Description
Compare centering before scaling with centering after scaling.
Normalization requires an explicit order of operations, center, scale and reference convention. Centering before scaling generally differs from subtracting the same center after scaling. A normalized weight or bounded uncertainty interval inherits supplied assumptions; zero entries, sentinel collisions and reference-category coding need separate interpretation.
Compare centering before scaling with centering after scaling.
When to use this tool
Use Scalar Centering After Scaling Delta when you already have value, center, scale and need to compare centering before scaling with centering after scaling.
How to use the tool and how it works
- Enter value, center, scale. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read centerThenScale, scaleThenCenter, difference. Use the output convention below.
Return (value-center)*scale and value*scale-center; difference=center*(scale-1) is the second result minus the first.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| value | Value | Required. Finite number. |
| center | Center | Required. Finite number. |
| scale | Scale | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| centerThenScale | Center Then Scale | Required. Finite number. |
| scaleThenCenter | Scale Then Center | Required. Finite number. |
| difference | scaleThenCenter-centerThenScale=center*(scale-1), preserving its sign. | Required. Finite number. |
{
"input": {
"value": 5,
"center": 2,
"scale": 3
},
"output": {
"centerThenScale": 9,
"scaleThenCenter": 13,
"difference": 4
}
}Limitations and assumptions
- Scale and center are supplied, with zero and signed scales allowed; no normalization parameters are estimated.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Specify the intended transformation and data basis before estimating or applying parameters. Review missing-value handling and reference coding across the full dataset; one affine term or normalized vector does not establish comparable measurements or a fitted model.
References
Similar or alternative tools
- Scaled Missing Sentinel Collision Check
Check whether a supplied affine normalization collides with a missing sentinel.
- Robust Center Uncertainty Shift
Propagate a supplied center-uncertainty bound through positive-scale normalization.