Random Clustered Point Dataset Generator

Description

Generate bounded-count caller-parameterized Gaussian point groups with retained source labels, shuffle them and delegate scale-normalized deterministic k-means; fitted labels are separate from generating groups and exact fixed-point verification is reported without an optimality claim.

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.

When to use this tool

Use this generator to create reproducible clustered point dataset 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 clusters, maximumIterations 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 points, sourceLabels, clusteringInputScale, clustering. Use the conventions below. Keep answer-bearing fields separate when presenting an exercise.

Draw and shuffle labeled Gaussian groups, scale coordinates for the existing k-means solver, and return centroids rescaled to source units. Independently check whether each nonempty cluster center equals the mean of its final assigned normalized points.^[1]

Input field	Meaning and units	Accepted input
clusters	Clusters	Required. Array of Object; no unknown keys.; minimum items 1; maximum items 8.
clusters[].center	Center	Required. Array of Finite number.; minimum items 1; maximum items 8.
clusters[].standardDeviation	Standard Deviation	Required. Finite number; minimum 0.
clusters[].pointCount	Point Count	Required. Safe integer; minimum 1; maximum 128.
maximumIterations	Maximum Iterations	Required. Safe integer; minimum 1; maximum 1000.
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
points	Points	Required. Array of Array of Finite number.; minimum items 1; maximum items 8.; minimum items 1; maximum items 128.
sourceLabels	Source Labels	Required. Array of Safe integer; minimum 0; maximum 7.; minimum items 1; maximum items 128.
clusteringInputScale	Clustering Input Scale	Required. Finite number; strictly above 0.
clustering	Clustering	Required. Object; no unknown keys.
clustering.centroids	Centroids	Required. Array of Array of Finite number.; minimum items 1; maximum items 8.; minimum items 1; maximum items 8.
clustering.labels	Labels	Required. Array of Safe integer; minimum 0; maximum 7.; minimum items 1; maximum items 128.
clustering.iterations	Iterations	Required. Safe integer; minimum 1; maximum 1000.
clustering.fixedPointVerified	Fixed Point Verified	Required. Boolean.
randomness	Replay source and normalized 32-bit seed, or null seed for an advancing context source.	Required. Object; no unknown keys.
randomness.seed	Optional safe-integer 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": {
    "clusters": [
      {
        "center": [
          0,
          0
        ],
        "standardDeviation": 0.3,
        "pointCount": 3
      },
      {
        "center": [
          8,
          8
        ],
        "standardDeviation": 0.3,
        "pointCount": 3
      }
    ],
    "maximumIterations": 50,
    "seed": 42
  },
  "output": {
    "points": [
      [
        7.919444682011827,
        7.459461974693873
      ],
      [
        8.169586058321237,
        8.301019804622003
      ],
      [
        -0.15883013811492458,
        0.36857720191893123
      ],
      [
        7.800200255522881,
        7.016276859999375
      ],
      [
        -0.2868486688152447,
        -0.08190783146478313
      ],
      [
        -0.552488155435079,
        -0.3422646212862072
      ]
    ],
    "sourceLabels": [
      1,
      1,
      0,
      1,
      0,
      0
    ],
    "clusteringInputScale": 8.301019804622003,
    "clustering": {
      "centroids": [
        [
          7.963076998618648,
          7.592252879771751
        ],
        [
          -0.33272232078841607,
          -0.01853175027735304
        ]
      ],
      "labels": [
        0,
        0,
        1,
        0,
        1,
        1
      ],
      "iterations": 1,
      "fixedPointVerified": true
    },
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

Source labels and inferred labels can differ. fixedPointVerified describes the returned assignment/centroid relationship, not a global optimum or recovery of generating groups. Empty clusters and bounded iteration behavior follow the linked solver.
A replay requires the same complete input and implementation. The stated sampling convention applies within its eligible space. A finite draw does not exhaust all possible outputs; repeats remain possible unless a distinct-selection rule is explicit.
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 Clustered Point Dataset Generator — tool.io

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