The Research On The Clustering Analysis Of Super-long Discrete Signals And Its Application

The paper discusses the method for clustering analysis of super-long discrete signals,because the traditional methods iscomputationally intensive and inefficient. Then thepaper applys the new method to the sea level database of tide stations all over theworld.Fourier transform is one of the most common and basic analysis method in the signalanalysis methods. It can transform signal from time domain to frequency domain andshow the frequency characteristic of the signal obviously. But only if the system isstable,Fourier transform can get more reliable results.In practice, most of the signals are non-stationary or nonlinear. Based on the empiricalmode decomposition, The HHT transforms the signal into series of intrinsic modefunctions, then use the Hilbert transforms IMF into Hilbert spectrum.Therefore, for long stable discrete signals, the paper uses Fourier transform to extractthe frequency components. For long non-stationary discrete signals, the paper usesEMD to decompose signals into IMFs and residue (unstable generally), then extractthe frequency components of IMFs which are stable. Moreover, we can use a varietyof methods to achieve clustering of the residue due to its monotonicity.In order toachieve a more accurate result of EMD, the paper improves the great impact on EMDby small pulses efficiently on the basic of Four-Midpoint Estimation Method whichcan completely remove boundary effect of EMD, gives a steady decompositionmethod of IMFs.Through the establishment of the mapping from long discrete signal space U to lowdimensional space V, the paper defines a generalized distance in long discrete signalspace U, moreover, the space V is characterized by main spectrum and frequency.Based on this, a new clustering method is established for long discrete signal spaceU. Compared with traditional methods, the computational cost is significantlyreduced. The paper also proposes some coping tactics for specific questions byadjusting parameters of the generalized distance flexibly. By applying the newmethod to the sea level database of tide stations all over the world, the paper depictsthe distribution of tidal stencils on the map.