LocalOutlierFactor¶

Local Outlier Factor (LOF).

The LOF of a sample measures how isolated it is relative to the density of its neighbors: a value around 1 means the sample lies in a region as dense as its neighborhood, while a value substantially above 1 flags an outlier sitting in a comparatively sparse region (Breunig et al., 2000).

Samples are stored in a fixed-size sliding window managed by a nearest-neighbor engine (see river.neighbors). learn_one simply adds a sample to the window, so it runs in constant time and the memory footprint is bounded by the window size. score_one computes the LOF of a sample against the current window on demand, without modifying it. The natural streaming pattern is therefore to call score_one and then learn_one on each sample.

Because scoring is done against the window only, the result matches the static LOF computed on those samples (e.g. scikit-learn's LocalOutlierFactor(novelty=True) fitted on the same window).

Parameters¶

• n_neighbors

  Type → int

  Default → 10

  The number of nearest neighbors used to define the local neighborhood.

• engine

  Type → BaseNN | None

  Default → None

  The nearest-neighbor search engine, which stores the samples in a sliding window and answers neighbor queries. Defaults to neighbors.LazySearch, an exact brute-force search over the window. Pass neighbors.SWINN for approximate search, or a configured engine to control the window_size and the distance function.

Examples¶

from river import anomaly

X = [0.5, 0.45, 0.43, 0.44, 0.445, 0.45, 0.0]
lof = anomaly.LocalOutlierFactor(n_neighbors=3)

for x in X[:3]:
    lof.learn_one({"x": x})  # warming up

for x in X:
    features = {"x": x}
    print(f"Anomaly score for x={x:.3f}: {lof.score_one(features):.3f}")
    lof.learn_one(features)

Anomaly score for x=0.500: 0.929
Anomaly score for x=0.450: 1.105
Anomaly score for x=0.430: 1.044
Anomaly score for x=0.440: 1.000
Anomaly score for x=0.445: 0.944
Anomaly score for x=0.450: 0.889
Anomaly score for x=0.000: 36.111

A mini-batch of samples can be learned at once from any narwhals-compatible eager dataframe (pandas, polars, pyarrow, ...) with learn_many:

import pandas as pd
from river import datasets

rows = [x for x, _ in datasets.CreditCard().take(500)]
lof = anomaly.LocalOutlierFactor(n_neighbors=20)
lof.learn_many(pd.DataFrame(rows))
[round(lof.score_one(x), 3) for x in rows[:5]]

[1.51, 1.355, 1.987, 1.566, 1.837]

Methods¶

References¶

• Markus M. Breunig, Hans-Peter Kriegel, Raymond T. Ng, and Jörg Sander (2000). LOF: Identifying Density-Based Local Outliers. In: Proceedings of the 2000 ACM SIGMOD International Conference on Management of Data. 93-104. DOI: 10.1145/342009.335388.

• David Pokrajac, Aleksandar Lazarevic, and Longin Jan Latecki (2007). Incremental Local Outlier Detection for Data Streams. In: Proceedings of the 2007 IEEE Symposium on Computational Intelligence and Data Mining (CIDM 2007). 504-515. DOI: 10.1109/CIDM.2007.368917.