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 2: LDA steps

1: Compute the d-dimensional mean vectors of the dataset classes:

m_{i} = 1 / n_{i} \sum_{x \in D_{i}}^{n} x_{k}

(4)

2: Compute the scatter matricesbetween-class and within-class scatter matrix.

The within-class scatter matrix

S_{W}

is computed by the following equation:

S_{w} = \sum_{i = 1}^{c} S_{i}

(5)

w h e r e S_{i} = \sum_{x \in D_{i}}^{n} (x - m_{i}) {(x - m_{i})}^{T}

(6)

The between-class scatter matrix

S_{B}

is computed by the following equation:

S_{B} = \sum_{i = 1}^{c} N_{i} (m_{i} - m) {(m_{i} - m)}^{T}

(7)

where m is the overall mean, and

m_{i}

and

N_{i}

are the sample mean and the size of the respective classes.

3: Compute the eigenvectors and associated eigenvalues for the scatter matrices.

4: Sort the eigenvectors by decreasing eigenvalues and select k eigenvectors with the highest eigenvalues to form a d x k dimensional matrix W.

5: Use the W eigenvector matrix to transform the original matrix onto the new subspace via the equation:

y = X W

(8)

where X is an n × d-dimensional matrix representing the n samples, and Y is the transformed n × k-dimensional sample in the new subspace.