├── README.md
└── mdr_tcca.m


/README.md:
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1 | # Multi-view dimensionality reduction using tensor canonical correlation analysis
2 | 
3 | MATLAB implementation of multi-view dimensionality reduction using Tensor Canonical Correlation Analysis, presented by Luo et al. in https://arxiv.org/pdf/1502.02330.pdf
4 | 


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/mdr_tcca.m:
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 1 | % mdr_tcca - MATLAB implementation of multi-view dimensionality reduction using 
 2 | % Tensor Canonical Correlation Analysis, presented by Luo et al. in 
 3 | % https://arxiv.org/pdf/1502.02330.pdf
 4 | %
 5 | % Syntax:  [reduction] = mdr_tcca(views,d,epsilon)
 6 | %
 7 | % Inputs:
 8 | %    views - Cell array of NxM matrices
 9 | %    d - Final dimensionality
10 | %    epsilon - Regularization trade-off factor, non-negative.
11 | %    maxiters - Maximum number of ALS iterations in CP decomposition
12 | %    verbosity - Fit error verbosity. If zero no info is printed, 
13 | %                otherwise info is printed every n iterations.
14 | %
15 | % Outputs:
16 | %    reduction - Multi-view dimensionality reduction
17 | %    f - Factorization as ktensor
18 | %
19 | % Example: 
20 | %    mvdr_tcca({first_view, second_view})
21 | %
22 | % Requires: Tensor Toolbox for MATLAB by Sandia National Labs.
23 | %           https://gitlab.com/tensors/tensor_toolbox
24 | %
25 | % Author: Robert Ciszek 
26 | % July 2016; Last revision: 24-June-2017
27 | 
28 | function [Z,f] = mdr_tcca(views,varargin)
29 |     %Parse inputs
30 |     params = inputParser;
31 |     params.addRequired('views',@iscell);
32 |     params.addParameter('d',2,@(x) isscalar(x) & x > 0);
33 |     params.addParameter('epsilon',1,@(x) isscalar(x) & x > 0);
34 |     params.addParameter('maxiters', 50,@(x) isscalar(x) & x > 0);
35 |     params.addParameter('verbosity', 1,@(x) isscalar(x));
36 |     
37 |     params.parse(views,varargin{:});
38 | 
39 |     views = params.Results.views;
40 |     d = params.Results.d;
41 |     epsilon = params.Results.epsilon;
42 |     maxiters = params.Results.maxiters;
43 |     verbosity = params.Results.verbosity;
44 |     
45 |     
46 |     %All views are assumed to contain equal number of samples
47 |     n_samples = size(views{1},1);
48 |     n_views = length(views);
49 |     
50 |     %Center each view
51 |     for i=1:n_views
52 |         views{i} = tensor(views{i} - repmat(mean(views{i} ), n_samples,1));
53 |     end
54 |     
55 |     %Calculate variances
56 |     variances = cell(size(views));
57 |     for i=1:n_views
58 |         variances{i} =  (double(views{i})'*double(views{i}))/n_samples;
59 |         variances{i} = variances{i} +  epsilon*ones(size(variances{i}));
60 |     end
61 |     %Calculate covariances
62 |     covariances = [];
63 |     for i=1:n_samples
64 |        outer_product = views{1}(i,:);
65 |        for j=2:length(views)
66 |            outer_product = ttt(outer_product,views{j}(i,:));
67 |        end
68 |        if isempty(covariances)
69 |            covariances = outer_product;
70 |        else
71 |            covariances = covariances+outer_product;
72 |        end
73 |     end   
74 |     covariances = covariances / n_samples;
75 |     
76 |     M = covariances;
77 |     for i=1:length(variances)
78 |        M = ttm(M,pinv(variances{i})^1/2,i);
79 |     end
80 |     
81 |     f = cp_als(M,d,'maxiters',maxiters,'printitn',verbosity);
82 |     Z = zeros(n_samples,d*2);
83 |     for i=1:n_views
84 |         Z(:,(1+(i-1)*d):(i*d)) = double(views{i})*(pinv(variances{i})^1/2)*f.U{i};
85 |     end
86 |     
87 | end
88 | 


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