© 2022, The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd.Although few performance evaluation instruments have been used conventionally in different machine learning-based classification problem domains, there are numerous ones defined in the literature. This study reviews and describes performance instruments via formally defined novel concepts and clarifies the terminology. The study first highlights the issues in performance evaluation via a survey of 78 mobile-malware classification studies and reviews terminology. Based on three research questions, it proposes novel concepts to identify characteristics, similarities, and differences of instruments that are categorized into ‘performance measures’ and ‘performance metrics’ in the classification context for the first time. The concepts reflecting the intrinsic properties of instruments such as canonical form, geometry, duality, complementation, dependency, and leveling, aim to reveal similarities and differences of numerous instruments, such as redundancy and ground-truth versus prediction focuses. As an application of knowledge representation, we introduced a new exploratory table called PToPI (Periodic Table of Performance Instruments) for 29 measures and 28 metrics (69 instruments including variant and parametric ones). Visualizing proposed concepts, PToPI provides a new relational structure for the instruments including graphical, probabilistic, and entropic ones to see their properties and dependencies all in one place. Applications of the exploratory table in six examples from different domains in the literature have shown that PToPI aids overall instrument analysis and selection of the proper performance metrics according to the specific requirements of a classification problem. We expect that the proposed concepts and PToPI will help researchers comprehend and use the instruments and follow a systematic approach to classification performance evaluation and publication.