An introduction to an adaptive data analysis method

The existing methods of data analysis, either the probability theory or the spectral analysis, are all developed by mathematicians or based on their rigorous mathematical rules. For analyzing data from the real physical world, we have to face the reality of nonstationarity and nonlinearity in the processes. The traditional analysis methods are based on rigorous approach, but cannot fully accommodate these conditions. A new adaptive data analysis was introduced by Huang et al (1998), which was designated by NASA as the Hilbert-Huang Transform (HHT). It consists of Empirical Mode Decomposition (EMD) and the Hilbert Spectral Analysis (HSA) methods; both were introduced recently by Huang et al. (1996, 1998, 1999 and 2003). The method is adaptive, and specifically designed for analyzing data from nonlinear and nonstationary processes. Since its introduction over ten years ago, the HHT has been applied to a wide range of applications, covering (among many others) biology, geophysics, ocean research, engineering, radar and medicine (see, for example, Huang and Attok-Okine, 2005; Huang and Shen, 2005; Huang and Wu, 2008). Yet, up to this time, a rigorous mathematical foundation is still lacking. Under this condition, progresses are still empirically based. An introduction and some of the recent advances on Ensemble Empirical Mode Decomposition (Wu and Huang, 2009), Instantaneous frequency and trend computations, Time-dependent Intrinsic Correlation (Chen, 2010) and its extension to multi-dimensional data (Wu et al. 2009) are summarized and briefly discussed. These advances have made the HHT method much more robust and mature.