1,926 research outputs found
Weighted Majorization Algorithms for Weighted Least Squares Decomposition Models
For many least-squares decomposition models efficient algorithms are well known. A more difficult problem arises in decomposition models where each residual is weighted by a nonnegative value. A special case is principal components analysis with missing data. Kiers (1997) discusses an algorithm for minimizing weighteddecomposition models by iterative majorization. In this paper, we for computing a solution. We will show that the algorithm by Kiers is a special case of our algorithm. Here, we will apply weighted majorization to weighted principal components analysis, robust Procrustes analysis, and logistic bi-additive models of which the two parameter logistic model in item response theory is a specialcase. Simulation studies show that weighted majorization is generally faster than the method by Kiers by a factor one to four and obtains the same or better quality solutions. For logistic bi-additive models, we propose a new iterative majorization algorithm called logistic majorization.iterative majorization;IRT;logistic bi-additive model;robust Procrustes analysis;weighted principal component analysis;two parameter logistic model
Data-Adaptive Wavelets and Multi-Scale Singular Spectrum Analysis
Using multi-scale ideas from wavelet analysis, we extend singular-spectrum
analysis (SSA) to the study of nonstationary time series of length whose
intermittency can give rise to the divergence of their variance. SSA relies on
the construction of the lag-covariance matrix C on M lagged copies of the time
series over a fixed window width W to detect the regular part of the
variability in that window in terms of the minimal number of oscillatory
components; here W = M Dt, with Dt the time step. The proposed multi-scale SSA
is a local SSA analysis within a moving window of width M <= W <= N.
Multi-scale SSA varies W, while keeping a fixed W/M ratio, and uses the
eigenvectors of the corresponding lag-covariance matrix C_M as a data-adaptive
wavelets; successive eigenvectors of C_M correspond approximately to successive
derivatives of the first mother wavelet in standard wavelet analysis.
Multi-scale SSA thus solves objectively the delicate problem of optimizing the
analyzing wavelet in the time-frequency domain, by a suitable localization of
the signal's covariance matrix. We present several examples of application to
synthetic signals with fractal or power-law behavior which mimic selected
features of certain climatic and geophysical time series. A real application is
to the Southern Oscillation index (SOI) monthly values for 1933-1996. Our
methodology highlights an abrupt periodicity shift in the SOI near 1960. This
abrupt shift between 4 and 3 years supports the Devil's staircase scenario for
the El Nino/Southern Oscillation phenomenon.Comment: 24 pages, 19 figure
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