{
  "context": "Evaluates whether the solution builds the requested unsupervised workflow using scikit-learn's preprocessing, decomposition, mixture, and manifold tools. Checks focus on correct use of StandardScaler, PCA-based variance retention, GaussianMixture model selection via BIC, and deterministic 2D manifold embedding driven by random_state.",
  "type": "weighted_checklist",
  "checklist": [
    {
      "name": "Scaling + PCA",
      "description": "Fits sklearn.preprocessing.StandardScaler then sklearn.decomposition.PCA with n_components reaching >=0.90 explained variance (e.g., n_components=0.9) on training data and reuses them for predictions.",
      "max_score": 25
    },
    {
      "name": "Mixture selection",
      "description": "Trains sklearn.mixture.GaussianMixture over the provided cluster_counts, compares Bayesian/Akaike information criterion (e.g., bic) to pick the best count, stores the selected count, and seeds the model with random_state.",
      "max_score": 30
    },
    {
      "name": "Soft predictions",
      "description": "predict() pipes data through the fitted scaler and PCA before calling GaussianMixture.predict and predict_proba, returns labels plus max responsibility per sample, and rejects calls before fit.",
      "max_score": 15
    },
    {
      "name": "Manifold embedding",
      "description": "embedding_2d() runs a manifold method from sklearn.manifold (e.g., Isomap or LocallyLinearEmbedding) on the PCA-transformed training data with n_components=2, passes random_state when supported, caches/returns deterministic output, and errors if unfitted.",
      "max_score": 20
    },
    {
      "name": "Validation errors",
      "description": "Raises ValueError during fit when non-finite entries are present or when min(cluster_counts) exceeds available samples before attempting to train any estimator.",
      "max_score": 10
    }
  ]
}