Random Rare Item Support Boundary Corpus Generator

Description

Construct synthetic baskets one occurrence below, at and above the discrete support cutoff, with sampled background items and delegated Apriori boundary outcomes.

Synthetic statistical data separates a specified generating model from the values observed in a finite draw. A model parameter, a sample summary, and the result of a fitted analysis answer different questions; retaining them separately makes numerical and statistical checks easier to interpret.

Construct synthetic baskets one occurrence below, at and above the discrete support cutoff, with sampled background items and delegated Apriori boundary outcomes.

When to use this tool

Use this generator to create reproducible rare item support boundary corpus cases from the supplied model or bank. Inspect the returned evidence before using cases in a test or exercise.

How to use the tool and how it works

Supply target, backgroundItems, transactionCount, minimumSupport in the field shapes below. Set seed when you need an explicit replay.
Run the tool and correct any input error. For generated controls, distinguish a successful fixture containing an invalid case from failure to generate the fixture.
Read minimumCount, cases. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.

Set the support boundary count to ceil(minimumSupport times transactionCount). Construct separate below, at, and above datasets with exactly boundary minus one, boundary, and boundary plus one target occurrences; delegate frequent singleton mining to retain actual frequency decisions.^[1]

Delegated operations used for this result: apriori. Their calculation or parsing conventions apply to the corresponding result fields.^[2]

Input field	Meaning and units	Accepted input
target	Target	Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 64.
backgroundItems	Background Items	Required. Array of Text; minimum UTF-16 length 1; maximum UTF-16 length 64.; minimum items 1; maximum items 5.
transactionCount	Transaction Count	Required. Safe integer; minimum 2; maximum 128.
minimumSupport	Minimum Support	Required. Finite number; maximum 1; strictly above 0.
seed	Optional numeric seed; takes precedence over context randomness. Without either, use the fixed tool.io default seed.	Optional. Safe integer.

Output field	Interpretation	Returned shape
minimumCount	Minimum Count	Required. Safe integer; minimum 1; maximum 127.
cases	Cases	Required. Array of Object; no unknown keys.; minimum items 3; maximum items 3.
cases[].position	Position	Required. Text; one of "below", "at", "above".
cases[].transactions	Transactions	Required. Array of Array of Text; minimum UTF-16 length 1; maximum UTF-16 length 64.; minimum items 1; maximum items 6.; minimum items 2; maximum items 128.
cases[].targetCount	Target Count	Required. Safe integer; minimum 0; maximum 128.
cases[].support	Support	Required. Finite number.
cases[].frequent	Frequent	Required. Boolean.
cases[].coreSupport	Core Support	Required. Finite number. or Null.
randomness	Replay metadata: source is seed or context; seed is the normalized 32-bit seed or null for a context source.	Required. Object; no unknown keys.
randomness.seed	Optional numeric replay seed; normalization and precedence are explained below.	Required. Safe integer. or Null.
randomness.source	Source	Required. Text; one of "context", "seed".

An explicit safe-integer seed takes precedence over injected context randomness and is normalized to an unsigned 32-bit integer. With no seed and no context source, replay uses the fixed tool.io default seed. A context source must return finite values from zero inclusive to one exclusive; its advancing state must be retained separately. randomness records the source and normalized seed, or null for context. These generators are not cryptographic random sources.

json

{
  "input": {
    "target": "rare",
    "backgroundItems": [
      "tea"
    ],
    "transactionCount": 4,
    "minimumSupport": 0.5,
    "seed": 42
  },
  "output": {
    "minimumCount": 2,
    "cases": [
      {
        "position": "below",
        "transactions": [
          [
            "rare",
            "tea"
          ],
          [
            "tea"
          ],
          [
            "tea"
          ],
          [
            "tea"
          ]
        ],
        "targetCount": 1,
        "support": 0.25,
        "frequent": false,
        "coreSupport": null
      },
      {
        "position": "at",
        "transactions": [
          [
            "rare",
            "tea"
          ],
          [
            "rare",
            "tea"
          ],
          [
            "tea"
          ],
          [
            "tea"
          ]
        ],
        "targetCount": 2,
        "support": 0.5,
        "frequent": true,
        "coreSupport": 0.5
      },
      {
        "position": "above",
        "transactions": [
          [
            "tea"
          ],
          [
            "rare",
            "tea"
          ],
          [
            "rare",
            "tea"
          ],
          [
            "rare",
            "tea"
          ]
        ],
        "targetCount": 3,
        "support": 0.75,
        "frequent": true,
        "coreSupport": 0.75
      }
    ],
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

Target and background labels must be distinct and the boundary must leave room above. The finite support controls are synthetic, not estimates of real population rarity or comprehensive Apriori coverage.
A replay requires the same complete input and implementation. Randomized construction does not guarantee uniform coverage of every feasible output; finite samples can repeat unless a distinct-selection rule is explicitly stated.
The field tables state structural bounds; cross-field constraints and bounded search or output budgets also apply. Unknown keys are rejected where the object contract disallows them. Input errors are distinct from null fields and deliberate invalid controls in a successful output.

Alternative or Complementary methods

For a supplied example, inspect the returned construction or delegated check directly. To evaluate a consumer, also test cases chosen for its own boundaries; a generated finite corpus does not establish exhaustive coverage.

References

Tool behavior and example: Random Rare Item Support Boundary Corpus Generator — tool.io
Calculation or validation: data-mining/apriori — tool.io

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