Description
Return original=component/total, smoothed=component/(total+epsilon), and difference=smoothed-original.
Normalization depends on the supplied center, scale, norm, range, reference distribution, or denominator. A zero spread and a missing denominator need an explicit policy, and clipping differs from fitting a scaler. Evaluating one scalar or derivative term does not estimate every parameter or establish a distributional improvement.
Return original=component/total, smoothed=component/(total+epsilon), and difference=smoothed-original.
When to use this tool
Use Denominator Smoothing One Component Effect when you already have the required normalization parameters and need this local scalar, range, policy, or derivative term.
How to use the tool and how it works
- Enter component, total, epsilon. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read original, smoothed, difference. Use the output convention below.
Require 0<=component<=total, total>0, and epsilon>=0. Return original=component/total, smoothed=component/(total+epsilon), and difference=smoothed-original.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| component | Component | Required. Finite number. |
| total | Total | Required. Finite number; strictly above 0. |
| epsilon | Nonnegative additive denominator term in total units. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| original | Supplied original-coordinate value or inverse result under the stated convention. | Required. Finite number. |
| smoothed | Smoothed | Required. Finite number. |
| difference | Difference | Required. Finite number. |
{
"input": {
"component": 2,
"total": 4,
"epsilon": 4
},
"output": {
"original": 0.5,
"smoothed": 0.25,
"difference": -0.25
}
}Limitations and assumptions
- Epsilon uses the total's unit and is added only to the denominator. This shrinks the component share rather than applying symmetric pseudocount smoothing; a set of such shares need not sum to one.
- 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
Fit or verify the intended scaler parameters and statistical model separately. Check units, zero policies, missingness, clipping, inverse conventions, and whether supplied norms or denominators belong to the same data.
References
Similar or alternative tools
- Unit Sum Residual
Measure the signed difference from unit sum without changing or constraining supplied signed weights.
- Rowwise Normalization Selected Cell
Return denominator=sum(row) and value=row[index]/denominator.