Diagnosis of Alzheimer’s Disease Using Dual-Tree Complex Wavelet Transform, PCA, and Feed-Forward Neural Network

Algorithm 1: PCA algorithm.

Let X be an input text file ( : matrix of dimensions )

Accomplish the following steps:

Step 1. Estimate the empirical mean: .

Step 2. Compute the deviations from the mean and save the data in the matrix : , here, h is a row vector of all 1’s: for .

Step 3. Obtain the covariance matrix .

Step 4. Get the eigenvectors and eigenvalues of the covariance matrix -the eigenvectors matrix; D -the diagonal matrix of eigenvalues of for is the mth eigenvalues of the covariance matrix C.

Step 5. Rearrange the eigenvectors and eigenvalues: .

Step 6. Selecting components and developing a feature vector: save the first L columns or V as the M×L matrix , for , where .

Step 7. Obtaining the fresh data set: The eigenvectors with the leading eigenvalues are forecasted into space, this projection appears in a vector depicted by fewer dimension () accommodating the essential coefficients.

Algorithm 1: PCA algorithm.

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