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paths

Scattering network paths

    Description

    spaths = paths(sf) returns the scattering paths for the scattering network, sf. spaths is a NO-by-1 cell array of MATLAB® tables, where NO is the number of orders in the network.

    example

    [spaths,npaths] = paths(sf) returns the number of wavelet scattering paths by order. npaths is a NO-by-1 vector, where NO is the number of orders in the scattering network. The ith element of npaths contains the number of scattering paths in the (i-1)th order.

    Examples

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    Create two wavelet scattering networks, both for a signal of length 500. In the second network, set the OptimizePath value to true.

    sf = waveletScattering('SignalLength',500);
    sfOpt = waveletScattering('SignalLength',500,'OptimizePath',true);

    Obtain the path information of both networks. Determine the total number of scattering paths in both networks.

    [spaths,npaths] = paths(sf);
    [spathsOpt,npathsOpt] = paths(sfOpt);
    str = sprintf('Paths in default network: %d\nPaths in path-optimized network: %d\n',...
        sum(npaths),sum(npathsOpt));
    fprintf(str)
    Paths in default network: 65
    Paths in path-optimized network: 52
    

    Both networks have two filter banks. Visualize the scattering paths that include the wavelets in the second filter bank. Create a directed graph. For every wavelet filter that is on at least one path, label the corresponding node as waveletNumber.filterbank. For each path, connect the corresponding nodes. Use the helper function helperPlotScatteringGraph to construct the graphs. Plot the graphs of both networks.

    scatGraph = helperPlotScatteringGraph(spaths);
    plot(scatGraph)
    title({'Scattering Paths',['OptimizePath: ',num2str(sf.OptimizePath)]})

    Figure contains an axes. The axes with title Scattering Paths OptimizePath: 0 contains an object of type graphplot.

    figure
    scatGraphOpt = helperPlotScatteringGraph(spathsOpt);
    plot(scatGraphOpt)
    title({'Scattering Paths',['OptimizePath: ',num2str(sfOpt.OptimizePath)]})

    Figure contains an axes. The axes with title Scattering Paths OptimizePath: 1 contains an object of type graphplot.

    Supporting Functions

    plotScatteringGraph

    function dirGraph = helperPlotScatteringGraph(networkPaths)
    % This function is intended for use only in this example. It may change or
    % be removed in a future release.
    
    path = networkPaths{3}.path;
    % set to 0 if want to show the multiple paths between 0 and each
    % first level node
    mkunique = 1; 
    
    if mkunique == 1
        f1 = path(:,1:2);
        c = unique(f1,'rows');
    else
        c = path(:,1:2);
    end
    
    p1 = string(c(:,1));
    p2 = string(c(:,2)+.1);
    p3 = string(path(:,2)+.1);
    p4 = string(path(:,3)+.2);
    dirGraph = digraph([p1;p3],[p2;p4]);
    
    end

    Input Arguments

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    Wavelet time scattering network, specified as a waveletScattering object.

    Output Arguments

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    Scattering paths, returned as a NO-by-1 cell array of MATLAB tables, where NO is the number of orders of the scattering network.

    Each MATLAB table in spaths contains three variables:

    • path — Scattering network paths. In the kth element of spaths, path is a N-by-k matrix where each row contains a path from the input data through the (k-1)th wavelet filter bank. For example, when k equals 1, N is equal to 1 and the only path is 0 denoting the input data. When k equals 2, N is equal to the number of wavelet filters in the first filter bank and path is a N-by-2 matrix describing the path from the input data, 0, through the wavelet filters in the first filter bank. The second column of path contains the wavelet filters in the first filter bank ordered by decreasing center frequency.

    • log2ds — The incremental base-2 log downsampling factor for the scalogram coefficients corresponding to the cumulative path in the same row.

    • log2res — The base-2 log resolution of the scalogram coefficients corresponding to the cumulative path in the same row.

    Number of wavelet scattering paths in the network by order, returned as a vector. npaths is a NO-by-1 vector where NO is the number of orders in the network. The ith element of npaths contains the number of scattering paths in the (i-1)th order. The sum of the elements of npaths is the total number of scattering paths.

    Extended Capabilities

    C/C++ Code Generation
    Generate C and C++ code using MATLAB® Coder™.

    Introduced in R2021a