Addressing misclassification costs in machine learning through asymmetric loss functions

Published

April 27, 2023

Author(s)

Bryan Barnes, Mark-Alexander Henn

Abstract

Background: Patterning defect metrology requires data interpretation with classification, each well-suited to machine learning (ML). Defect classification however has notable misclassification costs; mislabeling a defect as nominal has greater impact than the converse. Aim: Though quantified costs are not publicly available, total economic misclassification cost (total cost) is optimized across orders-of-magnitude variation in cost ratio C and classification threshold 0.01 < τ < 0.99. Approach: Convolutional neural networks are trained using the intrinsically weighted and scaled asymmetric focal losses (AFL, sAFL) with hyperparameter γ with weighted and unweighted binary cross-entropy (wBCE, BCE) functions trained for comparisons. Optimal functions and conditions are identified for reducing total cost. For reproducibility, publicly available ML data sets are surrogates for industrial imaging data. Results: For these data the sAFL mimimizes total cost at τ = 0.5, C ≥ 16. The AFL reduces total cost at 0.1 ≤ τ < 0.5, C > 128. Asymmetric loss functions lower total cost versus wBCE by 15 % to 40 % for 0.2 < τ < 0.5, C > 64. Conclusions: Total economic misclassification cost can be tailored using asymmetric focal losses. Estimations are presented to allow the extension of reported trends to industrial applications with strong class imbalances between defect-indicative and nominal-indicative data.

Proceedings Title

Proceedings Volume 12496, Metrology, Inspection, and Process Control XXXVII

Volume

12496

Conference Dates

February 26-March 2, 2023

Conference Location

San Jose, CA, US

Conference Title

SPIE 2023 Advanced Lithography + Patterning

Pub Type

Conferences

Download Paper

https://doi.org/10.1117/12.2662027

Local Download

Keywords

asymmetric loss functions, asymmetric focal loss, goal-oriented metrics, defect metrology, binary classification, machine learning, convolutional neural networks, scaled asymmetric focal loss

Citation

Barnes, B. and Henn, M. (2023), Addressing misclassification costs in machine learning through asymmetric loss functions, Proceedings Volume 12496, Metrology, Inspection, and Process Control XXXVII, San Jose, CA, US, [online], https://doi.org/10.1117/12.2662027, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=936548 (Accessed May 8, 2026)

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