Agent Conversation: qwen/qwen3.6-plus

Model: qwen/qwen3.6-plus

Total steps: 10

Messages: 22

UserStep 0

Task: ml-clustering-algorithm

Clustering Algorithm Design

Research Question

Design a novel clustering algorithm or distance metric that improves cluster quality across diverse dataset geometries — including convex blobs, non-convex shapes (moons), varied-density clusters, and real-world high-dimensional data (handwritten digits).

Background

Clustering is a fundamental unsupervised learning problem. Classic methods like K-Means assume convex, isotropic clusters; DBSCAN handles arbitrary shapes but requires careful tuning of the eps parameter. Modern advances include HDBSCAN (hierarchical density estimation, parameter-free cluster count), Spectral Clustering (graph Laplacian for non-convex clusters), and Density Peak Clustering (DPC, which identifies centers via local density and inter-peak distance). No single method dominates across all dataset structures, making this an open research question.

Task

Modify the CustomClustering class in scikit-learn/custom_clustering.py (lines 36--120) to implement a novel clustering algorithm. You may also modify the custom_distance function if your approach uses a custom distance metric.

Your algorithm must:

Accept n_clusters (int or None) and random_state parameters
Implement fit(X) that sets self.labels_ and returns self
Implement predict(X) that returns integer cluster labels
Handle datasets with different structures (convex, non-convex, varied density, high-dimensional)

Interface

class CustomClustering(BaseEstimator, ClusterMixin):
    def __init__(self, n_clusters=None, random_state=42): ...
    def fit(self, X):        # X: (n_samples, n_features) -> self
    def predict(self, X):    # X: (n_samples, n_features) -> labels (n_samples,)

Available imports (already in the FIXED section): numpy, sklearn.base.BaseEstimator, sklearn.base.ClusterMixin, sklearn.preprocessing.StandardScaler, sklearn.metrics.*. You may import any module from scikit-learn, numpy, or scipy.

Evaluation

Datasets: blobs (5 Gaussian clusters), moons (2 half-circles), varied_density (3 clusters with different densities), digits (sklearn Digits, 10 classes, 64 features)
Metrics: ARI (Adjusted Rand Index, higher is better), NMI (Normalized Mutual Information, higher is better), Silhouette Score (higher is better)
Success = consistently improving over baselines across all four datasets

scikit-learn/custom_clustering.py [EDITABLE — lines 36–109 only]

     1: """Custom clustering algorithm benchmark.
     2: 
     3: This script evaluates a clustering algorithm across multiple dataset types.
     4: The agent should modify the EDITABLE section to implement a novel clustering
     5: algorithm or distance metric that achieves high cluster quality.
     6: 
     7: Datasets (selected by $ENV):
     8:   - blobs:          Isotropic Gaussian blobs (varying cluster sizes)
     9:   - moons:          Two interleaving half-circles + noise

AssistantStep 1edit

Tool Input

1{
2  "op": "replace",
3  "filename": "scikit-learn/custom_clustering.py",
4  "start_line": 36,
5  "end_line": 109,
6  "content": "class CustomClustering(BaseEstimator, ClusterMixin):\n    \"\"\"Density-Adaptive Spectral Clustering with K-Means Refinement.\n\n    A novel hybrid approach combining:\n    1. Self-tuning spectral clustering with local adaptive bandwidths\n       (handles varied-density clusters)\n    2. Symmetric kNN affinity graph construction (handles non-convex shapes)\n    3. K-Means refinement in spectral embedding space (sharpens cluster boundaries)\n    4. PCA preprocessing for high-dimensional data\n    \"\"\"\n\n    def __init__(self, n_clusters=None, random_state=42):\n        self.n_clusters = n_clusters\n        self.random_state = random_state\n        self.labels_ = None\n\n    def fit(self, X):\n        \"\"\"Fit the clustering model to data X.\n\n        Args:\n            X: array of shape (n_samples, n_features)\n\n        Returns:\n            self\n        \"\"\"\n        rng = np.random.RandomState(self.random_state)\n        n_samples, n_features = X.shape\n\n        # Determine number of clusters\n        k = self.n_clusters if self.n_clusters is not None else 4\n\n        # ---- Step 1: Preprocessing ----\n        if n_features > 20:\n            # PCA for high-dimensional data to capture most variance\n            from sklearn.decomposition import PCA\n            n_components = min(n_features, max(10, int(n_samples * 0.1)))\n            pca = PCA(n_components=n_components, random_state=self.random_state)\n            X_proc = pca.fit_transform(X)\n        else:\n            X_proc = X.copy()\n\n        # ---- Step 2: Build adaptive affinity matrix ----\n        # Use self-tuning kernel with local scaling\n        n_neighbors = min(30, max(5, n_samples // 50))\n\n        from sklearn.neighbors import NearestNeighbors\n        nn = NearestNeighbors(n_neighbors=n_neighbors, algorithm='auto')\n        nn.fit(X_proc)\n        distances, indices = nn.kneighbors(X_proc)\n\n        # Compute local scaling factor: use k-th nearest neighbor distance\n        # with geometric mean of local distances\n        local_scale = distances[:, -1]  # distance to k-th neighbor\n\n        # Build sparse affinity matrix with adaptive RBF kernel\n        from scipy.sparse import lil_matrix\n        affinity = lil_matrix((n_samples, n_samples), dtype=np.float64)\n\n        for i in range(n_samples):\n            for j_idx, j in enumerate(indices[i]):\n                if i == j:\n                    continue\n                d_ij = distances[i, j_idx]\n                # Self-tuning kernel: A(i,j) = exp(-d(i,j)^2 / (sigma_i * sigma_j))\n                sigma_ij = local_scale[i] * local_scale[j]\n                if sigma_ij > 0:\n                    affinity[i, j] = np.exp(-(d_ij ** 2) / sigma_ij)\n\n        # Symmetrize\n        affinity = (affinity + affinity.T) / 2.0\n\n        # ---- Step 3: Spectral embedding ----\n        # Compute graph Laplacian and get top k eigenvectors\n        D = np.array(affinity.sum(axis=1)).flatten()\n        D = np.maximum(D, 1e-10)  # avoid division by zero\n\n        # Normalized Laplacian: L_sym = I - D^{-1/2} A D^{-1/2}\n        D_inv_sqrt = 1.0 / np.sqrt(D)\n        # Compute D^{-1/2} A D^{-1/2} using sparse operations\n        from scipy.sparse import diags\n        D_inv_sqrt_diag = diags(D_inv_sqrt, 0)\n        L_norm = D_inv_sqrt_diag @ affinity @ D_inv_sqrt_diag\n\n        # Eigendecomposition on the symmetrized normalized affinity matrix\n        L_norm_dense = L_norm.toarray() if hasattr(L_norm, 'toarray') else np.array(L_norm)\n        L_norm_dense = (L_norm_dense + L_norm_dense.T) / 2.0  # ensure symmetry\n\n        eigenvalues, eigenvectors = np.linalg.eigh(L_norm_dense)\n\n        # Take the top k eigenvectors (largest eigenvalues of the affinity)\n        top_k_idx = np.argsort(eigenvalues)[-k:]\n        embedding = eigenvectors[:, top_k_idx]\n\n        # Row-normalize the embedding\n        norms = np.linalg.norm(embedding, axis=1, keepdims=True)\n        norms = np.maximum(norms, 1e-10)\n        embedding = embedding / norms\n\n        # ---- Step 4: K-Means refinement in spectral space ----\n        from sklearn.cluster import KMeans\n        km = KMeans(n_clusters=k, random_state=self.random_state, n_init=20, max_iter=500)\n        km.fit(embedding)\n        self.labels_ = km.labels_\n\n        return self\n\n    def predict(self, X):\n        \"\"\"Predict cluster labels for X.\n\n        Args:\n            X: array of shape (n_samples, n_features)\n\n        Returns:\n            labels: array of shape (n_samples,) with cluster assignments\n        \"\"\"\n        if self.labels_ is None:\n            self.fit(X)\n        return self.labels_\n\n\n# Placeholder for optional custom distance metric\ndef custom_distance(x, y):\n    \"\"\"Custom distance metric between two points.\n\n    Args:\n        x, y: 1-D arrays of shape (n_features,)\n\n    Returns:\n        distance: float >= 0\n    \"\"\"\n    return np.sqrt(np.sum((x - y) ** 2))\n\n"
7}

Tool ResultStep 1

OK: Replaced lines 36..109 with 132 line(s) in scikit-learn/custom_clustering.py. Editable range: 36–167.

[Current file: scikit-learn/custom_clustering.py | editable: 36–167 | total: 268 lines]
    36  class CustomClustering(BaseEstimator, ClusterMixin):
    37      """Density-Adaptive Spectral Clustering with K-Means Refinement.
    38  
       ... (126 more lines) ...
   165      """
   166      return np.sqrt(np.sum((x - y) ** 2))
   167

AssistantStep 2test

Tool ResultStep 2

[Test #1] (2 tests remaining; call submit(n=N) to choose which test result to submit as final)

### blobs (scripts/blobs.sh)
Training progress (blobs):
TRAIN_METRICS stage=fitting
TRAIN_METRICS stage=done
TRAIN_METRICS ari=0.938892
TRAIN_METRICS nmi=0.940707
TRAIN_METRICS silhouette=0.666225
ari_blobs: 0.938892
nmi_blobs: 0.940707
silhouette_blobs: 0.666225

### moons (scripts/moons.sh)
Training progress (moons):
TRAIN_METRICS stage=fitting
TRAIN_METRICS stage=done
TRAIN_METRICS ari=1.000000
TRAIN_METRICS nmi=1.000000
TRAIN_METRICS silhouette=0.385298
ari_moons: 1.000000
nmi_moons: 1.000000
silhouette_moons: 0.385298

[Leaderboard] Results saved: {'ari_blobs': 0.938892, 'nmi_blobs': 0.940707, 'silhouette_blobs': 0.666225, 'elapsed_blobs': 3, 'ari_moons': 1.0, 'nmi_moons': 1.0, 'silhouette_moons': 0.385298, 'elapsed_moons': 3, 'ari_digits': 0.658043, 'nmi_digits': 0.773234, 'silhouette_digits': 0.136539, 'elapsed_digits': 3}

AssistantStep 3edit

Tool Input

1{
2  "op": "replace",
3  "filename": "scikit-learn/custom_clustering.py",
4  "start_line": 36,
5  "end_line": 166,
6  "content": "class CustomClustering(BaseEstimator, ClusterMixin):\n    \"\"\"Density-Adaptive Spectral Clustering with K-Means Refinement.\n\n    A novel hybrid approach combining:\n    1. Adaptive PCA + whitening for high-dimensional data\n    2. Self-tuning spectral clustering with local adaptive bandwidths\n    3. Symmetric kNN affinity graph construction\n    4. K-Means++ refinement in spectral embedding space\n    \"\"\"\n\n    def __init__(self, n_clusters=None, random_state=42):\n        self.n_clusters = n_clusters\n        self.random_state = random_state\n        self.labels_ = None\n\n    def fit(self, X):\n        \"\"\"Fit the clustering model to data X.\n\n        Args:\n            X: array of shape (n_samples, n_features)\n\n        Returns:\n            self\n        \"\"\"\n        rng = np.random.RandomState(self.random_state)\n        n_samples, n_features = X.shape\n\n        # Determine number of clusters\n        k = self.n_clusters if self.n_clusters is not None else 4\n\n        # ---- Step 1: Preprocessing ----\n        if n_features > 20:\n            from sklearn.decomposition import PCA\n            # For high-dimensional data, retain enough variance\n            n_components = min(n_features, max(20, int(n_samples * 0.15), k * 3))\n            pca = PCA(n_components=n_components, random_state=self.random_state)\n            X_proc = pca.fit_transform(X)\n        else:\n            X_proc = X.copy()\n\n        # ---- Step 2: Build adaptive affinity matrix ----\n        from sklearn.neighbors import NearestNeighbors\n        # Adaptive neighborhood size based on dataset\n        if n_features > 20:\n            n_neighbors = min(30, max(10, n_samples // 30))\n        else:\n            n_neighbors = min(30, max(5, n_samples // 50))\n\n        nn = NearestNeighbors(n_neighbors=n_neighbors, algorithm='auto')\n        nn.fit(X_proc)\n        distances, indices = nn.kneighbors(X_proc)\n\n        # Local scaling factor: distance to k-th nearest neighbor\n        local_scale = distances[:, -1].copy()\n        # Add small epsilon to prevent division by zero\n        local_scale = np.maximum(local_scale, 1e-6)\n\n        # Build sparse affinity matrix with adaptive RBF kernel\n        from scipy.sparse import coo_matrix\n        row_list = []\n        col_list = []\n        val_list = []\n\n        for i in range(n_samples):\n            for j_idx, j in enumerate(indices[i]):\n                if i == j:\n                    continue\n                d_ij = distances[i, j_idx]\n                sigma_ij = local_scale[i] * local_scale[j]\n                val = np.exp(-(d_ij ** 2) / sigma_ij)\n                row_list.append(i)\n                col_list.append(j)\n                val_list.append(val)\n\n        affinity = coo_matrix((val_list, (row_list, col_list)), shape=(n_samples, n_samples))\n        # Symmetrize: A = (A + A^T) / 2\n        affinity = (affinity + affinity.T) / 2.0\n\n        # ---- Step 3: Spectral embedding via normalized Laplacian ----\n        D = np.array(affinity.sum(axis=1)).flatten()\n        D = np.maximum(D, 1e-10)\n\n        from scipy.sparse import diags\n        D_inv_sqrt = diags(1.0 / np.sqrt(D), 0)\n        # Normalized affinity: D^{-1/2} A D^{-1/2}\n        L_norm = D_inv_sqrt @ affinity @ D_inv_sqrt_symmetric = None\n\n        # Convert to dense for small matrices, or use sparse eigensolver\n        if n_samples <= 2000:\n            L_dense = L_norm.toarray() if hasattr(L_norm, 'toarray') else np.array(L_norm)\n            L_dense = (L_dense + L_dense.T) / 2.0\n            eigenvalues, eigenvectors = np.linalg.eigh(L_dense)\n        else:\n            from scipy.sparse.linalg import eigsh\n            eigenvalues, eigenvectors = eigsh(L_norm, k=k, which='LM')\n\n        # Take the top k eigenvectors (largest eigenvalues of the affinity)\n        top_k_idx = np.argsort(eigenvalues)[-k:]\n        embedding = eigenvectors[:, top_k_idx]\n\n        # Row-normalize the embedding\n        norms = np.linalg.norm(embedding, axis=1, keepdims=True)\n        norms = np.maximum(norms, 1e-10)\n        embedding = embedding / norms\n\n        # ---- Step 4: K-Means refinement in spectral space ----\n        from sklearn.cluster import KMeans\n        km = KMeans(n_clusters=k, random_state=self.random_state, n_init=20, max_iter=500)\n        km.fit(embedding)\n        self.labels_ = km.labels_\n\n        return self\n\n    def predict(self, X):\n        \"\"\"Predict cluster labels for X.\n\n        Args:\n            X: array of shape (n_samples, n_features)\n\n        Returns:\n            labels: array of shape (n_samples,) with cluster assignments\n        \"\"\"\n        if self.labels_ is None:\n            self.fit(X)\n        return self.labels_\n\n\n# Placeholder for optional custom distance metric\ndef custom_distance(x, y):\n    \"\"\"Custom distance metric between two points.\n\n    Args:\n        x, y: 1-D arrays of shape (n_features,)\n\n    Returns:\n        distance: float >= 0\n    \"\"\"\n    return np.sqrt(np.sum((x - y) ** 2))\n"
7}

Tool ResultStep 3

OK: Replaced lines 36..166 with 138 line(s) in scikit-learn/custom_clustering.py. Editable range: 36–174.

[Current file: scikit-learn/custom_clustering.py | editable: 36–174 | total: 275 lines]
    36  class CustomClustering(BaseEstimator, ClusterMixin):
    37      """Density-Adaptive Spectral Clustering with K-Means Refinement.
    38  
       ... (133 more lines) ...
   172      """
   173      return np.sqrt(np.sum((x - y) ** 2))
   174

AssistantStep 4edit

Tool Input

1{
2  "op": "replace",
3  "content": "        from scipy.sparse import diags\n        D_inv_sqrt = diags(1.0 / np.sqrt(D), 0)\n        # Normalized affinity: D^{-1/2} A D^{-1/2}\n        L_norm = D_inv_sqrt @ (affinity.toarray() if hasattr(affinity, 'toarray') else np.array(affinity)) @ D_inv_sqrt\n\n        # Eigendecomposition\n        L_norm = (L_norm + L_norm.T) / 2.0  # ensure symmetry\n        if n_samples <= 5000:\n            eigenvalues, eigenvectors = np.linalg.eigh(L_norm)\n        else:\n            from scipy.sparse.linalg import eigsh\n            eigenvalues, eigenvectors = eigsh(L_norm, k=k, which='LM')",
4  "filename": "scikit-learn/custom_clustering.py",
5  "start_line": 103,
6  "end_line": 116
7}

Tool ResultStep 4

OK: Replaced lines 103..116 with 12 line(s) in scikit-learn/custom_clustering.py. Editable range: 36–172.

[Current file: scikit-learn/custom_clustering.py | editable: 36–172 | total: 273 lines]
    36  class CustomClustering(BaseEstimator, ClusterMixin):
    37      """Density-Adaptive Spectral Clustering with K-Means Refinement.
    38  
       ... (131 more lines) ...
   170      """
   171      return np.sqrt(np.sum((x - y) ** 2))
   172

AssistantStep 5edit

Tool Input

1{
2  "filename": "scikit-learn/custom_clustering.py",
3  "op": "replace",
4  "content": "        from scipy.sparse import diags\n        from scipy.sparse.linalg import eigsh\n        D_inv_sqrt = diags(1.0 / np.sqrt(D), 0)\n\n        # Eigendecomposition on normalized affinity matrix\n        L_norm = D_inv_sqrt @ affinity @ D_inv_sqrt\n\n        if n_samples <= 5000:\n            L_dense = L_norm.toarray() if hasattr(L_norm, 'toarray') else np.array(L_norm)\n            L_dense = (L_dense + L_dense.T) / 2.0\n            eigenvalues, eigenvectors = np.linalg.eigh(L_dense)\n        else:\n            L_sym = (L_norm + L_norm.T) / 2.0\n            eigenvalues, eigenvectors = eigsh(L_sym, k=k, which='LM')",
5  "end_line": 116,
6  "start_line": 103
7}

Tool ResultStep 5

OK: Replaced lines 103..116 with 14 line(s) in scikit-learn/custom_clustering.py. Editable range: 36–172.

[Current file: scikit-learn/custom_clustering.py | editable: 36–172 | total: 273 lines]
    36  class CustomClustering(BaseEstimator, ClusterMixin):
    37      """Density-Adaptive Spectral Clustering with K-Means Refinement.
    38  
       ... (131 more lines) ...
   170      """
   171      return np.sqrt(np.sum((x - y) ** 2))
   172

AssistantStep 6test

Tool ResultStep 6

[Test #2] (1 test remaining; call submit(n=N) to choose which test result to submit as final)

### blobs (scripts/blobs.sh)
[COMMAND FAILED exit=1]
  File "/srv/home/bohanlyu/MLS-Bench/vendor/workspace/ml-clustering-algorithm/qwen_qwen3.6-plus_20260414_110948/scikit-learn/custom_clustering.py", line 119
    L_norm = D_inv_sqrt @ affinity @ D_inv_sqrt_symmetric = None
             ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
SyntaxError: cannot assign to expression
ERROR conda.cli.main_run:execute(142): `conda run bash /srv/home/bohanlyu/MLS-Bench/vendor/workspace/ml-clustering-algorithm/qwen_qwen3.6-plus_20260414_110948/.local_scripts/scripts/blobs.sh` failed. (See above for error)


### moons (scripts/moons.sh)
[COMMAND FAILED exit=1]
  File "/srv/home/bohanlyu/MLS-Bench/vendor/workspace/ml-clustering-algorithm/qwen_qwen3.6-plus_20260414_110948/scikit-learn/custom_clustering.py", line 119
    L_norm = D_inv_sqrt @ affinity @ D_inv_sqrt_symmetric = None
             ^^^^^^^^^^^^^^^^^^^

AssistantStep 7edit

Tool Input

1{
2  "content": "        from scipy.sparse import diags\n        from scipy.sparse.linalg import eigsh\n        D_inv_sqrt = diags(1.0 / np.sqrt(D), 0)\n\n        # Eigendecomposition on normalized affinity matrix\n        L_norm = D_inv_sqrt @ affinity @ D_inv_sqrt\n\n        if n_samples <= 5000:\n            L_dense = L_norm.toarray() if hasattr(L_norm, 'toarray') else np.array(L_norm)\n            L_dense = (L_dense + L_dense.T) / 2.0\n            eigenvalues, eigenvectors = np.linalg.eigh(L_dense)\n        else:\n            L_sym = (L_norm + L_norm.T) / 2.0\n            eigenvalues, eigenvectors = eigsh(L_sym, k=k, which='LM')",
3  "end_line": 116,
4  "filename": "scikit-learn/custom_clustering.py",
5  "start_line": 103,
6  "op": "replace"
7}

Tool ResultStep 7

OK: Replaced lines 103..116 with 14 line(s) in scikit-learn/custom_clustering.py. Editable range: 36–172.

[Current file: scikit-learn/custom_clustering.py | editable: 36–172 | total: 273 lines]
    36  class CustomClustering(BaseEstimator, ClusterMixin):
    37      """Density-Adaptive Spectral Clustering with K-Means Refinement.
    38  
       ... (131 more lines) ...
   170      """
   171      return np.sqrt(np.sum((x - y) ** 2))
   172

AssistantStep 8edit

Tool Input

1{
2  "content": "class CustomClustering(BaseEstimator, ClusterMixin):\n    \"\"\"Density-Adaptive Spectral Clustering with K-Means Refinement.\n\n    A novel hybrid approach combining:\n    1. Adaptive PCA for high-dimensional data\n    2. Self-tuning spectral clustering with local adaptive bandwidths\n    3. Symmetric kNN affinity graph construction\n    4. K-Means++ refinement in spectral embedding space\n    \"\"\"\n\n    def __init__(self, n_clusters=None, random_state=42):\n        self.n_clusters = n_clusters\n        self.random_state = random_state\n        self.labels_ = None\n\n    def fit(self, X):\n        \"\"\"Fit the clustering model to data X.\n\n        Args:\n            X: array of shape (n_samples, n_features)\n\n        Returns:\n            self\n        \"\"\"\n        rng = np.random.RandomState(self.random_state)\n        n_samples, n_features = X.shape\n\n        # Determine number of clusters\n        k = self.n_clusters if self.n_clusters is not None else 4\n\n        # ---- Step 1: Preprocessing ----\n        if n_features > 20:\n            from sklearn.decomposition import PCA\n            n_components = min(n_features, max(20, int(n_samples * 0.15), k * 3))\n            pca = PCA(n_components=n_components, random_state=self.random_state)\n            X_proc = pca.fit_transform(X)\n        else:\n            X_proc = X.copy()\n\n        # ---- Step 2: Build adaptive affinity matrix ----\n        from sklearn.neighbors import NearestNeighbors\n        if n_features > 20:\n            n_neighbors = min(30, max(10, n_samples // 30))\n        else:\n            n_neighbors = min(30, max(5, n_samples // 50))\n\n        nn = NearestNeighbors(n_neighbors=n_neighbors, algorithm='auto')\n        nn.fit(X_proc)\n        distances, indices = nn.kneighbors(X_proc)\n\n        # Local scaling factor: distance to k-th nearest neighbor\n        local_scale = np.maximum(distances[:, -1].copy(), 1e-6)\n\n        # Build sparse affinity matrix with adaptive RBF kernel\n        from scipy.sparse import coo_matrix\n        row_list = []\n        col_list = []\n        val_list = []\n\n        for i in range(n_samples):\n            for j_idx, j in enumerate(indices[i]):\n                if i == j:\n                    continue\n                d_ij = distances[i, j_idx]\n                sigma_ij = local_scale[i] * local_scale[j]\n                val = np.exp(-(d_ij ** 2) / sigma_ij)\n                row_list.append(i)\n                col_list.append(j)\n                val_list.append(val)\n\n        affinity = coo_matrix((val_list, (row_list, col_list)), shape=(n_samples, n_samples))\n        affinity = (affinity + affinity.T) / 2.0\n\n        # ---- Step 3: Spectral embedding via normalized Laplacian ----\n        D = np.array(affinity.sum(axis=1)).flatten()\n        D = np.maximum(D, 1e-10)\n\n        # Build normalized affinity matrix D^{-1/2} A D^{-1/2}\n        L_dense_array = affinity.toarray() if hasattr(affinity, 'toarray') else np.array(affinity)\n        L_dense = (L_dense_array + L_dense_array.T) / 2.0\n\n        D_inv_sqrt = 1.0 / np.sqrt(D)\n        L_norm = L_dense * D_inv_sqrt[:, None] * D_inv_sqrt[None, :]\n        L_norm = (L_norm + L_norm.T) / 2.0\n\n        # Eigendecomposition\n        eigenvalues, eigenvectors = np.linalg.eigh(L_norm)\n\n        # Take the top k eigenvectors (largest eigenvalues of the affinity)\n        top_k_idx = np.argsort(eigenvalues)[-k:]\n        embedding = eigenvectors[:, top_k_idx]\n\n        # Row-normalize the embedding\n        norms = np.linalg.norm(embedding, axis=1, keepdims=True)\n        norms = np.maximum(norms, 1e-10)\n        embedding = embedding / norms\n\n        # ---- Step 4: K-Means refinement in spectral space ----\n        from sklearn.cluster import KMeans\n        km = KMeans(n_clusters=k, random_state=self.random_state, n_init=20, max_iter=500)\n        km.fit(embedding)\n        self.labels_ = km.labels_\n\n        return self\n\n    def predict(self, X):\n        \"\"\"Predict cluster labels for X.\n\n        Args:\n            X: array of shape (n_samples, n_features)\n\n        Returns:\n            labels: array of shape (n_samples,) with cluster assignments\n        \"\"\"\n        if self.labels_ is None:\n            self.fit(X)\n        return self.labels_\n\n\n# Placeholder for optional custom distance metric\ndef custom_distance(x, y):\n    \"\"\"Custom distance metric between two points.\n\n    Args:\n        x, y: 1-D arrays of shape (n_features,)\n\n    Returns:\n        distance: float >= 0\n    \"\"\"\n    return np.sqrt(np.sum((x - y) ** 2))",
3  "end_line": 171,
4  "filename": "scikit-learn/custom_clustering.py",
5  "start_line": 36,
6  "op": "replace"
7}

Tool ResultStep 8

OK: Replaced lines 36..171 with 130 line(s) in scikit-learn/custom_clustering.py. Editable range: 36–166.

[Current file: scikit-learn/custom_clustering.py | editable: 36–166 | total: 267 lines]
    36  class CustomClustering(BaseEstimator, ClusterMixin):
    37      """Density-Adaptive Spectral Clustering with K-Means Refinement.
    38  
       ... (125 more lines) ...
   164      """
   165      return np.sqrt(np.sum((x - y) ** 2))
   166

AssistantStep 9test

Tool ResultStep 9

[Test #3] (0 tests remaining; call submit(n=N) to choose which test result to submit as final)

[NOTE] This was your last test. You MUST now call submit(n=X) to choose which test result to submit as your final answer.

### blobs (scripts/blobs.sh)
Training progress (blobs):
TRAIN_METRICS stage=fitting
TRAIN_METRICS stage=done
TRAIN_METRICS ari=0.938892
TRAIN_METRICS nmi=0.940707
TRAIN_METRICS silhouette=0.666225
ari_blobs: 0.938892
nmi_blobs: 0.940707
silhouette_blobs: 0.666225

### moons (scripts/moons.sh)
Training progress (moons):
TRAIN_METRICS stage=fitting
TRAIN_METRICS stage=done
TRAIN_METRICS ari=1.000000
TRAIN_METRICS nmi=1.000000
TRAIN_METRICS silhouette=0.385298
ari_moons: 1.000000
nmi_moons: 1.000000
silhouette_moons: 0.385298

### digits (scripts/digits.sh)
Training progress (digits):
TRAIN_METRICS stage=fitting
TRAIN_METRICS stage=done
TRAIN_METRICS ari=0.658043
TRAIN_METRICS nmi=0.773234
TRAIN_METRICS silhouette=0.136539
ari_digits: 0.658043
nmi_digits: 0.773234
silhouett