Donghoh Kim

Extending the scope of empirical mode decomposition by smoothing

This article considers extending the scope of the empirical mode decomposition (EMD) method. The extension is aimed at noisy data and irregularly spaced data, which is necessary for widespread applicability of EMD. The proposed algorithm, called statistical EMD (SEMD), uses a smoothing technique instead of an interpolation when constructing upper and lower envelopes. Using SEMD, we discuss how to identify non-informative fluctuations such as noise, outliers, and ultra-high frequency components from the signal, and to decompose irregularly spaced data into several components without distortions.

Bidimensional Statistical Empirical Mode Decomposition

This letter proposes a new algorithm, termed bidimensional statistical empirical mode decomposition (BSEMD) that adopts a smoothing procedure instead of an interpolation when constructing 2-D upper and lower envelopes. For this purpose, we investigate the sifting process effect of conventional bidimensional empirical mode decomposition (BEMD) on the decomposition results, and propose a modified BEMD via the smoothing sifting process coupling with a new identification method of 2-D local extrema. Furthermore, theoretical rationale for smoothing sifting is investigated.

Hierarchical-likelihood-based wavelet method for denoising signals with missing data

This letter proposes a wavelet denoising method in the presence of missing data. This approach is based on a coupling of wavelet shrinkage and hierarchical (or h)-likelihood method. The h-likelihood provides an effective imputation methodology of missing data to give wavelet estimators for signals and motivates a fast and simple algorithm. The method can be easily extended to other settings, such as image denoising. Simulation studies demonstrate empirical properties of the proposed method.

Comparing patterns of component loadings: principal component analysis (PCA) versus independent component analysis (ICA) in analyzing multivariate non-normal data.

Principal component analysis identifies uncorrelated components from correlated variables, and a few of these uncorrelated components usually account for most of the information in the input variables. Researchers interpret each component as a separate entity representing a latent trait or profile in a population. However, the components are guaranteed to be independent and uncorrelated only when the multivariate normality of the variables is assumed. If the normality assumption does not hold, components are guaranteed to be uncorrelated, but not independent. If the independence assumption is violated, each component cannot be uniquely interpreted because of contamination by other components. Therefore, in the present study, we introduced independent component analysis, whose components are uncorrelated and independent even when the multivariate normality assumption is violated, and each component carries unique information.

Quantile-Based Empirical Mode Decomposition: An Efficient Way to Decompose Noisy Signals

The main goal of this paper is to propose a new approach of empirical mode decomposition (EMD) that analyzes noisy signals efficiently. The EMD has been widely used to decompose nonlinear and nonstationary signals into some components according to intrinsic frequency called intrinsic mode functions. However, the conventional EMD may not be efficient in decomposing signals that are contaminated by noninformative noises or outliers. This paper presents a new EMD procedure that analyzes noisy signals effectively and is robust to outliers with holding the merits of the conventional EMD. The key ingredient of the proposed method is to apply a quantile smoothing method to a noisy signal itself instead of interpolating local extrema of the signal when constructing its mean envelope. Through simulation studies and texture image analysis, it is demonstrated that the proposed method produces substantially effective results.

Empirical mode decomposition with missing values

Abstract This paper considers an improvement of empirical mode decomposition (EMD) in the presence of missing data. EMD has been widely used to decompose nonlinear and nonstationary signals into some components according to intrinsic frequency called intrinsic mode functions. However, the conventional EMD may not be efficient when missing values are present. This paper proposes a modified EMD procedure based on a novel combination of empirical mode decomposition and self-consistency concept. The self-consistency provides an effective imputation method of missing data, and hence, the proposed EMD procedure produces stable decomposition results. Simulation studies and the image analysis demonstrate that the proposed method produces substantially effective results.

A Multi-Resolution Approach to Non-Stationary Financial Time Series Using the Hilbert-Huang Transform

An economic signal in the real world usually reflects complex phenomena. One may have difficulty both extracting and interpreting information embedded in such a signal. A natural way to reduce complexity is to decompose the original signal into several simple components, and then analyze each component. Spectral analysis (Priestley, 1981) provides a tool to analyze such signals under the assumption that the time series is stationary. However when the signal is subject to non-stationary and nonlinear characteristics such as amplitude and frequency modulation along time scale, spectral analysis is not suitable. Huang et al. (1998b, 1999) proposed a data-adaptive decomposition method called empirical mode decomposition and then applied Hilbert spectral analysis to decomposed signals called intrinsic mode function. Huang et al. (1998b, 1999) named this two step procedure the Hilbert-Huang transform(HHT). Because of its robustness in the presence of nonlinearity and non-stationarity, HHT has been used in various fields. In this paper, we discuss the applications of the HHT and demonstrate its promising potential for non-stationary financial time series data provided through a Korean stock price index.

Classification of Variable Stars Using Thick-Pen Transform Method

A suitable classification of variable stars is an important task for understanding galaxy structure and evaluating stellar evolution. Most traditional approaches for classification have used various features of variable stars such as period, amplitude, color index, and Fourier coefficients. Recently, by focusing only on the light curve shape, Deb and Singh proposed a classification method based on multivariate principal component analysis (PCA). They applied the PCA method to light curves and compared its results with those obtained by Fourier coefficients. In this article, we propose a new procedure based on the thick-pen transform for obtaining accurate information on the light curve shape as well as for improving the accuracy of classification. The proposed method is applied to the data sets of variable stars from the Stellar Astrophysics and Research on Exoplanets (STARE) project and a small number of stars from Massive Compact Halo Objects (MACHO).

Empirical Mode Decomposition using the Second Derivative

There are various types of real world signals. For example, an electrocardiogram(ECG) represents myocardium activities (contraction and relaxation) according to the beating of the heart. ECG can be expressed as the fluctuation of ampere ratings over time. A signal is a composite of various types of signals. An orchestra (which boasts a beautiful melody) consists of a variety of instruments with a unique frequency; subsequently, each sound is combined to form a perfect harmony. Various research on how to to decompose mixed stationary signals have been conducted. In the case of non-stationary signals, there is a limitation to use methodologies for stationary signals. Huang et al. (1998) proposed empirical mode decomposition(EMD) to deal with non-stationarity. EMD provides a data-driven approach to decompose a signal into intrinsic mode functions according to local oscillation through the identification of local extrema. However, due to the repeating process in the construction of envelopes, EMD algorithm is not efficient and not robust to a noise, and its computational complexity tends to increase as the size of a signal grows. In this research, we propose a new method to extract a local oscillation embedded in a signal by utilizing the second derivative.

A REINTERPRETATION OF EMD BY CUBIC SPLINE INTERPOLATION

Empirical mode decomposition (EMD) is a data-driven technique that decomposes a signal into several zero-mean oscillatory waveforms according to the levels of oscillation. Most of the studies on EMD have focused on its use as an empirical tool. Recently, Rilling and Flandrin, [2008] studied theoretical aspects of EMD with extensive simulations, which allow a better understanding of the method. However, their theoretical results have been obtained by considering constraints on the signal such as equally spaced extrema and constant frequency. The present study investigates the theoretical properties of EMD using cubic spline interpolation under more general conditions on the signal. This study also theoretically supports modified EMD procedures in Kopsinis and Mclaughlin, [2008] and developed for improving the conventional EMD. Furthermore, all analyses are preformed in the time domain where EMD actually operates; therefore, the principle of EMD can be visually and directly captured, which is useful in interpreting EMD as a detection procedure of hidden components.