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.
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.
A statistical method for prediction and modeling of cyber-attack signal is proposed. The proposed method is developed by coupling the traditional ARIMA method with Hilbert-Huang transform (HHT), designed to reduce the dimensionality and to extract meaningful signals for reliable prediction. HHT decomposes cyber-attack signals of interest into several components including short-and long-term patterns, and random fluctuation. Due to Hilbert transform, the method selects significant decomposed signals that will be employed for signal prediction. Subsequently, by using the traditional dynamic models, the proposed method provides a stable prediction of cyber-attack signal. To show the performance of the proposed method, we analyze daily worm count data from
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.Index Terms-Empirical mode decomposition (EMD), intrinsic mode functions (IMFs), mean envelope, noisy signals, outliers, quantile smoothing.
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