{"ID":5938048,"CreatedAt":"2026-07-07T03:14:33.014478982Z","UpdatedAt":"2026-07-07T20:57:38.483094001Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.04028","arxiv_id":"2607.04028","title":"A Unified Algebraic Framework for Classification Performance Evaluation","abstract":"We propose a unified algebraic framework for classification performance evaluation that encompasses binary, multiclass, multilabel, ordinal, hierarchical, cost-sensitive, and soft-label settings within a single formalism. The foundation is a representation of actual and predicted labels as binary indicator matrices, combined with three aggregation operators -- global, column-wise, and row-wise -- that correspond exactly to micro, macro/weighted, and exemplar averaging. Any binary performance measure expressed in terms of true/positive/negative counts extends automatically to all settings by substituting these operators, generating multiclass and multilabel versions without measure-specific derivations. The framework further accommodates soft classifier outputs via argmax or thresholding, soft ground truth via triangular norms, ordinal classification via membership functions or cumulative encodings, and cost-sensitive evaluation via a cost matrix that subsumes MAE and MSE as special cases. We establish several theoretical results: micro-averaging equals denominator-weighted macro-averaging; the product $t$-norm is the unique one preserving the confusion-matrix partition; skew-invariant measures are characterised as functions of recall and specificity; and micro-precision, micro-recall, and micro-$F_1$ are all equal to accuracy in multiclass settings. Empirical illustrations on synthetic and real data confirm the theoretical findings.","short_abstract":"We propose a unified algebraic framework for classification performance evaluation that encompasses binary, multiclass, multilabel, ordinal, hierarchical, cost-sensitive, and soft-label settings within a single formalism. The foundation is a representation of actual and predicted labels as binary indicator matrices, co...","url_abs":"https://arxiv.org/abs/2607.04028","url_pdf":"https://arxiv.org/pdf/2607.04028v1","authors":"[\"Ronaldo C. Prati\"]","published":"2026-07-04T21:00:29Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\"]","methods":"[]","has_code":false}