Exploratory Analysis of Fossil-Fuel CO2 Emissions Time Series Using Independent Component Analysis

Exploratory Analysis of Fossil-Fuel CO2 Emissions Time Series Using Independent Component Analysis

Sargam Parmar, Bhuvan Unhelkar
Copyright: © 2011 |Pages: 19
DOI: 10.4018/978-1-61692-834-6.ch028
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Abstract

Carbon dioxide (CO2) is one of the most important gases in the atmosphere, and is necessary for sustaining life on Earth. However, it is also a major greenhouse gas out of the six that contribute to global warming and climate change. During the last decade technologists, economists and sociologists are taking substantial interest in studying the impact of greenhouse phenomenon. Scientists are trying to find solutions to reduce CO2 emissions by changes in structure of energy production and consumption. Every attempt is being made to use new models and methods to estimate measure and monitor greenhouse gases in the future. Independent Component Analysis (ICA) is a method for automatically identifying a set of underlying factors in a given data set. This chapter describes the use of the ICA algorithm in Environmentally Intelligent (EI) applications. EI applications have a wide ranging responsibilities including collection, analysis and reporting of environmental data related to the organization. ICA algorithm opens up the opportunity to improve the quality of data being analyzed by these EI applications. ICA finds application in several fields of interest and it is a tempting alternative to try ICA on multivariate time series such as a CO2 emission from fossil fuel for the period 1950 to 2006. This chapter describes the linear mapping of the observed multivariate time series into a new space of statistically independent components (ICs) that might reveal driving mechanisms for CO2 emissions that may otherwise remain hidden.
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Independent Component Analysis

Consider the classical ICA model Figure 1 with instantaneous mixingx = As + n(1)

Figure 1.

Schematic illustration of the mathematical model used to perform ICA decomposition

978-1-61692-834-6.ch028.f01
where the sources s = [s1,s2,…, sn]T are mutually independent random variables and Anxn is an unknown invertible mixing matrix and noise n = [n1,n2,…, nn]T . The goal is to find only from observations, x, a matrix W such that the outputy = Wx(2) is an estimate of the possible scaled and permutated source vectors.

Key Terms in this Chapter

y: separator output vector

pdf: probability density function

xi: ith sensor output

x: sensor signal vector

q: number of sources

ni: ith noise signal

PCA: Principal Component Analysis

s: source signal vector

ICA: Independent Component Analysis

W: demixing matrix

BSS: Blind Source Separation

A: mixing matrix

ICs: Independent Components

si: ith source signal

n: noise vector

p: number of observation

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