Machine Learning for Early Parkinson’s Disease Identification within SWEDD Group Using Clinical and DaTSCAN SPECT Imaging Features

. 2022 Apr 2;8(4):97. doi: 10.3390/jimaging8040097

Algorithm 1: PCA steps

1: Ignore the dataset (consists of d-dimensional sample) class labels.

2: Calculate the d-dimensional mean vectors: the mean for every dimension of the whole dataset. The mean vector is computed by the following equation:

m = 1 / n \sum_{k = 1}^{n} x_{k}

(1)

3: Calculate the scatter matrix or the covariance matrix of the dataset. The mean vector is computed by the following equation:

S = \sum_{k = 1}^{n} (x_{k} - m) {(x_{k} - m)}^{T}

(2)

4: Calculate the eigenvectors and corresponding eigenvalues of the covariance matrix.

5: Sort the eigenvalues by decreasing eigenvalues and pick k eigenvectors with the largest eigenvalues to form a d × k dimensional matrix W of eigenvectors.

6: Use the W eigenvector matrix to transform the sample (original matrix) into the new subspace via the equation:

y = W^{T} x

(3)

where x is a d × 1-dimensional vector representing one sample and y is the transformed k × 1-dimensional sample in the new subspace.