Random Cluster Shape Comparison Benchmark Generator

Description

Generate caller-parameterized compact, elongated Gaussian and radially perturbed arc groups, then compare deterministic k-means and flat-kernel mean shift on the same uniformly normalized points; retain source labels separately from fitted labels, finite-budget failures and model parameters without claiming universal clustering quality.

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 cluster shape comparison benchmark 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 shapes, settings, 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, distanceScale, runs. Use the conventions below. Keep answer-bearing fields separate when presenting an exercise.

Generate rotated compact, elongated, or arc-shaped two-dimensional groups with construction labels. Normalize coordinates and run k-means and mean shift for each supplied center-count and normalized-bandwidth setting.^[1]

Input field	Meaning and units	Accepted input
shapes	Shapes	Required. Array of Object; no unknown keys. or Object; no unknown keys. or Object; no unknown keys.; minimum items 1; maximum items 8.
settings	Settings	Required. Array of Object; no unknown keys.; minimum items 1; maximum items 8.
settings[].centerCount	Center Count	Required. Safe integer; minimum 1; maximum 8.
settings[].normalizedBandwidth	Normalized Bandwidth	Required. Finite number; strictly above 0.
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 -1; maximum 7.; minimum items 1; maximum items 128.
distanceScale	Distance Scale	Required. Finite number; strictly above 0.
runs	Runs	Required. Array of Object; no unknown keys.; minimum items 1; maximum items 8.
runs[].centerCount	Center Count	Required. Safe integer; minimum 1; maximum 8.
runs[].normalizedBandwidth	Normalized Bandwidth	Required. Finite number; strictly above 0.
runs[].kMeans	K Means	Required. Object; no unknown keys.
runs[].kMeans.centroids	Centroids	Required. Array of Array of Finite number.; minimum items 1; maximum items 8.; minimum items 1; maximum items 128.
runs[].kMeans.labels	Labels	Required. Array of Safe integer; minimum 0; maximum 127.; minimum items 1; maximum items 128.
runs[].kMeans.iterations	Iterations	Required. Safe integer; minimum 1; maximum 1000.
runs[].meanShift	Mean Shift	Required. Object; no unknown keys.
runs[].meanShift.modes	Modes	Required. Array of Array of Finite number.; minimum items 1; maximum items 8.; minimum items 1; maximum items 128.
runs[].meanShift.labels	Labels	Required. Array of Safe integer; minimum 0; maximum 127.; minimum items 1; maximum items 128.
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": {
    "shapes": [
      {
        "kind": "elongated",
        "center": [
          4,
          0
        ],
        "pointCount": 2,
        "rotationDegrees": 0,
        "majorDeviation": 1,
        "minorDeviation": 0.2
      },
      {
        "kind": "arc",
        "center": [
          -4,
          0
        ],
        "pointCount": 2,
        "rotationDegrees": 0,
        "radius": 2,
        "radialDeviation": 0,
        "startDegrees": 0,
        "sweepDegrees": 90
      }
    ],
    "settings": [
      {
        "centerCount": 1,
        "normalizedBandwidth": 3
      }
    ],
    "maximumIterations": 1,
    "seed": 42
  },
  "output": {
    "points": [
      [
        -3.631592769364688,
        1.9657762111734947
      ],
      [
        -3.580514346968061,
        1.9555131773783494
      ],
      [
        2.1583728152164032,
        -0.22817641419080484
      ],
      [
        3.043837770615851,
        -0.05460522097652209
      ]
    ],
    "sourceLabels": [
      1,
      1,
      0,
      0
    ],
    "distanceScale": 3.631592769364688,
    "runs": [
      {
        "centerCount": 1,
        "normalizedBandwidth": 3,
        "kMeans": {
          "centroids": [
            [
              -0.13836191570373313,
              0.2504760296968153
            ]
          ],
          "labels": [
            0,
            0,
            0,
            0
          ],
          "iterations": 1
        },
        "meanShift": {
          "modes": [
            [
              -0.13836191570373313,
              0.2504760296968153
            ]
          ],
          "labels": [
            0,
            0,
            0,
            0
          ]
        }
      }
    ],
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

Returned solver coordinates use the normalized scale. Shape labels describe generation rather than guaranteed recovered clusters, and bounded iterations or numeric work can fail. This is synthetic method comparison, not measured cluster quality.
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 Cluster Shape Comparison Benchmark Generator — tool.io

Similar or alternative tools

Random Cluster Initialization Sensitivity Benchmark Generator
Generate one labeled Gaussian mixture and compare k-means++ starting-center coverage across explicit seeds using uniformly scaled squared distances; report initial centers and nearest-center costs, not iterative fits or an optimality guarantee.
Random Fuzzy Cluster Membership Benchmark Generator
Generate one labeled Gaussian mixture and compare existing fuzzy memberships with possibilistic typicalities under supplied parameters in uniformly normalized coordinates; retain the cores' last-update weights and centroids without treating typicalities as probabilities or claiming convergence from an iteration count.