Confusion Error Flow Imbalance

Description

Compare incoming versus outgoing off-diagonal error weight for each label, retaining signed class error-flow imbalance.

A confusion table uses actual labels as rows and predicted labels as columns. Cells can contain occurrence counts or supplied nonnegative weights; the axis label order must stay with the matrix. Row, column and joint normalization have different denominators, and a zero denominator needs an explicit undefined result.

Compare incoming versus outgoing off-diagonal error weight for each label, retaining signed class error-flow imbalance.

When to use this tool

Use this tool to compare incoming versus outgoing off-diagonal error weight for each label, retaining signed class error-flow imbalance.

How to use the tool and how it works

Enter matrix, labels using the input definitions below.
Run the operation. Resolve malformed-input errors before interpreting the result.
Read result.classes. Interpret signs, units, ordering and null values using the rules below.

For each label, outgoing is its off-diagonal row sum and incoming its off-diagonal column sum. Return imbalance = incoming−outgoing with both component totals.^[1]

Input field	Meaning and units	Accepted input
matrix	Square nonnegative finite table: matrix[actualIndex][predictedIndex], both axes in labels order.	Dense list of at most 128 rows of at most 128 finite numbers; the operation’s shape constraints also apply.
labels	Distinct label strings defining actual row and predicted column order; score tools require at least one label.	Dense list of at most 128 strings, each at most 8,192 UTF-16 code units.

Output field	Interpretation
result	Object containing the fields below.
result.classes	Input-label-order {label,incoming,outgoing,imbalance} records, where imbalance is incoming minus outgoing.

json

{
  "input": {
    "matrix": [
      [
        2,
        1
      ],
      [
        0,
        1
      ]
    ],
    "labels": [
      "a",
      "b"
    ]
  },
  "output": {
    "result": {
      "classes": [
        {
          "label": "a",
          "incoming": 0,
          "outgoing": 1,
          "imbalance": -1
        },
        {
          "label": "b",
          "incoming": 1,
          "outgoing": 0,
          "imbalance": 1
        }
      ]
    }
  }
}

Limitations and assumptions

Signed error flow uses supplied support units and does not quantify error severity or causal bias.
Label strings are compared exactly. Confusion values may be nonnegative fractional weights; a count interpretation requires count data. Probability-like score rows use [0,1] entries with sum tolerance 10⁻⁸, without establishing calibration.
Every declared top-level input is required and unknown fields are rejected. Ordinary strings are limited to 8,192 UTF-16 code units and lists to 128 entries, with tighter operation-specific bounds where stated. JSON text has bounded nesting and node counts.
Numeric outputs must be finite and within the absolute safe-integer magnitude; exact larger integers use decimal text. Source positions are zero-based UTF-16 offsets and span ends are exclusive unless a different convention is explicitly stated.

Alternative or Complementary methods

Check label coverage and axis order before comparing tables. Use a separate evaluation design for uncertainty, calibration, operating thresholds and the consequences of real-world decisions.

References

Tool behavior and example: Confusion Error Flow Imbalance — tool.io

Similar or alternative tools

Confusion Actual Support Table
Report actual row support totals without calculating per-class rates.
Confusion Column Rate Table
Normalize each predicted column independently with null for zero-support columns; no calibrated probability claim.