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Condensed prototype-based domain description

Algorithms AIMech:CondensedPrototypeBasedDomainDescription DRAFT

Aliases: CPDD, Greedy prototype domain condensation

A greedy prototype-selection procedure that constructs kth-neighbor radius offsets from the full reference dataset and repeatedly chooses the prototype covering the most still-uncovered eligible reference locations under the PDD distance rule.

Identity Notes & Concept Scope CPDD chooses radius-bearing prototypes for PDD. It is distinct from the PDD prediction rule, CNNDD subset selection with neighbor distances recomputed by an NNDD classifier, and the sampled FastCPDD heuristic. The baseline here follows the prose-defined full-cover stopping condition at rho=eta=1; the source's printed loop guard is explicitly inconsistent with that stopping description. Compared all 442 pinned AIO IDs, labels and scoped synonyms with all 508 preceding native IDs, names and aliases. No normalized candidate identity collision was found. Fixed-string whole-word searches included ignored and hidden files in both checkouts, candidate aliases, acronyms and source identifiers. All 103 matched lines per checkout, 61 distinct texts at 206 locations, were inspected: these are the preceding NNDD record and its generated pages, provenance, discovery and review context, including explicit pending CPDD/FastCPDD leads. The 85 semantic AIO rows and 65 preceding native identity matches were unchanged from their fully read prior search; the two new native neighbors were fully read. Twelve annotated AIO nodes and outgoing edges were read; twenty-three contextual YAMLs were reused after unchanged-byte checks. Absence is bounded to this pin and corpus, and wider identity-field matches are not full scientific reviews.

Claims & Grounded Evidence

4 Claims

Mechanism #greedy-cover-construction

Compute r_i as each x_i's kth self-included neighbor distance in full D, and retain candidate prototypes with r_i<=theta. Form N_i={y in D:d(x_i,y)+r_i<=rho*theta}. Starting from empty S and covered set C, select a candidate maximizing |N_i minus C|, break gain ties in favor of smaller r_i, and add its pair (x_i,r_i) and neighborhood to S and C. The baseline rho=eta=1 stops once every eligible prototype location is covered, following the surrounding prose. Further equal-gain, equal-radius ties are unspecified. Prediction uses the stored radii and original theta.

supports Source: Prototype-based Domain Description for One-Class Classification · Locator: Figure 1, author p4 / PDF p5; Section 4 algorithm and parameter descriptions, author p5 / PDF p6

Scope #baseline-approximation-scope

For nonempty derived prototype set P at rho=eta=1, each prototype covers itself and its neighborhood contains only eligible reference locations. The intended full-cover loop is greedy set cover, so its selected count is at most (1+ln|P|) times a minimum cover count. This is a cardinality approximation for the finite reference-consistency objective, not exact minimum size, equality of all new-query decisions or a classification-risk guarantee. It is not automatically a guarantee for partial-cover settings or FastCPDD.

supports Source: Prototype-based Domain Description for One-Class Classification · Locator: Section 4 and Theorem 4.1, author p5 / PDF p6; Definition 2.5, author p3 / PDF p4

Limitation #printed-guard-and-parameter-boundaries

Figure 1 prints while |C|<=eta|P|. At eta=1 and complete coverage, that guard remains true while every residual gain is zero, so the literal loop need not terminate. The narrative instead stops after at least the requested fraction is covered. Shrinking rho below 1 can make that requested coverage infeasible: D={0,2}, k=2, theta=2 gives two eligible radius-2 prototypes, but rho=3/4 makes both N_i empty. Reducing eta permits partial coverage; with the same D and rho=1, eta=1/2 can stop after one prototype and lose the other original accepted decision. These source-boundary calculations are not an attributed implementation repair.

supports Source: Prototype-based Domain Description for One-Class Classification · Locator: Figure 1 and Section 4, author pp4-5 / PDF pp5-6; exact curator calculations in research/discovery/prototype-domain-boundaries.py

Limitation #computation-and-evaluation-boundaries

The described construction computes all reference pairwise distances, giving quadratic distance-evaluation work in |D|; stored neighborhood incidence can also be quadratic. That fact alone does not bound every implementation's greedy-update cost by quadratic time. Reported size, timing and accuracy comparisons are conditional on datasets, metrics, thresholds, k, rho, eta and implementations, and both CPDD and CNNDD can have favorable comparison outcomes. The shuttle contamination experiment draws added training contaminants from the abnormal test population; the forest example reports the two best-separated abnormal classes. No universal speed or accuracy advantage is inferred.

supports Source: Prototype-based Domain Description for One-Class Classification · Locator: Section 5 introduction, author p6 / PDF p7; Sections 6.1-6.5 and Figures 5-12, author pp8-13 / PDF pp9-14

⚠️ Curated Limitations & Negative Results

This record identifies the intended greedy full-cover method, not a certified execution of the literal pseudocode. Empty candidate sets, unattainable shrunken coverage and no-progress termination require explicit implementation handling.
At rho<1 the selection neighborhoods are smaller than the final PDD acceptance neighborhoods; the parameter does not simply replace theta at prediction. Eta denotes a covered fraction in baseline CPDD, unlike its marginal-gain role in FastCPDD.
The general-metric hardness discussion does not establish a fixed-dimensional Euclidean claim. Full-cover set-cover approximation does not imply calibrated probability or universally lower true error.
All 15 primary pages, algorithm figures and evaluation panels were visually read. Exact finite boundary checks were executed; original software, historical timings and the preliminary 2008 full text remain unverified.

Artificial Intelligence Ontology (AIO) Grounding

Mapped AIO Classes

AIO Target Class	Mapping Relation	Mapping Rationale
`AIO:BinaryClassification` Binary Classification	related_match	The PDD accept-versus-reject task, including detectors constructed by CPDD or FastCPDD, is related to AIO:BinaryClassification. This is an algorithm-to-task association, not equivalence or subclass membership. The target has Classification and SupervisedLearning ancestry, but the link does not assert representative abnormal-class training data. Inspected Classification, BinaryClassification, SupervisedLearning, UnsupervisedLearning, MachineLearningTask, all three KnearestNeighbor nodes, DimensionalityReduction, Distillation, DataPreparation and SelectionAndSamplingBias with annotations and outgoing edges. Neighbor voting or value averaging is distinct from radius-offset decisions; condensation does not reduce feature dimensions or assert a bias condition. Generic preparation and teacher-student distillation do not identify these covering procedures. Eleven native contexts distinguish NNDD distance norms, CNNDD reference selection, local distance ratios, bootstrap variability, density clustering, supervised metric learning, sphere support estimation and medoid optimization.

Evidence Sources & Primary Literature

1 Source

Source ID	Publication / Document	Type / Access	Reference & Checksum
`angiulli2012`	Prototype-based Domain Description for One-Class Classification Fabrizio Angiulli	primary paper full_text	ID: https://doi.org/10.1109/TPAMI.2011.204 sha256:a75e67435eb6…

Curation Provenance

Curator: Codex

Method: ai_assisted

Model: GPT-6

Created: 2026-10-12T08:31:31Z

Updated: 2026-10-12T08:31:31Z

Source File: data/curated/CondensedPrototypeBasedDomainDescription.yaml