Random Cluster Initialization Sensitivity Benchmark Generator

Description

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.

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 initialization sensitivity 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 clusters, centerCount, initializationSeeds 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 one labeled Gaussian dataset and run seeded k-means++ initialization for each initialization seed on normalized points. Return selected original points, nearest-center indexes, normalized squared distances, and normalized initial SSE.^[1]

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

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.
centerCount	Center Count	Required. Safe integer; minimum 1; maximum 8.
initializationSeeds	Initialization Seeds	Required. Array of Safe integer.; minimum items 1; maximum items 16.
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 16.
runs[].seed	Optional numeric seed; takes precedence over context randomness. Without either, use the fixed tool.io default seed.	Required. Safe integer.
runs[].effectiveSeed	Effective Seed	Required. Safe integer; minimum 0; maximum 4294967295.
runs[].centroidIndices	Centroid Indices	Required. Array of Safe integer; minimum 0; maximum 127.; minimum items 1; maximum items 8.
runs[].centroids	Centroids	Required. Array of Array of Finite number.; minimum items 1; maximum items 8.; minimum items 1; maximum items 8.
runs[].nearestCenterIndices	Nearest Center Indices	Required. Array of Safe integer; minimum 0; maximum 7.; minimum items 1; maximum items 128.
runs[].squaredDistances	Squared Distances	Required. Array of Finite number; minimum 0.; minimum items 1; maximum items 128.
runs[].normalizedSse	Normalized Sse	Required. Finite number; minimum 0.
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
        ],
        "standardDeviation": 0,
        "pointCount": 2
      },
      {
        "center": [
          2
        ],
        "standardDeviation": 0,
        "pointCount": 2
      },
      {
        "center": [
          10
        ],
        "standardDeviation": 0,
        "pointCount": 2
      }
    ],
    "centerCount": 2,
    "initializationSeeds": [
      1,
      7,
      42
    ],
    "seed": 42
  },
  "output": {
    "points": [
      [
        2
      ],
      [
        2
      ],
      [
        10
      ],
      [
        0
      ],
      [
        0
      ],
      [
        10
      ]
    ],
    "sourceLabels": [
      1,
      1,
      2,
      0,
      0,
      2
    ],
    "distanceScale": 10,
    "runs": [
      {
        "seed": 1,
        "effectiveSeed": 1,
        "centroidIndices": [
          3,
          0
        ],
        "centroids": [
          [
            0
          ],
          [
            2
          ]
        ],
        "nearestCenterIndices": [
          1,
          1,
          1,
          0,
          0,
          1
        ],
        "squaredDistances": [
          0,
          0,
          0.6400000000000001,
          0,
          0,
          0.6400000000000001
        ],
        "normalizedSse": 1.2800000000000002
      },
      {
        "seed": 7,
        "effectiveSeed": 7,
        "centroidIndices": [
          0,
          2
        ],
        "centroids": [
          [
            2
          ],
          [
            10
          ]
        ],
        "nearestCenterIndices": [
          0,
          0,
          1,
          0,
          0,
          1
        ],
        "squaredDistances": [
          0,
          0,
          0,
          0.04000000000000001,
          0.04000000000000001,
          0
        ],
        "normalizedSse": 0.08000000000000002
      },
      {
        "seed": 42,
        "effectiveSeed": 42,
        "centroidIndices": [
          3,
          2
        ],
        "centroids": [
          [
            0
          ],
          [
            10
          ]
        ],
        "nearestCenterIndices": [
          0,
          0,
          1,
          0,
          0,
          1
        ],
        "squaredDistances": [
          0.04000000000000001,
          0.04000000000000001,
          0,
          0,
          0,
          0
        ],
        "normalizedSse": 0.08000000000000002
      }
    ],
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

This compares initialization only and performs no subsequent k-means optimization. Effective seeds are unsigned 32-bit values; repeated effective seeds can repeat runs. SSE uses normalized rather than original coordinate units.
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 Initialization Sensitivity Benchmark Generator — tool.io
Calculation or validation: clustering/k-means-plus-plus — tool.io

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