OPTICS outlier factor
Algorithms AIMech:OPTICSOutlierFactor DRAFT
Aliases: OPTICS-OF, OPTICS with outlier factors
An unsupervised local outlier-scoring procedure that uses self-inclusive, tie-inclusive nearest neighborhoods to compute inverse mean neighbor-radius reachability and averages neighbor-to-query density ratios.
Identity Notes & Concept Scope
This record denotes OPTICS-OF with the self-inclusive convention corroborated by the inspected ELKI implementation. It is distinct from OPTICS ordering, DBSCAN noise labels, original self-excluded LOF, neighbor-label voting and raw distance ranking. Original 1999 parsed text is context; mechanism claims are grounded in immutable official source and exact neighbor contracts. Compared all 442 pinned AIO IDs, labels and scoped synonyms with all 512 preceding native IDs, names and aliases. No normalized identity collision was found. Fixed-string whole-word searches of both checkouts included ignored and hidden files, all aliases, the original title and DOI: 23 matches in each checkout were read in 19 distinct context windows at 46 locations. These are LOF comparison notes, prior searches and unresolved discovery context, not an existing OPTICS-OF record. All 99 semantic AIO rows, 13 annotated CLASS nodes with outgoing edges, 71 native identity-field matches and 21 contextual YAMLs were inspected or reused after unchanged-content checks. This is a bounded local corpus assessment.
Claims & Grounded Evidence
7 Claims
Mechanism
#self-inclusive-locality
For a finite reference dataset D of n observations, a finite metric and 2<=m<=n, core_m(p) is the mth ordered distance to observations in D, including p itself. N_m(p) retains every observation at distance at most that boundary, including all ties. The inspected exact linear scans and heap include the indexed query and boundary ties; a fixed-count truncation is not the same convention. The m range describes the well-defined distinct-point metric case, not a claim that every constructor enforces it.
Mechanism
#reachability-and-density-ratios
For o in N_m(p), reach_m(p,o)=max(core_m(o),d(p,o)), using the neighbor radius. Set lrd_m(p)=|N_m(p)| divided by the sum of these reaches, and OF_m(p) to the mean of lrd_m(o)/lrd_m(p) over N_m(p). Thus self reachability is core_m(p), not zero, and the self term contributes a ratio of one when defined. The formulas require positive finite mean reaches for all densities used. These inverse-distance quantities are not normalized probability densities, and the resulting relative score is not an outlier probability or an automatic binary decision.
Mechanism
#standalone-three-pass-computation
The inspected implementation first stores neighborhoods and core radii, then computes all local reachability densities, then averages their neighbor-to-query ratios. It does not run an OPTICS ordering or extract a clustering. Pairwise reachability in the score must not be replaced with a minimum reachability accumulated during an OPTICS traversal.
Scope
#distinct-from-self-excluded-lof
OPTICS-OF and original LOF are retained separately because including the query changes both density and score averaging. Under absolute distance, D={0,1,3} gives OPTICS-OF scores {1,1,3/2} at m=2, whereas self-excluded LOF gives {1,1,2} at k=1, despite identical core radii. At m=3, OPTICS-OF gives {1,1,1}, while LOF at k=2 gives {11/12,6/5,11/12}. These exact curator calculations rule out identifying the two procedures merely by shifting the neighbor-count parameter.
Limitation
#ties-and-scale-boundaries
Boundary ties can change scores: for D={0,2,4,5} and m=2, point 2 has three retained neighbors and score 4/3; selecting only itself and neighbor 0 instead gives score 1. Positive uniform scaling of every distance cancels from defined density ratios, but feature-specific scaling can change neighborhoods. When m=n, every neighborhood is D and reach_m(p,o)=core_m(o), so all densities are equal and all defined scores are one. A score of one therefore does not by itself establish domain normality.
Limitation
#zero-distance-and-parameter-limits
With m=1 and a unique query location, the self-only neighborhood has zero mean reachability; duplicates can also produce zero means at larger m. The mathematical ratios are then undefined. The inspected parameterizer requires m>1 and defaults to Euclidean distance, but its constructor does not enforce m<=n. KNNList may report an infinite boundary when fewer than m neighbors exist. The scoring loop adds no epsilon; its lrd>0 guard does not resolve infinity/infinity from coincident neighborhoods. A fallback zero or nonfinite output outside the stated finite domain is not evidence of normality.
Limitation
#implementation-and-computation-scope
The evidence establishes the inspected release source and exact linear-query/tie contracts, not every index backend, historical implementation or runtime result. Stored all-ties neighborhoods can contain every observation even for small m, requiring quadratic neighbor incidences. All-pairs neighbor search can require quadratic distance evaluations, and selection/index costs need separate analysis; no universal near-linear or n-log-n complexity follows. The historical paper text and versioned test fixture provide context, but no figure-derived claim, numerical performance advantage, library benchmark or probability calibration is curated.
⚠️ Curated Limitations & Negative Results
- Reference population, metric, feature scaling and m determine local contrast; scores alone do not establish errors, fraud, disease or another domain conclusion.
- The original nine-page paper was inspected as parsed text only. No successful PDF download, checksum, figure reading or visual equation verification is claimed. The exact ELKI main class, test and six neighbor files were fully read; other index backends and QueryBuilder internals were not fully audited.
- The full twelve-page LOF source was visually read in the preceding round and reused for comparison. Exact rational calculations were executed; no Java, library backend, trained model or historical benchmark was executed.
- This is a maintained native DRAFT concept with an explicit related AIO mapping, not an accepted upstream class or an assertion that local-density discovery is complete.
Artificial Intelligence Ontology (AIO) Grounding
Mapped AIO Classes
| AIO Target Class | Mapping Relation | Mapping Rationale |
|---|---|---|
AIO:UnsupervisedLearning
Unsupervised Learning
|
related_match | OPTICS-OF computes relative local outlier scores from unlabeled observations, supporting a related algorithm-to-task association with AIO:UnsupervisedLearning. The target is a MachineLearningTask, so the link asserts neither equivalence nor subclassing. BinaryClassification and its supervised ancestry do not describe the unthresholded core. Clustering, DBSCAN and OPTICS produce cluster structure or a reachability ordering; this standalone score needs neither a partition nor an OPTICS traversal. The three AIO KnearestNeighbor classes concern voting or response averaging, unlike these density ratios. RegressionAnalysis, DimensionalityReduction, DataPreparation and SelectionAndSamplingBias do not identify the procedure. Native LOF differs by explicit self exclusion; domain-description and metric-learning methods have different rules or outputs. |
Evidence Sources & Primary Literature
8 Sources| Source ID | Publication / Document | Type / Access | Reference & Checksum |
|---|---|---|---|
elki-opticsof
|
ELKI developers
|
official documentation
documentation
|
sha256:67331ab9311a…
|
elki-wrapper
|
ELKI developers
|
official documentation
documentation
|
sha256:9970de97961c…
|
elki-heap
|
ELKI developers
|
official documentation
documentation
|
sha256:f2f56eb3d72b…
|
elki-list
|
ELKI developers
|
official documentation
documentation
|
sha256:f7480775c25b…
|
elki-linear-object
|
ELKI developers
|
official documentation
documentation
|
sha256:9b40694372e8…
|
elki-linear-id
|
ELKI developers
|
official documentation
documentation
|
sha256:72bf3d5626ba…
|
breunig2000
|
Markus M. Breunig, Hans-Peter Kriegel, Raymond T. Ng, Jörg Sander
|
primary paper
full_text
|
ID: https://doi.org/10.1145/342009.335388
sha256:d6e378582bf7…
|
breunig1999-context
|
Markus M. Breunig, Hans-Peter Kriegel, Raymond T. Ng, Jörg Sander
|
primary paper
full_text
|
ID: https://doi.org/10.1007/978-3-540-48247-5_28
|
Curation Provenance
Curator: Codex
Method: ai_assisted
Model: GPT-6
Created: 2026-10-12T09:12:41Z
Updated: 2026-10-12T09:12:41Z
Source File:
data/curated/OPTICSOutlierFactor.yaml