https://github.com/htpusa/ptd-cca

Tensor Canonical Correlation Analysis (TCCA) via penalised tensor decomposition
https://github.com/htpusa/ptd-cca

canonical-correlation-analysis cca scca stcca tcca tensor-canonical-correlation-analysis

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Tensor Canonical Correlation Analysis (TCCA) via penalised tensor decomposition

• Host: GitHub
• URL: https://github.com/htpusa/ptd-cca
• Owner: htpusa
• Created: 2024-02-06T13:45:37.000Z (11 months ago)
• Default Branch: main
• Last Pushed: 2024-04-17T11:12:22.000Z (9 months ago)
• Last Synced: 2024-04-17T12:33:13.659Z (9 months ago)
• Topics: canonical-correlation-analysis, cca, scca, stcca, tcca, tensor-canonical-correlation-analysis
• Language: MATLAB
• Homepage:
• Size: 10.7 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# PTD-CCA: Sparse Tensor Canonical Correlation Analysis (STCCA) via penalised tensor decomposition

PTD-CCA is an unsupervised dimensionality reduction method for 2 or more views/data modalities. The algorithm is a straightforward extension of the penalised matrix decomposition CCA (PMD-CCA) proposed by Witten et al. (2009) to more than 2 views and maximises the "higher-order covariance" between the linear projections `X_m*w_m` where each `X_m` is data matrix and `w_m` a vector of coefficients. It reduces to PMD-CCA if there are just 2 views.

## EXAMPLE

Set up some synthetic data

```MATLAB

a = [ones(20,1); -ones(20,1); zeros(60,1)];

b = [zeros(60,1); -ones(20,1); ones(20,1)];

c = [ones(20,1); zeros(60,1); -ones(20,1)];

d = [-ones(10,1); ones(10,1); zeros(60,1); -ones(10,1); ones(10,1)];

Z = rand(100,4); Z = Z./sum(Z,2);

X1 = normrnd(Z(:,1)*a',0.1);

X2 = normrnd(Z(:,2)*b',0.1);

X3 = normrnd(Z(:,3)*c',0.1);

X4 = normrnd(Z(:,4)*d',0.1);

X = {X1;X2;X3;X4};

```

Run `PTDCCA` with "intermediate" sparsity and compare the model to the ground truth.

```MATLAB

W = PTDCCA(X,0.5);

wtrue = [a,b,c,d];

figure

for m=1:4

    subplot(2,4,m);bar(wtrue(:,m));title(sprintf('True w_%d',m))

    xlabel('variable');ylabel('coefficient')

    subplot(2,4,4+m);bar(W{m});title(sprintf('Inferred w_%d',m))

end

```

Sparsity can also be set for each view separately:

```MATLAB

c = [0.05,0.25,0.75,1];

W = PTDCCA(X,c);

for m=1:4

    subplot(1,4,m);bar(W{m});title(sprintf('c = %.2f',c(m)))

    xlabel('variable');ylabel('coefficient')

end

```

To calculate multiple canonical variable tuples, use the name-value input `D`

```MATLAB

W = PTDCCA(X,0.5,'D',3);

```

If you've ran the examples above, you may have noticed the function takes some time to return. Most of the running time is in fact spent calculating the cross-covariance tensor which is used to initialise the algorithm. This can be avoided by using a random initialisation instead:

```MATLAB

W = PTDCCA(X,0.5,'initType','random');

```

The covariance tensor also takes up a lot of memory, and if the dimensions of the data are high enough, might exceed the largest allowed array size. If this happens, `PTDCCA` defaults to the random initialisation.

## References

Witten, Daniela M., Robert Tibshirani, and Trevor Hastie. "A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis." Biostatistics 10.3 (2009): 515-534.