Mechanics
- Neighbourhood N_eps(p): points within eps of p (p included).
- Core point: |N_eps(p)| >= min_samples.
- Directly density-reachable: q in N_eps(p) and p is core.
- Cluster: maximal set of points density-connected through core points.
- Border point: not core, but in the neighbourhood of a core point; assigned to the first cluster that reaches it (order-dependent when it neighbours two clusters).
- Noise: neither core nor border (label −1).
Parameter interplay
| Change | Effect |
|---|---|
| eps up | more core points, clusters grow and merge, less noise |
| eps down | clusters shrink and split, more noise |
| min_samples up | fewer core points, more noise, small groups disappear, more robust to chaining |
| min_samples down | more core points, chaining between clusters, tiny clusters appear |
Rule of thumb: decide min_samples from the domain (noise tolerance, smallest group), then tune eps.
Determinism
Core points and noise are deterministic; border points between two clusters depend on processing order. scikit-learn's implementation is deterministic for a given input order.
Complexity and scale
- Neighbourhood queries dominate: O(n log n) average with a tree index in low dimensions, O(n²) worst case or in high dimensions.
algorithm="ball_tree"/"kd_tree"/"brute";n_jobs=-1parallelises queries.- Memory: scikit-learn materialises neighbourhoods; large eps on big data can exhaust memory. Sample, reduce eps, or use HDBSCAN.
OPTICS
Orders points by reachability distance; clusters are valleys in the reachability plot.
from sklearn.cluster import OPTICS
op = OPTICS(min_samples=10, xi=0.05, min_cluster_size=0.02).fit(X)
reach = op.reachability_[op.ordering_] # plot: valleys = clusterscluster_optics_dbscan(reachability=..., core_distances=..., ordering=..., eps=e) extracts the DBSCAN result
for any eps from one OPTICS run, which is cheap for exploring eps.
HDBSCAN
from sklearn.cluster import HDBSCAN
hdb = HDBSCAN(min_cluster_size=20, min_samples=10, cluster_selection_epsilon=0.0,
cluster_selection_method="eom").fit(X)| Parameter | Meaning |
|---|---|
| min_cluster_size | smallest group to report as a cluster |
| min_samples | noise strictness (defaults to min_cluster_size) |
| cluster_selection_epsilon | merge clusters below this distance (DBSCAN-like floor) |
| cluster_selection_method | "eom" (excess of mass, fewer larger clusters) or "leaf" (finer clusters) |
Assigning new points
DBSCAN has no predict. Options:
- Nearest core point within eps -> its cluster; otherwise noise:
python from sklearn.neighbors import NearestNeighbors core = db.components_; core_labels = db.labels_[db.core_sample_indices_] nn = NearestNeighbors(n_neighbors=1).fit(core) dist, idx = nn.kneighbors(X_new) new_labels = np.where(dist[:, 0] <= db.eps, core_labels[idx[:, 0]], -1) - Train a classifier on (X, labels) for non-noise points.
- Re-run clustering periodically on fresh data.
anomaly-detection-model-builder
Build and evaluate anomaly detection for tabular, sensor and transaction data with few or no labels: define the anomaly type (point, contextual, collective), choose detectors (robust z-score/MAD and IQR rules, Mahalanobis with robust covariance, k-NN distance, LOF, Isolation Forest, one-class SVM, PCA reconstruction / autoencoders, forecasting residuals for time series), combine them by rank, explain each alert by its deviating features, set thresholds from an alert budget or the score distribution, and evaluate with precision@k, PR-AUC and recall on known incidents, or detector agreement when no labels exist. Includes pure-Python detectors (robust z, Mahalanobis, kNN, Isolation Forest, ensemble) and an evaluation script.
catboost-model-builder
Build CatBoost models that use its strengths correctly: raw categorical columns as cat_features (ordered target statistics, no manual encoding), text_features, Pool construction with NaN-safe categories, ordered boosting and has_time for temporal data, symmetric (oblivious) trees, overfitting detector with eval_set and use_best_model, losses for classification, regression (Quantile, Poisson, Tweedie) and ranking (YetiRank), class weights, monotone constraints, feature importance (PredictionValuesChange, LossFunctionChange) and SHAP values, GPU training and model export. Plans cat/text/numeric columns from a CSV and generates a runnable training script, and checks parameter sets for the conflicts CatBoost rejects (iterations vs n_estimators, Bayesian bootstrap with subsample, multiple class-weight options, depth > 16, use_best_model without eval_set).
categorical-encoding-selector
Choose and implement the right encoding for every categorical column given the model family and the data: one-hot (with infrequent-level grouping and handle_unknown), ordinal with an explicit order, cross-fitted target encoding (scikit-learn TargetEncoder, CatBoost ordered statistics, category_encoders inside CV), frequency/count encoding, feature hashing, native categorical support in LightGBM, HistGradientBoosting, XGBoost and CatBoost, prefix levels for codes (zip3, NAICS-2), and embeddings. Measures cardinality, rare-level share, unseen-level rate on a time-ordered holdout and target signal per column, emits the ColumnTransformer, and quantifies target-encoding leakage (in-sample vs out-of-fold vs holdout AUC).
classification-model-selector
Choose the right classification algorithm for tabular, text or mixed data and prove the choice with a fair bake-off: logistic regression (L2, L1, elastic net), linear SVM, naive Bayes, k-NN, RBF SVM, decision trees, random forest, extra trees, HistGradientBoosting, LightGBM, XGBoost, CatBoost, explainable boosting machines (EBM/GAM), points scorecards and MLPs, matched to data size, width, categorical and high-cardinality share, missingness, class imbalance, text, and constraints such as interpretability, monotonic constraints, calibrated probabilities, latency budgets and tiny deployable models. Ranks candidates with starting hyperparameters and cautions, then generates a bake-off script running every candidate on identical CV folds with per-fold metrics, fit time and prediction latency.
clustering-algorithm-selector
Choose the right clustering algorithm and check that clustering makes sense at all: cluster tendency (Hopkins statistic with a correlated-features caveat, nearest-neighbour isolation), then k-means / MiniBatchKMeans, Gaussian mixtures with BIC, agglomerative (Ward, average, complete, single) with dendrograms, DBSCAN, HDBSCAN, OPTICS, spectral clustering, BIRCH, mean shift, k-prototypes and k-modes for mixed or categorical data, and Gower distance, matched to data size, expected shapes, noise, varying density, known k, soft memberships, hierarchy and streaming. Covers preprocessing (scaling, encoding, dimensionality, distance metrics), validation (internal indices, bootstrap stability, external labels, business profiling) and assigning new points.
collaborative-filtering-implementer
Implement collaborative filtering recommenders that beat popularity: item-based kNN with cosine, Jaccard or asymmetric similarity, shrinkage, neighbourhood size, positive-only or mean-centred rating signals and 'because you liked X' explanations; implicit ALS with confidence weighting, BPR pairwise ranking and the closed-form EASE model in plain NumPy, tuned on a temporal validation split by recall@k and NDCG@k and refit on all data; plus user-kNN, explicit matrix factorisation, the implicit/LightFM libraries, hyperparameter ranges, cold-start fallbacks, scaling with sparse matrices and approximate nearest neighbours. Produces top-k lists in the format of the recommendation evaluator.