Journal
ADVANCES IN DATA SCIENCE AND ADAPTIVE ANALYSIS
Volume 3, Issue 1-2, Pages 95-113Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S1793536911000660
Keywords
Physical analysis of data; global domain analysis; adaptivity; locality; noise-assisted data analysis; empirical mode decomposition; ensemble empirical mode decomposition
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Funding
- NSF of USA [ATM-0653136, ATM-0917743]
- Federal Highway Administration of USA [DTFH61-08-00028]
- NSC of Republic of China [NSC95-2119-M-008-031-MY3, NSC97-2627-B-008-007]
- NCU [NCU 965941]
- National Basic Research Program of China [2007CB816002]
- National Science Foundation of China [40776018]
- National Key Technology RandD Program [2006BAB18B02]
- Chinese Polar Science Strategy Foundation [20070208]
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In this paper, we present some general considerations about data analysis from the perspective of a physical scientist and advocate the physical, instead of mathematical, analysis of data. These considerations have been accompanying our development of novel adaptive, local analysis methods, especially the empirical mode decomposition and its major variation, the ensemble empirical mode decomposition, and its preliminary mathematical explanations. A particular emphasis will be on the advantages and disadvantages of mathematical and physical constraints associated with various analysis methods. We argue that, using data analysis in a given temporal domain of observation as an example, the mathematical constraints imposed on data may lead to difficulties in understanding the physics behind the data. With such difficulties in mind, we promote adaptive, local analysis method, which satisfies fundamental physical principle of consequent evolution of a system being not able to change the past evolution of the system. We also argue, using the ensemble empirical mode decomposition as an example, that noise can be helpful to extract physically meaningful signals hidden in noisy data.
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