Table 1 Data scaling techniques used in this work.
From: Cost function for low-dimensional manifold topology assessment
Name | Scaling factor \(d_j\) | Center \(c_j\) |
|---|---|---|
None | 1 | 0 |
Auto51 | \(s_j\) | \(\bar{X}_j\) |
Pareto52 | \(\sqrt{s_j}\) | \(\bar{X}_j\) |
VAST49 | \(s_j^2 / \bar{X}_j\) | \(\bar{X}_j\) |
Range51 | \(\text {max}(X_j) - \text {min}(X_j)\) | \(\bar{X}_j\) |
\(\langle 0, 1 \rangle\) | \(\text {max}(X_j) - \text {min}(X_j)\) | \(\text {min}(X_j)\) |
\(\langle -1, 1 \rangle\) | \(1/2 (\text {max}(X_j) - \text {min}(X_j))\) | \(1/2 (\text {max}(X_j) + \text {min}(X_j))\) |
Level51 | \(\bar{X}_j\) | \(\bar{X}_j\) |
Max | \(\text {max}(X_j)\) | \(\bar{X}_j\) |
Poisson50 | \(\sqrt{\bar{X}_j}\) | \(\bar{X}_j\) |
S1 | \(s_j^2 k_j^2 / \bar{X}_j\) | \(\bar{X}_j\) |
S2 | \(s_j^2 k_j^2 / \text {max}(X_j)\) | \(\bar{X}_j\) |
S3 | \(s_j^2 k_j^2 / ( \text {max}(X_j) - \text {min}(X_j))\) | \(\bar{X}_j\) |
