Processing streaming data as they arrive is often necessary for high dimensional data analysis. In this paper, we analyze the convergence of a subspace online PCA iteration, as a followup of the recent work of Li, Wang, Liu, and Zhang [Math. Program., Ser. B, DOI 10.1007/s10107-017-1182-z] who considered the case for the most significant principal component only, i.e., a single vector. Under the sub-Gaussian assumption, we obtain a finite-sample error bound that closely matches the minimax information lower bound.
We propose to combine cepstrum and nonlinear time–frequency (TF) analysis
to study multiple component oscillatory signals with time-varying frequency and
amplitude and with time-varying non-sinusoidal oscillatory pattern. The concept of
cepstrum is applied to eliminate the wave-shape function influence on the TF analysis,
and we propose a new algorithm, named de-shape synchrosqueezing transform (deshape
SST). The mathematical model, adaptive non-harmonic model, is introduced
and the de-shape SST algorithm is theoretically analyzed. In addition to simulated
signals, several different physiological, musical and biological signals are analyzed to
illustrate the proposed algorithm.