Clusterers & Outlier Detectors

Three ClusterMixin and six OutlierMixin estimators wrap functional-data grouping and anomaly-detection methods as standard sklearn estimators, composing naturally in Pipeline and cross_val_score.

All estimators follow the plain-ndarray contract: input X is (n_obs, n_points); argvals (default None) sets the evaluation grid at construction. See the coverage / EXCLUDE list for excluded functional clustering and outlier methods (cluster_optim).

Clusterers

ClusterMixin estimators perform unsupervised grouping of functional curves. fit_predict is the primary interface — it returns integer cluster labels directly.

Estimator	sklearn mixin	fdars source	Key constructor params
FunctionalKMeans	ClusterMixin	fdars._native.clustering.kmeans_fd	n_clusters=3, max_iter=100, tol=1e-6, argvals=None
FuzzyFunctionalCMeans	ClusterMixin	fdars._native.clustering.fuzzy_cmeans_fd	n_clusters=3, fuzziness=2.0, max_iter=..., argvals=None
FunctionalGMM	ClusterMixin	fdars._native.clustering.gmm_cluster	n_clusters=3, nbasis=5, max_iter=200, argvals=None

FunctionalKMeans

k-means clustering on functional data using the fdars-native functional distance. Cluster centres are functional curves, not scalar vectors. Converges when the maximum centre movement falls below tol. This estimator passed the full check_estimator battery at zero failures without fixes (Phase 55 baseline).

FuzzyFunctionalCMeans

Fuzzy c-means clustering where each observation has a soft membership degree to every cluster (not a hard assignment). The fuzziness parameter (default 2.0) controls the degree of fuzziness: higher values blur cluster boundaries. n_iter_ is set to max_iter at fit time (the native method does not expose an iteration count; this follows the same convention as LogisticFPCClassifier).

FunctionalGMM

Gaussian mixture model for functional data, represented in a B-spline basis of nbasis elements. Cluster membership is probabilistic. n_iter_ is set to max_iter at fit time (native exposes BIC/ICL but no EM iteration count).

Outlier Detectors

OutlierMixin estimators label each observation as an inlier (+1) or outlier (-1) via predict. The continuous anomaly score is available via score_samples (higher = more normal / more inlier).

Estimator	sklearn mixin	fdars source	Key constructor params
LRTOutlierDetector	OutlierMixin	fdars._native.outliers.detect_outliers_lrt_with_dist (fit-time provenance); depth surrogate at score time	contamination=0.1, alpha=0.05, argvals=None
OutliergramDetector	OutlierMixin	fdars._native.depth.modified_band_1d (surrogate score); MEI/MBD stored as provenance	contamination=0.1, factor=1.5, argvals=None
MagnitudeShapeDetector	OutlierMixin	fdars._native.outliers.magnitude_shape (method-faithful MS-plot score)	contamination=0.1, argvals=None
TVDMSSDetector	OutlierMixin	fdars._native.depth.modified_band_1d (surrogate); TVD/MSS arrays stored as provenance	contamination=0.1, emp_factor_mss=1.5, argvals=None
MUODDetector	OutlierMixin	fdars._native.depth.modified_band_1d (surrogate); MUOD index arrays stored as provenance	contamination=0.1, factor=1.5, argvals=None
DepthgramDetector	OutlierMixin	fdars._native.depth.modified_band_1d (surrogate); shape/magnitude outlier indices stored as provenance	contamination=0.1, outliergram_factor=1.5, argvals=None

Method-accuracy honesty

MagnitudeShapeDetector is the only method-faithful detector in this module. Its score_samples uses a genuine MS-plot decomposition:

• Magnitude outlyingness MO(x) = mean_t(|x(t) − μ(t)|) against the stored pointwise training mean mu_.
• Shape outlyingness VO(x) = mean_t(|(x(t) − μ(t))² − σ²(t)|) against the stored pointwise training variance var_.
• Combined score −(MO² + VO²) (higher = more inlier).

These statistics are computed against fixed stored training statistics (mu_, var_), so scoring a subset of test curves returns the same values as scoring them individually — check_methods_subset_invariance passes.

The other five detectors (LRTOutlierDetector, OutliergramDetector, TVDMSSDetector, MUODDetector, DepthgramDetector) rank by a subset-invariant modified-band-depth surrogate in the sklearn layer. Their eponymous batch-relative native methods (LRT bootstrap, outliergram MEI/MBD, TVDMSS, MUOD, depthgram) are whole-batch statistics with no per-row decomposition — they cannot satisfy check_methods_subset_invariance directly. The sklearn wrappers compute modified_band_1d(X_new, X_fit_) (depth of new curves against the stored training population) as a subset-invariant proxy, while retaining the original native-method outputs as provenance attributes (e.g. mbd_train_, mei_train_, tvd_train_, mss_train_).

Use fdars.outliers directly when you need the exact batch-relative scores from these methods.

Typical Usage

Clustering (unsupervised):

from sklearn.pipeline import Pipeline
from fdars.sklearn._skeletons import BSplineSmoother, FunctionalKMeans

pipe = Pipeline([
    ("smoother",  BSplineSmoother()),
    ("clusterer", FunctionalKMeans(n_clusters=3)),
])
labels = pipe.fit_predict(X)

Outlier detection:

from fdars.sklearn._skeletons import MagnitudeShapeDetector

det = MagnitudeShapeDetector(contamination=0.05)
det.fit(X_train)
labels = det.predict(X_test)   # +1 inlier, -1 outlier
scores = det.score_samples(X_test)  # higher = more normal

For the five surrogate-scored detectors, score_samples is available and returns the modified-band-depth values; use fdars.outliers for the method-exact scores.