in Practice. Analysis of Processes with Mixed Spectra.
5,238 citations
Book•
01 Jan 1997
TL;DR: Getting Started with DSPs 30: Complex Numbers 31: The Complex Fourier Transform 32: The Laplace Transform 33: The z-Transform Chapter 27 Data Compression / JPEG (Transform Compression)
Abstract: In early 1980s, DSP was taught as a graduate level course in electrical engineering. A decade later, DSP had become a standart part of the ungraduate curriculum.
3,046 citations
Additional excerpts
...The estimation of H(ω) is done from its relationship with VAR model in frequency domain, represented as H(ω) = Ā−1(ω) where (5) Ā(ω) =I − A(ω) and (6) A(ω) = p∑ r=1 Arz −r|z=ejω (7) is the Fourier transform [Smith, 1997] of the VAR coefficients, Ar....
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