Table 3 Distance norms employed to convert dataset to graph representation

Chebyshev

\(d_{i,j} = \max _{p} |s_{i,p} - s_{j,p}|\)

Metric induced by the supremum norm

Euclidean

\(d_{i,j} = \sqrt{\sum _{p=1}^{m}(s_{i,p} - s_{j,p})^2}\)

Length of a line segment between two vectors

Manhattan

\(d_{i,j} = \sum _{p=1}^{m}|s_{i,p} - s_{j,p}|\)

Sum of the lengths of the projections onto axes

Correlation

\(d_{i,j} = 1 - \frac{(s_i-\overline{s_i})\cdot (s_j-\overline{s_j})}{\sqrt{\sum _{p=1}^{m}s_{i,p}^2 \cdot \sum _{p=1}^{m}s_{i,p}^2 }}\)

Correlation distance between two vectors

Cosine

\(d_{i,j} = 1 - \frac{(s_i,s_j)}{\sqrt{\sum _{p=1}^{m}s_{i,p}^2 \cdot \sum _{p=1}^{m}s_{i,p}^2 }}\)

Cosine distance between two vectors