Multidimensional empirical mode decomposition: Difference between revisions

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The major disadvantage of this method is that although we could extend this algorithm to any dimensional data we only use it for Two dimension applications. Because the computation time of higher dimensional data would be proportional to the number of IMF's of the succeeding dimensions. Hence, it could exceed the computation capacity for a Geo-Physical data processing system when the number of EMD in the algorithm is large. Hence, we have mentioned below faster and better techniques to tackle this disadvantage.

=== Multi-dimensional ensemble empirical mode decomposition. ===
Source:<ref name=":7" /> ===

A Fast and efficient data analysis is very important for large sequences hence the MDEEMD focuses on two important things

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The advantage of this algorithm is that an optimized division and an optimized selection of PC/EOF pairs for each region would lead to a higher rate of compression and result into significantly lower computation as compared to a Pseudo BEMD extended to higher dimensions.

=== Fast multidimensional ensemble empirical mode decomposition ===
Source:<ref name=":7" /> ===

For a temporal signal of length ''M'', the complexity of cubic spline sifting through its local extrema is about the order of ''M,'' and so is that of the EEMD as it only repeats the spline fitting operation with a number that is not dependent on ''M''. However, as the sifting number (often selected as 10) and the ensemble number (often a few hundred) multiply to the spline sifting operations, hence the EEMD is time-consuming compared with many other time series analysis methods such as Fourier transforms and wavelet transforms. The MEEMD employs EEMD decomposition of the time series at each division grids of the initial temporal signal, the EEMD operation is repeated by the number of total grid points of the ___domain. The idea of the fast MEEMD is very simple. As PCA/EOF-based compression expressed the original data in terms of pairs of PCs and EOFs, through decomposing PCs, instead of time series of each grid, and using the corresponding spatial structure depicted by the corresponding EOFs, the computational burden can be significantly reduced.

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# Its implementation is like the sequential one, which makes it more straightforward.

=== OpenMP implementation<ref name=":8" /> ===

The EEMDs comprising MEEMD are assigned to independent threads for parallel execution, relying on the OpenMP runtime to resolve any load imbalance issues. Stride memory accesses of high-dimensional data are eliminated by transposing these data to lower dimensions, resulting in better utilization of cache lines. The partial results of each EEMD are made thread-private for correct functionality. Memory requirements depend on the number of OpenMP threads and are managed by OpenMP runtime.<ref name=":8" />

=== CUDA implementation<ref name=":8" /> ===

In the GPU CUDA implementation, each EMD, is mapped to a thread. The memory layout, especially of high-dimensional data, is rearranged to meet memory coalescing requirements and fit into the 128-byte cache lines. The data is first loaded along the lowest dimension and then consumed along a higher dimension. This step is performed when the Gaussian noise is added to form the ensemble data. In the new memory layout, the ensemble dimension is added to the lowest dimension to reduce possible branch divergence. The impact of the unavoidable branch divergence from data irregularity, caused by the noise, is minimized via a regularization technique using the on-chip memory. Moreover, the cache memory is utilized to amortize unavoidable uncoalesced memory accesses.<ref name=":8" />

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Based on the algorithm of BEMD, the implementation method of FABEMD is really similar to BEMD, but the FABEMD approach just changes the interpolation step into a direct envelope estimation method and restricts the number of iterations for every BIMF to one. As a result, two order statistics, including MAX and MIN, will be used for approximating the upper and lower envelope. The size of the filter will depend on the maxima and minima maps obtained from the input. The steps of the FABEMD algorithm are listed below.

===FABEMD algorithm===
Source:<ref name=":0" />===

;Step 1 – Determine and detect local maximum and minimum

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Here, we take 2-D PDE-based EMD as an example.

===PDE-based BEMD algorithm===
Source:<ref name=":2" />===

;Step 1 – Extend super diffusion model from 1-D to 2-D

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There are some problems in BEMD and boundary extending implementation in the iterative sifting process, including time-consuming, shape and continuity of the edges, decomposition results comparison and so on. In order to fix these problems, the '''Boundary Processing in Bidimensional Empirical Decomposition (BPBEMD)''' method was created. The main points of the new method algorithm will be described next.

===BPBEMD algorithm<ref name=":3" />===

The few core steps for BPBEMD algorithm are:<ref name=":3" />

;Step 1